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A neuro-fuzzy approach to real-time trajectory generation for robotic rehabilitation
Robotics and Autonomous Systems 62 (2014) 568–578
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Robotics and Autonomous Systems journal homepage: www.elsevier.com/locate/robot
A neuro-fuzzy approach to real-time trajectory generation for robotic rehabilitation Peter Martin, M. Reza Emami ∗ University of Toronto Institute for Aerospace Studies, 4925 Dufferin Street, Toronto, Ontario M3H 5T6, Canada
highlights • A neuro-fuzzy schema introduces compliance into the human–robot interaction to emulate a wide-variety of exercises. • Implemented as a manipulator independent solution. • Preliminary results indicate that the system is able to very closely replicate a generic patient–therapist interaction.
article
info
Article history: Received 20 January 2012 Received in revised form 16 October 2013 Accepted 2 January 2014 Available online 20 January 2014 Keywords: Neuro-fuzzy control Compliant trajectory generator Rehabilitation robotics
abstract This paper proposes a method for the design of a real-time neuro-fuzzy trajectory generator for the robotic rehabilitation of patients with upper limb dysfunction due to neurological diseases. The primary objective of the methodology is to assist therapists by allowing them to delegate repetitive therapy tasks to a mechatronic system. The trajectory generator is packaged as a platform-independent solution to facilitate the rehabilitation of patients using multiple manipulator configurations. The system utilizes a fuzzy-logic schema to introduce compliance into the human–robot interaction, and to allow the emulation of a wide variety of therapy techniques. This approach also allows for the fine-tuning of patient specific behaviour using linguistic variables. The rule base for the system is trained using a fuzzy clustering algorithm and applied to the experimental data gathered during traditional therapy sessions. The compliance rule base is combined with a hybrid neuro-fuzzy compensator to automatically tune the dynamics of the robot–patient interaction. Preliminary results indicate that the approach can accurately reproduce a prescribed patient/therapist interaction, validating the proposed approach. © 2014 Elsevier B.V. All rights reserved.
1. Introduction Though a considerable body of research has been conducted in the field of rehabilitation robotics over the past decades, the commercial viability and widespread use of robotic systems for rehabilitation therapy are still very limited. This lack of large-scale commercially-viable systems has been attributed to several factors, the most significant of which are cost and usability, essentially non-technical issues. It is imperative to the development of a successful robotic rehabilitation system, therefore, to appeal to the needs of physiotherapists. Therapists are ultimately responsible for deciding whether a rehabilitation system is a worthwhile investment of their time and money [1]. The primary objective of the methodology proposed in this paper is to assist therapists by allowing them to delegate repetitive therapy tasks to a mechatronic system that is able to replicate
∗
Corresponding author. Tel.: +1 416 946 3357; fax: +1 416 946 7109. E-mail addresses: [email protected] (P. Martin), [email protected] (M.R. Emami). 0921-8890/$ – see front matter © 2014 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.robot.2014.01.001
the patient–therapist interaction as closely as possible. This approach aims to mitigate the cost and labour-intensive aspects of neurorehabilitation to improve clinical efficiency and efficacy [2,3]. The system was developed as a platform-independent, modelbased solution. This approach was taken to give the therapist the flexibility to perform a wide range of both established and emerging therapy techniques, using a wide variety of manipulator systems. This can also serve to mitigate the costs associated with developing specialized rehabilitation platforms by offering a software framework that is compatible with off-the-shelf industrial manipulators. The fundamental design challenge for robotic rehabilitation therapy is the replication of the complex movements with resistive and/or assistive forces applied at specific positions associated with traditional physiotherapy. Traditionally, a hybrid force–position controller would be required to regulate the interaction forces while precisely monitoring and controlling the position and velocity of the movement. Since during rehabilitation, the patient is also a part of the dynamic system, traditional control parameters are difficult to develop based on the system model and its parameters [4].
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Impedance control, which is well established in the field of rehabilitation robotics [5], allows for variable deviation from a given limb trajectory while keeping the limbs within a predefined range. One of the most prevalent forms of impedance-based force control in rehabilitation robotics is adaptive impedance control [6,7]. In adaptive impedance control, the human represents a component of the control system that influences its behaviour. This enables the control structure to adapt to changes in the reference trajectory initiated by the patient to regulate the interaction forces between the patient and the manipulator system. Though adaptive impedance control has become the standard method of robotic force control for rehabilitation, there remain some fundamental shortcomings inherent in the approach. The complexity of the traditional control approach dictates that changes in the environmental dynamics require significant tuning and parameter alteration. Once a control system has been tuned to perform a specific exercise with a specific patient, the system parameters must be altered and tuned by an expert if the therapist wishes to change the way the exercise is performed. An approach to the implementation of force control that is able to inherently overcome the difficulties associated with impedance control is through the use of fuzzy logic [4,8–10]. Fuzzy logic control has the advantage of being able to provide rule based force control while compensating for nonlinearity and parameter uncertainty. This feature enables the system designers to create a model of the prescribed interaction between the robot and the patient based on the therapist’s qualitative description of the desired behaviour of the coupled system. The control parameters can also be tuned quite easily to modify specific aspects of the interaction. The traditional approach to the generation of the rule base for fuzzy rehabilitation systems does, however, create a fundamental reliance on the expert knowledge of the therapy professionals. Given the complexity of traditional therapy tasks, this dependency on an accurate understanding of the dynamics of the interaction has meant that the fuzzy based rehabilitation systems are normally only able to perform very simple trajectory profiles. To overcome this limitation, our methodology utilizes fuzzy clustering and a hybrid neuro-fuzzy schema to generate a representative model of a wide variety of force–position profiles. 2. Material and methods In order to create a system that is able to emulate the behaviour of a therapist as closely as possible, our trajectory generator utilizes a fuzzy-logic based inference system. Using a fuzzy approach enables the system to emulate the humanistic dynamics of traditional therapy more effectively than traditional control approaches by making use of model-based variable compliance. In addition, each unique exercise and each patient can take advantage of a unique rule base to better emulate each specific treatment scenario. Therefore, it should be emphasized that the system is not meant to replace the therapist, but to enable the autonomous treatment of patients at home or in the clinic. 2.1. Data gathering The first stage in the generation of a fuzzy model of the patient–therapist interaction is the acquisition of a suitable dataset. There are several considerations that must be paid due diligence during the data gathering stage including: (1) the need for a representative dataset, (2) the specification of appropriate protocols for handling exceptional circumstances, and (3) verification that there are no conflicting relationships contained in the dataset. The need for a representative dataset is a fundamental requirement for all fuzzy modelling based controllers. The nature
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of fuzzy logic enables a fuzzy controller to infer appropriate system responses to undefined input values by extrapolating based on the behaviour contained within the system model. It is for this reason that fuzzy logic-based inference systems are widely applied in situations where a humanistic or reasoned approach is appropriate. However, if the universe of discourse defined by the fuzzy input space is too limited in its scope with respect to the input variables passed to the system during its application, the system will not respond properly when the input lies outside of the realm of knowledge. Therefore, in the case of knowledge based systems such as the fuzzy trajectory generator proposed in this paper, a dataset that contains a reasonably complete input space is essential to ensure that the system is able to react to all potential training scenarios in a controlled manner. The specification of protocols for the proper compensation during exceptional circumstances involves the inclusion of situations within the experimental data that specify the proper system reactions during abnormal conditions. Given the interactive nature of the neuro-fuzzy training system, it is imperative that the system responds gracefully under exceptional circumstances such as a large patient jerk or spasm to ensure the safety of the patient at all times. During the therapist training sessions used for the generation of the fuzzy rules, therefore, proper responses to unanticipated patient reactions should be prescribed. The confirmation that the therapist dataset does not contain conflicting behaviour is required to ensure that the system response is consistent and well defined. For this reason, it is important to specify a clear and consistent protocol for the therapy action taken during the data gathering stage. For instance, during the training sessions, the therapist must consistently lead the patient along the trajectory while providing consistent compensation. If the patient is allowed to lead, or ‘‘push’’ the therapist along the trajectory then the interaction will result in two conflicting compliant conditions for the same measured forces. This is also the case if the therapist has allowed the patient to deviate laterally from the specified trajectory, and the resistive force applied by the patient is reduced without the therapist leading the patient back to the proper trajectory. In this case, both low and high force conditions will be measured corresponding to the same deviation from the desired trajectory. If the behaviour expressed by the dataset used to generate the compliance model is clear and consistent, then the ability of the fuzzy system to replicate the prescribed interaction when working with the patient is greatly increased. 2.2. Fuzzy clustering The purpose of the trajectory generator module is to generate the end-effector positions necessary to follow the position trajectory specified by the exercise, while providing a forcedependent level of compliance to the human–patient interaction. The fuzzy rule base, thus, expresses the dynamics of the relationship between changes in the interaction forces measured at the end-effector and the resultant compliant position increment. The first stage in the application of the proposed methodology is to create a representative rule base using clustering. In order to provide a basis for the initial selection of the number of clusters c and exponent m, an iterative heuristic algorithm described in [11] is used. Once the appropriate initial conditions are obtained, the output space of the experimental dataset is clustered using the FCM optimization algorithm. Using the unlabelled data X = {x1 , x2 , . . . , xN } ⊂ Rh , where N is number of data arrays and h is the dimension of each data array, clustering can be viewed as the assignment of labels c to the arrays in X . The problem of fuzzy clustering is thus expressed as the problem of finding the optimum (c × N ) matrix of membership values {uik }, U = [uik ]. The FCM
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algorithm minimizes a weighted within-groups sum of squarederrors objective function Jm as follows: min {Jm (U , V ; X )} =
(U ,V )
N c (uik )m ∥xk − vi ∥2A
(1)
k=1 i=1
yˆ =
where,
0 ≤ uik ≤ 1 ∀i, k; N cn = U ∈R uik < n ∀i; 0 < k=1
& &
∀k, uik > 0 ∃i c ; (2) uik = 1 ∀k i =1
where V = {v1 v2 , . . . , vc } is the set of cluster centres and ∥x∥A = √ xT Ax is any inner product norm. Matrix A, which is usually selected as the identity matrix, is an h × h positive-definite matrix that specifies the shapes of the clusters. N , c and r are the number of data points, clusters and input dimensions, respectively. Fuzzy partitions are thus identified using the fuzzy c-means algorithm through an iterative optimization of (1). Trapezoidal membership functions are then fitted to the output space based on the generated cluster centres. The output membership functions are then projected onto the input space using the fuzzy line clustering technique, to generate the appropriate input membership functions. First, it is supposed that for each output cluster i (i = 1, 2, . . . , n), there are several points on the axis of input variable xj (j = 1, 2, . . . , r ) which have output membership equal or close to one. These points lie between vij1 and
vij2 (vij1 < vij2 ). The distance of each point xjk on the axis xj to the j
line vij1 vij2 is then determined. The membership grades uik for the input data xjk (j = 1, 2, . . . , r ; k = 1, 2, . . . , N ) corresponding to output cluster i are then formed such that the points closer to the line vij1 vij2 obtain higher membership grades. In order to optimize j
the membership grades uik , an objective function analogous to the FCM function Jm is defined: J¯m U j , Xj =
N n (ujik )m dis xjk , vij1 vij2 .
(3)
k=1 i=1
Solutions to the optimization problem to minimize the above objective function are directly obtained by distinguishing between j
two cases where xjk < vij1 and xjk > vij2 , and solving for d/duik
J¯m = 0. The final resultant membership grade is obtained as follows in Box I: for i = 1, 2, . . . , n, j = 1, 2, . . . , r and k = 1, 2, . . . , N; where, n is the number of rules, r is the number of input variables, and N is the number of data points. To complete the modelling process, the system parameters are tuned to reduce the system error with respect to the test data using a derivative of the Sugeno–Yasukawa iterative tuning algorithm [12]. To complete the fuzzy inference system, Takagi–Sugeno–Kang (TSK) inference is integrated into the system to determine the corresponding crisp outputs for each input set. The TSK reasoning method is associated with a rule base of a special format that is characterized by functional consequents instead of the more traditional fuzzy consequents. In the case of the inference system used in this paper, the fuzzy consequent di is the centre of area of the consequent membership function, Di , in the ith rule. The inferred crisp output, yˆ , is then determined by first evaluating the degree of membership in the premises of each rule as:
w =
Bi1
n i =1
U ϵ Mfcn
i
where Bij (i = 1, . . . , n, j = 1, 2, 3) are the fuzzy sets over the input space and 1 ≤ i ≤ n. The inferred crisp output, yˆ , is then determined by taking the weighted average of di with respect to w i as:
0
x1 ×
Bi2
0
x2 × · · ·
Bin
0 xn
(5)
w i di
n
wi
(6)
i=1
where n is the number of rules, and di is the centre of area of the consequent membership function, Di , in the ith rule. Finally, to increase the accuracy of the generated model, a derivative of the Sugeno–Yasukawa iterative tuning algorithm [13] is applied. The algorithm evaluates the mean-squared-error of the system based on a subset of the experimental data, to evaluate the effect of changing the parameters of the input and output membership functions. The adjustment value for each data space is modified during each iteration to more precisely adjust the placement of the modified membership functions. This process for the generation of a fuzzy rule base for compliant position trajectory generation was first proposed in [14]. 2.3. Fuzzy trajectory generator When the current forces between the patient and the robot, Fn , are fed back from the force transducer, they are compared with a corresponding desired interaction force, Fd , as specified by the therapist. The resultant force error, Fe = (Fd − Fn ), is then passed into the fuzzy trajectory generator module along with the desired trajectory position for the exercise in the task space. In order to reduce the influence of high-frequency noise inherent in the signal from the force sensor, a moving average of three consecutive measurements is used as a simple low-pass filter. To reduce the complexity of the fuzzy inference system necessary to generate each compliant increment vector, three separate rule bases are used for each component of the consequent change in the end-effector position. The force errors across all axes are input into the fuzzy consequent layer in order to allow the fuzzy rules to evaluate the state of the system including any coupling between the forces acting along all axes. The control action of the fuzzy system for each rule base can be expressed linguistically as: IFFex is B11 AND Fey is B12 AND Fez is B13 THEN ∂ pos is D1 ALSO
...
(7)
ALSO IF Fex is Bn1 AND Fey is Bn2 AND Fez is Bn3 THEN ∂ pos is Dn where n is the number of rules, Bij (i = 1, . . . , n, j = 1, 2, 3) and Dk (k =1, . . . , n) are fuzzy sets over the input and output spaces, Fe = Fex , Fey , Fez , and ∂ pos is either ∂ x, ∂ y or ∂ z depending on the rule base. The resultant trajectory point is then added to the desired trajectory position and the additional compensator position to generate the total position command to be passed to the manipulator servo controller. The overall trajectory generation scheme is illustrated in Fig. 1. 2.4. Hybrid neuro-fuzzy compensator The fuzzy rule base representing the compliance behaviour of the therapy action is structured as an outer-loop module to enable the trajectory generator to remain kinematically independent.
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m−1 1 −1 m−1 1 −1 2 1 n n | x − v | | x − v | jk jk ij ij 1 2 : x < v or x > v , jk j jk ij ij 1 2 uik = Max |xjk − v1j | |xjk − v1j | 1 =1 1 =1 1 2 1 : vij ≤ xjk ≤ vij
571
(4)
Box I.
Fig. 1. Neuro-fuzzy trajectory generator design methodology.
This schema addresses both the need for specialized humancentred systems designed especially for rehabilitation and the high cost of custom robotic manipulators. By enabling the proposed system to be applied to multiple manipulator configurations, the trajectory generator can be packaged as a self-contained software module to facilitate the automated rehabilitation therapy using both custom and industrial manipulators with various degrees of freedom. However, in order to ensure that the system is able to replicate the behaviour dictated by the fuzzy rule base regardless of the dynamics of the manipulator, an additional control module was necessary. Several fuzzy impedance compensators have been proposed in the literature for industrial tasks in order to compensate for situations where the environmental dynamics are unknown and for parameter uncertainty [15,13]. To maintain a computationally-efficient system, a position-based fuzzy compensator was implemented based on the approach taken in [13]. This module provides an additional position correction to the trajectory based on the measured force error. The task of the fuzzy compensator module is to generate additional position increments based on the interaction force measured at the end-effector in order to compensate for the difference
in dynamics between the manipulator and therapist. Three separate inference systems are utilized, one for each position increment component, to allow the dynamic components to be independently tuned. Each module is implemented as a MISO fuzzy system utilizing TSK inference. The antecedent inputs for each system are force and force increment along each respective axis. A rule base with n × m rules is used where n and m are the number of input membership functions for each input, respectively. To simplify the tuning of the resultant systems, constant consequents are used for each rule. For example, the rules for the x-axis component of the fuzzy compensator can be expressed linguistically as: IF Fex is B1 AND δ F ex is D1 THEN ∂ xc is c1 ALSO
...
(8)
ALSO IFFex is Bn AND δ F ex is Dn THEN ∂ xc is cn where n is the number of rules, Bi (i = 1, . . . , n) and Di are the ith antecedent fuzzy sets for the three inputs, respectively, and ci is the consequent constant of the ith rule.
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Given the complex nature of the interaction between the patient and the manipulator system, a learning algorithm was integrated into the trajectory generator module in the final stage of development to form the hybrid neuro-fuzzy system shown in Fig. 1 (block B). The neuro-fuzzy algorithm, shown in Fig. 1 (block C), enables the system to autonomously tune the consequent constants in real-time to improve the performance of the system, and to compensate for changes in the manipulator configuration. The hybrid neuro-fuzzy scheme used in this paper is very similar to the Adaptive-Network-based Fuzzy Inference System (ANFIS) [16], but was developed independently in [17]. In the first stage of the neuro-fuzzy scheme, similar to the traditional fuzzy control methodology, the two crisp input values are assigned to the appropriate fuzzy sets and corresponding linguistic variables based on the trapezoidal antecedent membership functions. In the second stage the activation degree of each rule is calculated. The error signal between the model inferred value Pˆ d , and the corresponding training value, pˆ ′d is then evaluated and integrated into an objective function E which expresses the mean quadratic error of the system. The training value based on the experimental data is generated using a lookup table and a linear search algorithm of O(n) time; if the value is not found in the table, then the three closest values based on the input vector are averaged to generate an appropriate reference. The error is evaluated as: E=
1 2
Pˆ d − pˆ ′d
2
(9)
where the model inferred value, Pˆ d , is the overall compliant position generated by the trajectory generator system, and pˆ ′d is the corresponding training value. The inferred response to the input vector X is consequently calculated as:
n n ′
Pˆ d X
=
i =1
Bij
j =1
n n i=1
0
Bij
xj
ωi
+ δ pr + pd 0
(10)
xj
j =1
where ωi is the weighted consequent rule conclusion, δ pr is the output from the compliance rule base, pd is the desired trajectory point, and Bij (i = 1, . . . , n, j = 1, 2, 3) are the fuzzy sets over the input space. The algorithm utilizes the gradient-decent method to adjust the weight of the rule conclusions as a function of the objective function as:
ωi (t + 1) = ωi (t ) − α
∂E ∂ωi
(11)
where α is the learning rate. By calculating the variation of the objective function E, in relation to the variation that occurred in ωi in the anterior instant, the adjustment of each conclusion value can be expressed as:
ωi (t + 1) = ωi (t ) − α
Pˆ d − pˆ ′d di n i
(12)
d
i=1 i
where d is the contribution of rule i to the final neuro-fuzzy inference. The adjustment to the weight of the rule conclusion can thus be interpreted as being proportional to the error between the model inferred value and the experimental value, weighted by the contribution of the rule to the overall crisp output. This online tuning algorithm ensures that the overall trajectory generator is able to replicate the proper therapist inspired interaction and eliminate errors in the clustered compliance rule base independent of the manipulator system kinematic configuration
3. Experimental 3.1. Software design The implementation of the proposed methodology necessitates the utilization of a software development approach that is compatible with a wide range of software-based manipulator systems. The fuzzy modules discussed in this paper, therefore, have R been implemented on the Microsoft Windows⃝ operating system as Win32 dynamically-linked libraries (DLLs) using Microsoft Visual C++. These libraries are accessible from all Windows-based controllers by making external calls to the libraries from the proprietary manipulator control development environment that manages the execution of the specified movement commands. The neuro-fuzzy trajectory generator is divided into two independent libraries that are used to generate the compliant position and the additional compensation offset, respectively. Both libraries utilize an object-oriented approach to the design of the fuzzy algorithms to allow the systems to be applied to various fuzzy control configurations. 3.2. Graphical user interface The fundamental goal of the Graphical User Interface (GUI) developed for the neuro-fuzzy trajectory generator system is to facilitate the specification of a number of system parameters by the therapist. The use of a fuzzy architecture for the control structure of the trajectory generator makes it possible for the therapist to specify and alter the interaction dynamics between the manipulator system and the patient linguistically. This potentially alleviates the need for a team of engineers or technical support staff traditionally necessary for the modification and tuning of robotic rehabilitation systems. To this end, the linguistic rules are presented in the GUI as a set of linguistic IF–THEN expressions that can be easily modified based on the fuzzy system model. Several additional characteristics of the system behaviour can be displayed and edited through the GUI including: the desired position trajectory, the membership function parameters, and the characteristics of the reference data used by the learning algorithms in the neuro-fuzzy compensator module. Configuration changes are made to the trajectory generator through the GUI offline, and are loaded into the fuzzy control modules at R runtime. The GUI was developed using the Microsoft⃝ Visual C# programming language in conjunction with the .NET framework. 3.3. Implementation and validation As a preliminary means to validate the proposed approach, a number of experimental datasets were recorded during mock therapy sessions to generate a number of behaviour models using the fuzzy clustering procedure outlined in Section 2.2. Given that the data were to be used as a proof of concept validation of the proposed methodology, the trials were performed by two researchers acting as a therapist and patient. The position and force information were recorded using a 6 d.o.f ATI Mini45 force R transducer, in conjunction with an NDI Optotrack⃝ Certus optical motion tracking system. The force transducer was capable of measuring applied forces at a resolution of up to 1/64 N over an Fx /Fy sensing range of ±145 N. The motion tracking system was able to measure three dimensional positions at a resolution of 0.01 mm. A custom handle mechanism was designed to be mounted on the top of the force transducer interface, to allow the therapist to train the patient in the same orientation as the manipulator end-effector. Various two-dimensional circular and linear trajectories were performed to generate a representative body of data for different therapy actions. For the linear trajectories
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Fig. 2. (a) X -axis, (b) Y -axis comparative compliance for the lead mode x-axis linear trajectory. The top profiles represent the measured human lead interaction, while the bottom profiles represent the replicated interaction between the human and robot.
that are presented in Section 4, the mock patient was lead back and forth along a 40 cm linear path, and 30 cm in diameter circular path. An average of 10 trials were performed for each trajectory with a wide variety of disturbances introduced into the coupled motion by the mock patient in order to create a representative dataset. Multiple datasets were used to generate each rule base to ensure a robust system. Once the force and compliant position datasets were generated, the datasets were clustered to generate representative fuzzy inference systems. To complete the implementation process, the fuzzy rule base was tuned using various subsets of the training data to more accurately match the desired compliance profiles. During the subsequent implementation and testing, the proposed system was integrated into the control framework of the 4 d.o.f Epson E2L853 industrial manipulator. This SCARA-type manipulator uses high torque AC servo motors, combined with harmonic drives to give the manipulator a standard (1′′ × 12′′ × 1′′ and back) cycle time of 0.437 s with high repeatability (0.020 mm). The manipulator has a horizontal reach of 850 mm and a Z axis vertical stroke of 320 mm. The system was tested using the same trajectories that were performed during the human/therapist trials. Three dimensional position profiles were not tested due to restrictions inherent to the manipulator system, though the system is theoretically applicable as a 3D trajectory generator. During testing, a desired force, Fd , of zero was used since the experimental trials were performed without a specific desirable force profile. The neuro-fuzzy compensator was given the reference datasets used to create the compliance rule base to enable it to tune the compliance of the human/robot interaction on-line. 4. Results The fundamental goal of the testing stage of development was to show that the robotic manipulator was able to replicate the therapist’s behaviour by providing an appropriate level of compliance during a therapy action. We were unconcerned with the efficacy of the particular chosen exercise, assuming that a therapist would be uniquely qualified to access an appropriate interaction, and demonstrate that action to the system during the data-gathering stage. The ability of the system to accurately replicate a prescribed exercise is an inherently quantifiable objective, and therefore a comparison of the proposed system and a traditional impedance-based controller was deemed unnecessary. The ability of the proposed system to effectively replicate a specific
force profile was implemented and tested using a minimum-force ‘‘follower’’ mode and compared to conventional impedance control approaches in [18]. In this section, the neuro-fuzzy system is compared to a conventional fuzzy controller and the recorded human interaction in order to demonstrate the need for the additional compensator and learning algorithm. 4.1. Compliance rule base implementation results The first stage of the implementation of the proposed system on the Epson E2L853 included only the compliance rule base. This stage was performed in order to validate the rule base, while gathering initial benchmark results to compare to the overall system. Some examples of the results gathered during this stage are presented in this section. A comparison between the compliance that was recorded during the data gathering stage while following an x-axis linear trajectory and the compliance generated by the fuzzy rule base while leading the mock patient along the same trajectory is presented in Fig. 2(a) and (b). The results indicate that the fuzzy trajectory generator is able to successfully replicate the behaviour of the human/therapist interaction. It is apparent from a visual inspection of the two result sets that the system is able to more accurately replicate the compliance along the trajectory axis than the off-axis compliance. The duplicity that appears in the desired compliance dataset can be attributed to the difficulty in maintaining consistent compliance over multiple experiments during the initial therapy sessions. This leads to multiple compliance values for the same force values when using the data from multiple experimental trials. The fuzzy rule base is able to inherently interpolate the appropriate level of compliance on-line, though the inferred compliance might have been more accurate had the system been applied to only a single experimental dataset. This would, however, have greatly reduced the universe of discourse of the generated rule base. A compromise was therefore reached between the robustness of the rule base and the inherent inconsistencies in the recorded human data as discussed in Section 2.1. The comparative compliance for a y-axis linear trajectory is presented in Fig. 3(a) and (b). Once again the compliance rule base is able to successfully replicate the inferred compliant behaviour of the human/robot interaction. Similar to the x-axis linear trajectory results, however, the rule base is better able to replicate the compliance along the position trajectory than perpendicular to the
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Fig. 3. X -axis, Y -axis comparative compliance for the lead mode y-axis linear trajectory. The top profiles represent the measured human lead interaction, while the bottom profiles represent the replicated interaction between the human and robot.
desired motion. Overall, though the rule base is able to infer a reasonable approximation of the desired compliance for the y-axis linear trajectory, the results are not as accurate as the x-axis linear trajectory. This difference is likely a result of the greater degree of discontinuity present in the training data used to generate the y-axis trajectory rule base compared to the x-axis trajectory. This is confirmed through a visual comparison of the upper portions of the figures which show a higher number of ‘‘branches’’ in the y-axis trajectory data. The results of the application of the compliance rule base to a circular trajectory are shown in Fig. 4(a) and (b). Overall, the fuzzy system is able to more accurately reproduce the desired compliance along this trajectory than the linear trajectories. This result is contrary to the observed inconsistencies in the performance of the system during testing. The ‘‘feel’’ of the interaction between the patient and the robot during the execution of the circular trajectory was noticeably more erratic than during the linear trajectory exercises. This behaviour was likely a result of the greater difficulty inherent in generating a representative and consistent training dataset for the relatively more complex circular trajectory. The cyclic nature of the circular trajectory makes it more prone to the conflicting data as a result of the greater likelihood of the same interaction force occurring at different points in the circle, requiring different compliant position commands. In order to alleviate the potential for inconsistent behaviour, one approach could be to divide more complex, or cyclic trajectories into multiple consecutive trajectories with individual rules. This could also provide potential for conditional behaviour profiles dependent on the state of the patient or exercise (e.g. fatigue, emergency protocols, etc.) This approach will be investigated further in future experimental trials. Despite these complications, however, the results indicate that the system is able to maintain and recreate the desired compliance as long as the patient behaviour remains within the known input space. The results for all trajectories that were implemented on the Epson E2L853 manipulator indicate that the fuzzy compliance rule base methodology is able to replicate the interaction between a therapist and patient based on the datasets gathered during the experimental trials. The inconsistencies apparent in several of the results, however, highlight the need for an automated approach to the tuning of the system parameters to ensure that the desired interaction dynamics are reliably maintained during training.
4.2. Preliminary neuro-fuzzy results The critical objective for the application of a learning algorithm to the fuzzy compensator module was to improve the performance of the trajectory generator system on-line without detrimentally affecting the computational efficiency of the overall system. In order to first determine if the integration of the fuzzy compensator into a hybrid neuro-fuzzy framework would successfully improve the accuracy of the overall trajectory generator, the compliance rule base was first tested with a manually tuned compensator. The algorithm was applied to the resultant compliant trajectories as an offline simulation. The output from the compliance rule base for each recorded end-effector force set was combined with the generated neuro-fuzzy compensator output to generate an approximation of how the system would have performed had the learning algorithm been present. An example of a comparison of the compliant positions generated by: (a) the fuzzy compliance rule base; (b) the compliance rule base combined with the fuzzy compensator to form the fuzzy trajectory generator; and (c) the neuro-fuzzy trajectory generator is shown in Fig. 5(a) and (b) when applied to a linear trajectory along the manipulator x-axis. The results clearly show that the error between the generated compliant position and the desired compliant position can be reduced by the incorporation of learning into the fuzzy trajectory generator. As expected, without the neuro-fuzzy scheme, the manually-tuned fuzzy compensator merely adds an additional offset to the output from the compliance rule base as a function of the measured force without any regard for the desired compliant position. The complete hybrid neuro-fuzzy system, however, is able to provide the offset necessary to match the desired compliance regardless of the measured forces at the end-effector. The flat lines that are shown in the response of the compliance rule base and fuzzy compensator are likely a result of either missing data in the compliance rule base, or problems with the manual tuning of the fuzzy compensator. This highlights that potential for the additional learning algorithm to adjust the compliance to match the reference data much better than the manually tuned compensator despite errors in the rule base. Overall, the addition of a learning component into the fuzzy trajectory generator significantly improved the performance of the system offline, providing a firm basis for the implementation of a real-time neurofuzzy trajectory generator.
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Fig. 4. X -axis, Y -axis comparative compliance for the lead mode circular trajectory. The top profiles represent the measured human lead interaction, while the bottom profiles represent the replicated interaction between the human and robot.
Fig. 5. (a) Learning algorithm applied to: X -axis rule base, (b) Y -axis rule base with multiple branches for a linear X -axis trajectory.
4.3. Neuro-fuzzy implementation results Once the potential for the application of a hybrid neuro-fuzzy scheme was established, the neuro-fuzzy trajectory generator was implemented as a real-time module on the Epson E2L853 manipulator shown in Fig. 9. The system was tested using the linear trajectories, which showed the most consistent results in preliminary testing, in order to generate a reliable comparison between the reference data, fuzzy rule base, and complete neurofuzzy trajectory generator. On average, the complete neuro-fuzzy algorithm was able to generate the next compliant trajectory point in 3.3 ms while simultaneously tuning the dynamics of the interaction using the compensator. This was well within the computational bounds outlined for the algorithm. The performance of the neuro-fuzzy trajectory generator while leading the patient along an x-axis trajectory is evaluated in Fig. 6(a) and (b). The results clearly indicate that the ability of the neuro-fuzzy algorithm to better replicate the human–robot interaction, shown in the preliminary testing, was confirmed. According to the results shown in Fig. 6(a), the manually-tuned fuzzy compensator actually had a negative effect on the performance of the system, in some cases driving the magnitude of the compliant position far higher than the desired position. To determine the influence of multiple compliant trends for the same force profiles, or ‘‘branches’’, the experiment was repeated with a refined reference
dataset. The additional results are shown in Fig. 7(a) and (b). Table 1 indicates that the refined reference dataset somewhat negatively affected the performance of the system along both axes, reinforcing the need for a comprehensive reference database outlined in Section 2.1. It should be noted that the additional ‘‘branches’’ were not removed from the compliance rule base, which likely influenced the deviation in the compliance trend between 5 N and 10 N in Fig. 7(a). Though the performance of the system was detrimentally affected by the removal of multiple branches from the compliance rule base, these results indicate that the neuro-fuzzy system is able to adapt a complete rule base to a specific implementation or experiment. The specialization of the system using a general purpose rule base highlights the further potential for development of a library of generic fuzzy rule bases for a variety of diseases or levels of impairment. The results of the implementation of a linear y-axis trajectory are shown in Fig. 8(a) and (b). The y-axis was also implemented using a ‘‘single branch’’ training set, to overcome some conflicts in the training set as outlined in Section 2.1, and to further investigate the potential for generic rule bases with specialized on-line neuro-fuzzy tuning. The performance of the x-axis component of the neuro-fuzzy system is significantly better than both the fuzzy rule base and the manually-tuned system in this case, further confirming the effectiveness of the learning algorithm.
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Fig. 6. (a) X -axis comparative results, (b) Y -axis comparative results using multiple branches for an X -axis linear trajectory.
Fig. 7. (a) X -axis comparative results, (b) Y -axis comparative results using single branches for an X -axis linear trajectory.
Fig. 8. (a) X -axis comparative results, (b) Y -axis comparative results using single branches for a Y -axis linear trajectory.
5. Conclusions The fundamental overarching objective of the proposed approach was to develop a framework for the application of hybrid neuro-fuzzy control systems design to the field of rehabilitation robotics. The human-in-the-loop nature of rehabilitation robotics
requires a fundamentally different approach to the design and development of manipulator control systems that emphasizes the interaction between the patient and the manipulator system. This human-centred approach to design is ideally suited for the application of soft-computing approaches including FCM clustering and neuro-fuzzy control. To this end, several real-time trajectory
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577
Fig. 9. Implementation of the proposed system on the Epson E2L853.
Table 1 Comparative lead mode mean-square error. Trajectory tested (result set) X axis line multiple branches (X -axis) X axis line multiple branches (Y -axis) X axis line single branches (X -axis) X axis line single branches (Y -axis) Y axis line single branches (X -axis) Y axis line single branches (Y -axis)
Compliance rule base
Fuzzy trajectory generator
Neuro-fuzzy trajectory generator
209.45
630.72
14.49
100.81
952.64
25.81
659.10
N/A
29.58
234.96
N/A
86.85
637.81
83.68
1855.3
121.98
1289.9 100.81
generator modules were developed to evaluate the effectiveness of a neuro-fuzzy approach to the challenges inherent to upper-limb rehabilitation therapy. The primary approach to physical therapy employed in conventional therapy training sessions involves guiding the affected limb along a series of predetermined position profiles. During training, the proposed trajectory generator regulates the interaction force to offer variable levels of compliance as they are led along the specified trajectories by the manipulator servo controller. The critical objective of the architecture was to show that a robotic manipulator is able to replicate the therapist behaviour by providing the prescribed level of compliance during a therapy action. Implementation results showed that the fuzzy trajectory generator was able to successfully replicate the recorded patient/therapist interaction, validating the proposed approach. The fuzzy compensator module was then integrated into a hybrid neuro-fuzzy structure to automate the tuning process on-line. The introduction of learning into the trajectory generator significantly improved the performance of the proposed system. Overall, the neuro-fuzzy trajectory generator fulfilled all expectations providing an efficient and effective framework for the replication of therapy actions on almost any robotic manipulator system. To provide a user-friendly interface for the customization of a wide variety of system parameters, a graphical user interface was developed and implemented. The interface was created as an offline software module for the visual and linguistic specification
of the system behaviour to easily customize the human–robot interaction. In the future, this non-technical approach to the specification of system parameters may prove instrumental in the adoption of the proposed system as a feasible clinical approach to robotic rehabilitation. At the outset of the design and development of the proposed approach to robotic rehabilitation, the overarching objective for the performance of the trajectory generator system was identified as: the flexibility to perform a diverse range of exercises with the adaptability to conform to different patients and a high level of usability to appeal directly to the needs of the therapists. The successful results of the implementation and testing of the proposed real-time neuro-fuzzy trajectory generator attest to the fulfilment of these fundamental objectives. The robotic rehabilitation system presented in this paper may one day contribute to the improvement of the effectiveness of physical therapy in reducing the longterm functional impairment in patients with upper-limb dysfunction due to neurological diseases. References [1] M. Lee, M. Rittenhouse, H.A. Abdullah, Design issues for therapeutic robot systems: results from a survey of physiotherapists, J. Intell. Robot. Syst. 42 (2005) 239–252. [2] P.S. Lum, C.G. Burgar, M. Van der Loos, P.C. Shor, M. Majmundar, R. Yap, MIME robotic device for upper-limb neurorehabilitation in subacute stroke subjects: a follow-up study, J. Rehabil. Res. Dev. 43 (5) (2006) 631–642. [3] L.E. Sucar, R. Ledger, J. Hernández, I. Sánchez, G. Azcárate, Clinical evaluation of a low-cost alternative for stroke rehabilitation, in: IEEE International Conference on Rehabilitation Robotics, June 2009, pp. 863–866. [4] M.S. Ju, C.K. Lin, D.H. Lin, I. Hwang, S.M. Chen, A rehabilitation robot with forceposition hybrid fuzzy controller: hybrid fuzzy control of rehabilitation robot, IEEE Trans. Neural Syst. Rehabil. Eng. 13 (2005) 349–358. [5] R. Riener, Robot-aided rehabilitation of neural function in the upper extremities, in: Operative Neuromodulation, Vol. 97, Springer, Vienna, 2007, pp. 465–471 (1). [6] S.P. Buerger, J.J. Palazzolo, H.I. Krebs, N. Hogan, Rehabilitation robotics: adapting robot behavior to suit patient needs and abilities, in: Proceedings of the American Control Conference, Vol. 4, June–July 2004, pp. 3239–3244. [7] S. Chen, W. Harwin, T. Rahman, The application of discrete-time adaptive impedance control to rehabilitation robot manipulators, in: IEEE International Conference on Robotics and Automation, vol. 1, 1994, pp. 636–642. [8] C. Ellsworth, J. Winters, An innovative system to enhance upper-extremity stroke rehabilitation, in: Proceedings of the Second Joint EMBS/BMES Conference, vol. 3, 2002, pp. 2367–2368. [9] H. Sun, L. Zhang, X. Hu, L. Tian, Experiment study of fuzzy impedance control on horizontal lower limbs rehabilitation robot, in: International Conference on Electronics, Communications and Control, 2011, pp. 2640–2643.
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[10] H. Ho, T. Chen, Hybrid CPM/CAM physiotherapy by use of the slide-mode fuzzy neural network control, in: International Conference on Innovative Computing Information and Control, June 2008, pp. 510–514. [11] M.R. Emami, I.B. Türksen, A.A. Goldenberg, Development of a systematic methodology of fuzzy logic modeling, IEEE Trans. Fuzzy Syst. 6 (3) (1998) 346–361. [12] M. Sugeno, T. Yasukawa, A fuzzy-logic-based approach to qualitative modeling, IEEE Trans. Fuzzy Syst. 1 (1) (1993). [13] F. Nagata, K. Watanabe, K. Izumi, Position-based impedance control using a fuzzy compensator, Knowl.-Based Intell. Inf. Eng. Syst. (1999) 125–128. [14] P. Martin, M.R. Emami, Real-time fuzzy trajectory generation for robotic rehabilitation therapy, in: IEEE International Conference on Rehabilitation Robotics, June 2009, pp. 354–359. [15] D. Surdilovic, Z. Cojbasic, Robust robot compliant motion control using intelligent adaptive impedance approach, in: Proceedings Robotics and Automation, vol. 3, 1999, pp. 2128–2133. [16] J.S.R. Jang, C.T. Sun, Neuro-fuzzy modeling and control, Proc. IEEE 83 (3) (1995) 378–406. [17] L.X. Wang, J.M. Mendel, Back-propagation fuzzy system as nonlinear dynamic system identifiers, in: IEEE International Conference on Fuzzy Systems, March 1992, pp. 1409–1418. [18] P. Martin, Real-time neuro-fuzzy trajectory generation for robotic rehabilitation therapy, University of Toronto, 2010. http://hdl.handle.net/1807/18909.
Peter Martin received a B.Sc. Eng. in Systems and Computer Engineering with a specialization in mechatronics from the University of Guelph in 2007. He then completed a M.A.Sc. in Mechatronics at the University of Toronto Institute for Aerospace Studies in 2009. Since completing his master’s degree, he has gone on to pursue a career in robotics and controls education. His research interests include soft computing, artificial intelligence and rehabilitation robotics.
M. Reza Emami, Ph.D. in robotics and mechatronics from the University of Toronto. He has been the Director of Aerospace Mechatronics group and the Coordinator of Aerospace and Design Laboratories at the University of Toronto Institute for Aerospace Studies since 2001. Prior to joining the academia as a faculty member, he worked in the industry as a project manager for several years. He is a professional engineer, and his research interests centre on the intelligent control design for robotic systems, as well as concurrent engineering of mechatronic systems such as space manipulators.
Contents lists available at ScienceDirect
Robotics and Autonomous Systems journal homepage: www.elsevier.com/locate/robot
A neuro-fuzzy approach to real-time trajectory generation for robotic rehabilitation Peter Martin, M. Reza Emami ∗ University of Toronto Institute for Aerospace Studies, 4925 Dufferin Street, Toronto, Ontario M3H 5T6, Canada
highlights • A neuro-fuzzy schema introduces compliance into the human–robot interaction to emulate a wide-variety of exercises. • Implemented as a manipulator independent solution. • Preliminary results indicate that the system is able to very closely replicate a generic patient–therapist interaction.
article
info
Article history: Received 20 January 2012 Received in revised form 16 October 2013 Accepted 2 January 2014 Available online 20 January 2014 Keywords: Neuro-fuzzy control Compliant trajectory generator Rehabilitation robotics
abstract This paper proposes a method for the design of a real-time neuro-fuzzy trajectory generator for the robotic rehabilitation of patients with upper limb dysfunction due to neurological diseases. The primary objective of the methodology is to assist therapists by allowing them to delegate repetitive therapy tasks to a mechatronic system. The trajectory generator is packaged as a platform-independent solution to facilitate the rehabilitation of patients using multiple manipulator configurations. The system utilizes a fuzzy-logic schema to introduce compliance into the human–robot interaction, and to allow the emulation of a wide variety of therapy techniques. This approach also allows for the fine-tuning of patient specific behaviour using linguistic variables. The rule base for the system is trained using a fuzzy clustering algorithm and applied to the experimental data gathered during traditional therapy sessions. The compliance rule base is combined with a hybrid neuro-fuzzy compensator to automatically tune the dynamics of the robot–patient interaction. Preliminary results indicate that the approach can accurately reproduce a prescribed patient/therapist interaction, validating the proposed approach. © 2014 Elsevier B.V. All rights reserved.
1. Introduction Though a considerable body of research has been conducted in the field of rehabilitation robotics over the past decades, the commercial viability and widespread use of robotic systems for rehabilitation therapy are still very limited. This lack of large-scale commercially-viable systems has been attributed to several factors, the most significant of which are cost and usability, essentially non-technical issues. It is imperative to the development of a successful robotic rehabilitation system, therefore, to appeal to the needs of physiotherapists. Therapists are ultimately responsible for deciding whether a rehabilitation system is a worthwhile investment of their time and money [1]. The primary objective of the methodology proposed in this paper is to assist therapists by allowing them to delegate repetitive therapy tasks to a mechatronic system that is able to replicate
∗
Corresponding author. Tel.: +1 416 946 3357; fax: +1 416 946 7109. E-mail addresses: [email protected] (P. Martin), [email protected] (M.R. Emami). 0921-8890/$ – see front matter © 2014 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.robot.2014.01.001
the patient–therapist interaction as closely as possible. This approach aims to mitigate the cost and labour-intensive aspects of neurorehabilitation to improve clinical efficiency and efficacy [2,3]. The system was developed as a platform-independent, modelbased solution. This approach was taken to give the therapist the flexibility to perform a wide range of both established and emerging therapy techniques, using a wide variety of manipulator systems. This can also serve to mitigate the costs associated with developing specialized rehabilitation platforms by offering a software framework that is compatible with off-the-shelf industrial manipulators. The fundamental design challenge for robotic rehabilitation therapy is the replication of the complex movements with resistive and/or assistive forces applied at specific positions associated with traditional physiotherapy. Traditionally, a hybrid force–position controller would be required to regulate the interaction forces while precisely monitoring and controlling the position and velocity of the movement. Since during rehabilitation, the patient is also a part of the dynamic system, traditional control parameters are difficult to develop based on the system model and its parameters [4].
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Impedance control, which is well established in the field of rehabilitation robotics [5], allows for variable deviation from a given limb trajectory while keeping the limbs within a predefined range. One of the most prevalent forms of impedance-based force control in rehabilitation robotics is adaptive impedance control [6,7]. In adaptive impedance control, the human represents a component of the control system that influences its behaviour. This enables the control structure to adapt to changes in the reference trajectory initiated by the patient to regulate the interaction forces between the patient and the manipulator system. Though adaptive impedance control has become the standard method of robotic force control for rehabilitation, there remain some fundamental shortcomings inherent in the approach. The complexity of the traditional control approach dictates that changes in the environmental dynamics require significant tuning and parameter alteration. Once a control system has been tuned to perform a specific exercise with a specific patient, the system parameters must be altered and tuned by an expert if the therapist wishes to change the way the exercise is performed. An approach to the implementation of force control that is able to inherently overcome the difficulties associated with impedance control is through the use of fuzzy logic [4,8–10]. Fuzzy logic control has the advantage of being able to provide rule based force control while compensating for nonlinearity and parameter uncertainty. This feature enables the system designers to create a model of the prescribed interaction between the robot and the patient based on the therapist’s qualitative description of the desired behaviour of the coupled system. The control parameters can also be tuned quite easily to modify specific aspects of the interaction. The traditional approach to the generation of the rule base for fuzzy rehabilitation systems does, however, create a fundamental reliance on the expert knowledge of the therapy professionals. Given the complexity of traditional therapy tasks, this dependency on an accurate understanding of the dynamics of the interaction has meant that the fuzzy based rehabilitation systems are normally only able to perform very simple trajectory profiles. To overcome this limitation, our methodology utilizes fuzzy clustering and a hybrid neuro-fuzzy schema to generate a representative model of a wide variety of force–position profiles. 2. Material and methods In order to create a system that is able to emulate the behaviour of a therapist as closely as possible, our trajectory generator utilizes a fuzzy-logic based inference system. Using a fuzzy approach enables the system to emulate the humanistic dynamics of traditional therapy more effectively than traditional control approaches by making use of model-based variable compliance. In addition, each unique exercise and each patient can take advantage of a unique rule base to better emulate each specific treatment scenario. Therefore, it should be emphasized that the system is not meant to replace the therapist, but to enable the autonomous treatment of patients at home or in the clinic. 2.1. Data gathering The first stage in the generation of a fuzzy model of the patient–therapist interaction is the acquisition of a suitable dataset. There are several considerations that must be paid due diligence during the data gathering stage including: (1) the need for a representative dataset, (2) the specification of appropriate protocols for handling exceptional circumstances, and (3) verification that there are no conflicting relationships contained in the dataset. The need for a representative dataset is a fundamental requirement for all fuzzy modelling based controllers. The nature
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of fuzzy logic enables a fuzzy controller to infer appropriate system responses to undefined input values by extrapolating based on the behaviour contained within the system model. It is for this reason that fuzzy logic-based inference systems are widely applied in situations where a humanistic or reasoned approach is appropriate. However, if the universe of discourse defined by the fuzzy input space is too limited in its scope with respect to the input variables passed to the system during its application, the system will not respond properly when the input lies outside of the realm of knowledge. Therefore, in the case of knowledge based systems such as the fuzzy trajectory generator proposed in this paper, a dataset that contains a reasonably complete input space is essential to ensure that the system is able to react to all potential training scenarios in a controlled manner. The specification of protocols for the proper compensation during exceptional circumstances involves the inclusion of situations within the experimental data that specify the proper system reactions during abnormal conditions. Given the interactive nature of the neuro-fuzzy training system, it is imperative that the system responds gracefully under exceptional circumstances such as a large patient jerk or spasm to ensure the safety of the patient at all times. During the therapist training sessions used for the generation of the fuzzy rules, therefore, proper responses to unanticipated patient reactions should be prescribed. The confirmation that the therapist dataset does not contain conflicting behaviour is required to ensure that the system response is consistent and well defined. For this reason, it is important to specify a clear and consistent protocol for the therapy action taken during the data gathering stage. For instance, during the training sessions, the therapist must consistently lead the patient along the trajectory while providing consistent compensation. If the patient is allowed to lead, or ‘‘push’’ the therapist along the trajectory then the interaction will result in two conflicting compliant conditions for the same measured forces. This is also the case if the therapist has allowed the patient to deviate laterally from the specified trajectory, and the resistive force applied by the patient is reduced without the therapist leading the patient back to the proper trajectory. In this case, both low and high force conditions will be measured corresponding to the same deviation from the desired trajectory. If the behaviour expressed by the dataset used to generate the compliance model is clear and consistent, then the ability of the fuzzy system to replicate the prescribed interaction when working with the patient is greatly increased. 2.2. Fuzzy clustering The purpose of the trajectory generator module is to generate the end-effector positions necessary to follow the position trajectory specified by the exercise, while providing a forcedependent level of compliance to the human–patient interaction. The fuzzy rule base, thus, expresses the dynamics of the relationship between changes in the interaction forces measured at the end-effector and the resultant compliant position increment. The first stage in the application of the proposed methodology is to create a representative rule base using clustering. In order to provide a basis for the initial selection of the number of clusters c and exponent m, an iterative heuristic algorithm described in [11] is used. Once the appropriate initial conditions are obtained, the output space of the experimental dataset is clustered using the FCM optimization algorithm. Using the unlabelled data X = {x1 , x2 , . . . , xN } ⊂ Rh , where N is number of data arrays and h is the dimension of each data array, clustering can be viewed as the assignment of labels c to the arrays in X . The problem of fuzzy clustering is thus expressed as the problem of finding the optimum (c × N ) matrix of membership values {uik }, U = [uik ]. The FCM
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algorithm minimizes a weighted within-groups sum of squarederrors objective function Jm as follows: min {Jm (U , V ; X )} =
(U ,V )
N c (uik )m ∥xk − vi ∥2A
(1)
k=1 i=1
yˆ =
where,
0 ≤ uik ≤ 1 ∀i, k; N cn = U ∈R uik < n ∀i; 0 < k=1
& &
∀k, uik > 0 ∃i c ; (2) uik = 1 ∀k i =1
where V = {v1 v2 , . . . , vc } is the set of cluster centres and ∥x∥A = √ xT Ax is any inner product norm. Matrix A, which is usually selected as the identity matrix, is an h × h positive-definite matrix that specifies the shapes of the clusters. N , c and r are the number of data points, clusters and input dimensions, respectively. Fuzzy partitions are thus identified using the fuzzy c-means algorithm through an iterative optimization of (1). Trapezoidal membership functions are then fitted to the output space based on the generated cluster centres. The output membership functions are then projected onto the input space using the fuzzy line clustering technique, to generate the appropriate input membership functions. First, it is supposed that for each output cluster i (i = 1, 2, . . . , n), there are several points on the axis of input variable xj (j = 1, 2, . . . , r ) which have output membership equal or close to one. These points lie between vij1 and
vij2 (vij1 < vij2 ). The distance of each point xjk on the axis xj to the j
line vij1 vij2 is then determined. The membership grades uik for the input data xjk (j = 1, 2, . . . , r ; k = 1, 2, . . . , N ) corresponding to output cluster i are then formed such that the points closer to the line vij1 vij2 obtain higher membership grades. In order to optimize j
the membership grades uik , an objective function analogous to the FCM function Jm is defined: J¯m U j , Xj =
N n (ujik )m dis xjk , vij1 vij2 .
(3)
k=1 i=1
Solutions to the optimization problem to minimize the above objective function are directly obtained by distinguishing between j
two cases where xjk < vij1 and xjk > vij2 , and solving for d/duik
J¯m = 0. The final resultant membership grade is obtained as follows in Box I: for i = 1, 2, . . . , n, j = 1, 2, . . . , r and k = 1, 2, . . . , N; where, n is the number of rules, r is the number of input variables, and N is the number of data points. To complete the modelling process, the system parameters are tuned to reduce the system error with respect to the test data using a derivative of the Sugeno–Yasukawa iterative tuning algorithm [12]. To complete the fuzzy inference system, Takagi–Sugeno–Kang (TSK) inference is integrated into the system to determine the corresponding crisp outputs for each input set. The TSK reasoning method is associated with a rule base of a special format that is characterized by functional consequents instead of the more traditional fuzzy consequents. In the case of the inference system used in this paper, the fuzzy consequent di is the centre of area of the consequent membership function, Di , in the ith rule. The inferred crisp output, yˆ , is then determined by first evaluating the degree of membership in the premises of each rule as:
w =
Bi1
n i =1
U ϵ Mfcn
i
where Bij (i = 1, . . . , n, j = 1, 2, 3) are the fuzzy sets over the input space and 1 ≤ i ≤ n. The inferred crisp output, yˆ , is then determined by taking the weighted average of di with respect to w i as:
0
x1 ×
Bi2
0
x2 × · · ·
Bin
0 xn
(5)
w i di
n
wi
(6)
i=1
where n is the number of rules, and di is the centre of area of the consequent membership function, Di , in the ith rule. Finally, to increase the accuracy of the generated model, a derivative of the Sugeno–Yasukawa iterative tuning algorithm [13] is applied. The algorithm evaluates the mean-squared-error of the system based on a subset of the experimental data, to evaluate the effect of changing the parameters of the input and output membership functions. The adjustment value for each data space is modified during each iteration to more precisely adjust the placement of the modified membership functions. This process for the generation of a fuzzy rule base for compliant position trajectory generation was first proposed in [14]. 2.3. Fuzzy trajectory generator When the current forces between the patient and the robot, Fn , are fed back from the force transducer, they are compared with a corresponding desired interaction force, Fd , as specified by the therapist. The resultant force error, Fe = (Fd − Fn ), is then passed into the fuzzy trajectory generator module along with the desired trajectory position for the exercise in the task space. In order to reduce the influence of high-frequency noise inherent in the signal from the force sensor, a moving average of three consecutive measurements is used as a simple low-pass filter. To reduce the complexity of the fuzzy inference system necessary to generate each compliant increment vector, three separate rule bases are used for each component of the consequent change in the end-effector position. The force errors across all axes are input into the fuzzy consequent layer in order to allow the fuzzy rules to evaluate the state of the system including any coupling between the forces acting along all axes. The control action of the fuzzy system for each rule base can be expressed linguistically as: IFFex is B11 AND Fey is B12 AND Fez is B13 THEN ∂ pos is D1 ALSO
...
(7)
ALSO IF Fex is Bn1 AND Fey is Bn2 AND Fez is Bn3 THEN ∂ pos is Dn where n is the number of rules, Bij (i = 1, . . . , n, j = 1, 2, 3) and Dk (k =1, . . . , n) are fuzzy sets over the input and output spaces, Fe = Fex , Fey , Fez , and ∂ pos is either ∂ x, ∂ y or ∂ z depending on the rule base. The resultant trajectory point is then added to the desired trajectory position and the additional compensator position to generate the total position command to be passed to the manipulator servo controller. The overall trajectory generation scheme is illustrated in Fig. 1. 2.4. Hybrid neuro-fuzzy compensator The fuzzy rule base representing the compliance behaviour of the therapy action is structured as an outer-loop module to enable the trajectory generator to remain kinematically independent.
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m−1 1 −1 m−1 1 −1 2 1 n n | x − v | | x − v | jk jk ij ij 1 2 : x < v or x > v , jk j jk ij ij 1 2 uik = Max |xjk − v1j | |xjk − v1j | 1 =1 1 =1 1 2 1 : vij ≤ xjk ≤ vij
571
(4)
Box I.
Fig. 1. Neuro-fuzzy trajectory generator design methodology.
This schema addresses both the need for specialized humancentred systems designed especially for rehabilitation and the high cost of custom robotic manipulators. By enabling the proposed system to be applied to multiple manipulator configurations, the trajectory generator can be packaged as a self-contained software module to facilitate the automated rehabilitation therapy using both custom and industrial manipulators with various degrees of freedom. However, in order to ensure that the system is able to replicate the behaviour dictated by the fuzzy rule base regardless of the dynamics of the manipulator, an additional control module was necessary. Several fuzzy impedance compensators have been proposed in the literature for industrial tasks in order to compensate for situations where the environmental dynamics are unknown and for parameter uncertainty [15,13]. To maintain a computationally-efficient system, a position-based fuzzy compensator was implemented based on the approach taken in [13]. This module provides an additional position correction to the trajectory based on the measured force error. The task of the fuzzy compensator module is to generate additional position increments based on the interaction force measured at the end-effector in order to compensate for the difference
in dynamics between the manipulator and therapist. Three separate inference systems are utilized, one for each position increment component, to allow the dynamic components to be independently tuned. Each module is implemented as a MISO fuzzy system utilizing TSK inference. The antecedent inputs for each system are force and force increment along each respective axis. A rule base with n × m rules is used where n and m are the number of input membership functions for each input, respectively. To simplify the tuning of the resultant systems, constant consequents are used for each rule. For example, the rules for the x-axis component of the fuzzy compensator can be expressed linguistically as: IF Fex is B1 AND δ F ex is D1 THEN ∂ xc is c1 ALSO
...
(8)
ALSO IFFex is Bn AND δ F ex is Dn THEN ∂ xc is cn where n is the number of rules, Bi (i = 1, . . . , n) and Di are the ith antecedent fuzzy sets for the three inputs, respectively, and ci is the consequent constant of the ith rule.
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Given the complex nature of the interaction between the patient and the manipulator system, a learning algorithm was integrated into the trajectory generator module in the final stage of development to form the hybrid neuro-fuzzy system shown in Fig. 1 (block B). The neuro-fuzzy algorithm, shown in Fig. 1 (block C), enables the system to autonomously tune the consequent constants in real-time to improve the performance of the system, and to compensate for changes in the manipulator configuration. The hybrid neuro-fuzzy scheme used in this paper is very similar to the Adaptive-Network-based Fuzzy Inference System (ANFIS) [16], but was developed independently in [17]. In the first stage of the neuro-fuzzy scheme, similar to the traditional fuzzy control methodology, the two crisp input values are assigned to the appropriate fuzzy sets and corresponding linguistic variables based on the trapezoidal antecedent membership functions. In the second stage the activation degree of each rule is calculated. The error signal between the model inferred value Pˆ d , and the corresponding training value, pˆ ′d is then evaluated and integrated into an objective function E which expresses the mean quadratic error of the system. The training value based on the experimental data is generated using a lookup table and a linear search algorithm of O(n) time; if the value is not found in the table, then the three closest values based on the input vector are averaged to generate an appropriate reference. The error is evaluated as: E=
1 2
Pˆ d − pˆ ′d
2
(9)
where the model inferred value, Pˆ d , is the overall compliant position generated by the trajectory generator system, and pˆ ′d is the corresponding training value. The inferred response to the input vector X is consequently calculated as:
n n ′
Pˆ d X
=
i =1
Bij
j =1
n n i=1
0
Bij
xj
ωi
+ δ pr + pd 0
(10)
xj
j =1
where ωi is the weighted consequent rule conclusion, δ pr is the output from the compliance rule base, pd is the desired trajectory point, and Bij (i = 1, . . . , n, j = 1, 2, 3) are the fuzzy sets over the input space. The algorithm utilizes the gradient-decent method to adjust the weight of the rule conclusions as a function of the objective function as:
ωi (t + 1) = ωi (t ) − α
∂E ∂ωi
(11)
where α is the learning rate. By calculating the variation of the objective function E, in relation to the variation that occurred in ωi in the anterior instant, the adjustment of each conclusion value can be expressed as:
ωi (t + 1) = ωi (t ) − α
Pˆ d − pˆ ′d di n i
(12)
d
i=1 i
where d is the contribution of rule i to the final neuro-fuzzy inference. The adjustment to the weight of the rule conclusion can thus be interpreted as being proportional to the error between the model inferred value and the experimental value, weighted by the contribution of the rule to the overall crisp output. This online tuning algorithm ensures that the overall trajectory generator is able to replicate the proper therapist inspired interaction and eliminate errors in the clustered compliance rule base independent of the manipulator system kinematic configuration
3. Experimental 3.1. Software design The implementation of the proposed methodology necessitates the utilization of a software development approach that is compatible with a wide range of software-based manipulator systems. The fuzzy modules discussed in this paper, therefore, have R been implemented on the Microsoft Windows⃝ operating system as Win32 dynamically-linked libraries (DLLs) using Microsoft Visual C++. These libraries are accessible from all Windows-based controllers by making external calls to the libraries from the proprietary manipulator control development environment that manages the execution of the specified movement commands. The neuro-fuzzy trajectory generator is divided into two independent libraries that are used to generate the compliant position and the additional compensation offset, respectively. Both libraries utilize an object-oriented approach to the design of the fuzzy algorithms to allow the systems to be applied to various fuzzy control configurations. 3.2. Graphical user interface The fundamental goal of the Graphical User Interface (GUI) developed for the neuro-fuzzy trajectory generator system is to facilitate the specification of a number of system parameters by the therapist. The use of a fuzzy architecture for the control structure of the trajectory generator makes it possible for the therapist to specify and alter the interaction dynamics between the manipulator system and the patient linguistically. This potentially alleviates the need for a team of engineers or technical support staff traditionally necessary for the modification and tuning of robotic rehabilitation systems. To this end, the linguistic rules are presented in the GUI as a set of linguistic IF–THEN expressions that can be easily modified based on the fuzzy system model. Several additional characteristics of the system behaviour can be displayed and edited through the GUI including: the desired position trajectory, the membership function parameters, and the characteristics of the reference data used by the learning algorithms in the neuro-fuzzy compensator module. Configuration changes are made to the trajectory generator through the GUI offline, and are loaded into the fuzzy control modules at R runtime. The GUI was developed using the Microsoft⃝ Visual C# programming language in conjunction with the .NET framework. 3.3. Implementation and validation As a preliminary means to validate the proposed approach, a number of experimental datasets were recorded during mock therapy sessions to generate a number of behaviour models using the fuzzy clustering procedure outlined in Section 2.2. Given that the data were to be used as a proof of concept validation of the proposed methodology, the trials were performed by two researchers acting as a therapist and patient. The position and force information were recorded using a 6 d.o.f ATI Mini45 force R transducer, in conjunction with an NDI Optotrack⃝ Certus optical motion tracking system. The force transducer was capable of measuring applied forces at a resolution of up to 1/64 N over an Fx /Fy sensing range of ±145 N. The motion tracking system was able to measure three dimensional positions at a resolution of 0.01 mm. A custom handle mechanism was designed to be mounted on the top of the force transducer interface, to allow the therapist to train the patient in the same orientation as the manipulator end-effector. Various two-dimensional circular and linear trajectories were performed to generate a representative body of data for different therapy actions. For the linear trajectories
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Fig. 2. (a) X -axis, (b) Y -axis comparative compliance for the lead mode x-axis linear trajectory. The top profiles represent the measured human lead interaction, while the bottom profiles represent the replicated interaction between the human and robot.
that are presented in Section 4, the mock patient was lead back and forth along a 40 cm linear path, and 30 cm in diameter circular path. An average of 10 trials were performed for each trajectory with a wide variety of disturbances introduced into the coupled motion by the mock patient in order to create a representative dataset. Multiple datasets were used to generate each rule base to ensure a robust system. Once the force and compliant position datasets were generated, the datasets were clustered to generate representative fuzzy inference systems. To complete the implementation process, the fuzzy rule base was tuned using various subsets of the training data to more accurately match the desired compliance profiles. During the subsequent implementation and testing, the proposed system was integrated into the control framework of the 4 d.o.f Epson E2L853 industrial manipulator. This SCARA-type manipulator uses high torque AC servo motors, combined with harmonic drives to give the manipulator a standard (1′′ × 12′′ × 1′′ and back) cycle time of 0.437 s with high repeatability (0.020 mm). The manipulator has a horizontal reach of 850 mm and a Z axis vertical stroke of 320 mm. The system was tested using the same trajectories that were performed during the human/therapist trials. Three dimensional position profiles were not tested due to restrictions inherent to the manipulator system, though the system is theoretically applicable as a 3D trajectory generator. During testing, a desired force, Fd , of zero was used since the experimental trials were performed without a specific desirable force profile. The neuro-fuzzy compensator was given the reference datasets used to create the compliance rule base to enable it to tune the compliance of the human/robot interaction on-line. 4. Results The fundamental goal of the testing stage of development was to show that the robotic manipulator was able to replicate the therapist’s behaviour by providing an appropriate level of compliance during a therapy action. We were unconcerned with the efficacy of the particular chosen exercise, assuming that a therapist would be uniquely qualified to access an appropriate interaction, and demonstrate that action to the system during the data-gathering stage. The ability of the system to accurately replicate a prescribed exercise is an inherently quantifiable objective, and therefore a comparison of the proposed system and a traditional impedance-based controller was deemed unnecessary. The ability of the proposed system to effectively replicate a specific
force profile was implemented and tested using a minimum-force ‘‘follower’’ mode and compared to conventional impedance control approaches in [18]. In this section, the neuro-fuzzy system is compared to a conventional fuzzy controller and the recorded human interaction in order to demonstrate the need for the additional compensator and learning algorithm. 4.1. Compliance rule base implementation results The first stage of the implementation of the proposed system on the Epson E2L853 included only the compliance rule base. This stage was performed in order to validate the rule base, while gathering initial benchmark results to compare to the overall system. Some examples of the results gathered during this stage are presented in this section. A comparison between the compliance that was recorded during the data gathering stage while following an x-axis linear trajectory and the compliance generated by the fuzzy rule base while leading the mock patient along the same trajectory is presented in Fig. 2(a) and (b). The results indicate that the fuzzy trajectory generator is able to successfully replicate the behaviour of the human/therapist interaction. It is apparent from a visual inspection of the two result sets that the system is able to more accurately replicate the compliance along the trajectory axis than the off-axis compliance. The duplicity that appears in the desired compliance dataset can be attributed to the difficulty in maintaining consistent compliance over multiple experiments during the initial therapy sessions. This leads to multiple compliance values for the same force values when using the data from multiple experimental trials. The fuzzy rule base is able to inherently interpolate the appropriate level of compliance on-line, though the inferred compliance might have been more accurate had the system been applied to only a single experimental dataset. This would, however, have greatly reduced the universe of discourse of the generated rule base. A compromise was therefore reached between the robustness of the rule base and the inherent inconsistencies in the recorded human data as discussed in Section 2.1. The comparative compliance for a y-axis linear trajectory is presented in Fig. 3(a) and (b). Once again the compliance rule base is able to successfully replicate the inferred compliant behaviour of the human/robot interaction. Similar to the x-axis linear trajectory results, however, the rule base is better able to replicate the compliance along the position trajectory than perpendicular to the
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Fig. 3. X -axis, Y -axis comparative compliance for the lead mode y-axis linear trajectory. The top profiles represent the measured human lead interaction, while the bottom profiles represent the replicated interaction between the human and robot.
desired motion. Overall, though the rule base is able to infer a reasonable approximation of the desired compliance for the y-axis linear trajectory, the results are not as accurate as the x-axis linear trajectory. This difference is likely a result of the greater degree of discontinuity present in the training data used to generate the y-axis trajectory rule base compared to the x-axis trajectory. This is confirmed through a visual comparison of the upper portions of the figures which show a higher number of ‘‘branches’’ in the y-axis trajectory data. The results of the application of the compliance rule base to a circular trajectory are shown in Fig. 4(a) and (b). Overall, the fuzzy system is able to more accurately reproduce the desired compliance along this trajectory than the linear trajectories. This result is contrary to the observed inconsistencies in the performance of the system during testing. The ‘‘feel’’ of the interaction between the patient and the robot during the execution of the circular trajectory was noticeably more erratic than during the linear trajectory exercises. This behaviour was likely a result of the greater difficulty inherent in generating a representative and consistent training dataset for the relatively more complex circular trajectory. The cyclic nature of the circular trajectory makes it more prone to the conflicting data as a result of the greater likelihood of the same interaction force occurring at different points in the circle, requiring different compliant position commands. In order to alleviate the potential for inconsistent behaviour, one approach could be to divide more complex, or cyclic trajectories into multiple consecutive trajectories with individual rules. This could also provide potential for conditional behaviour profiles dependent on the state of the patient or exercise (e.g. fatigue, emergency protocols, etc.) This approach will be investigated further in future experimental trials. Despite these complications, however, the results indicate that the system is able to maintain and recreate the desired compliance as long as the patient behaviour remains within the known input space. The results for all trajectories that were implemented on the Epson E2L853 manipulator indicate that the fuzzy compliance rule base methodology is able to replicate the interaction between a therapist and patient based on the datasets gathered during the experimental trials. The inconsistencies apparent in several of the results, however, highlight the need for an automated approach to the tuning of the system parameters to ensure that the desired interaction dynamics are reliably maintained during training.
4.2. Preliminary neuro-fuzzy results The critical objective for the application of a learning algorithm to the fuzzy compensator module was to improve the performance of the trajectory generator system on-line without detrimentally affecting the computational efficiency of the overall system. In order to first determine if the integration of the fuzzy compensator into a hybrid neuro-fuzzy framework would successfully improve the accuracy of the overall trajectory generator, the compliance rule base was first tested with a manually tuned compensator. The algorithm was applied to the resultant compliant trajectories as an offline simulation. The output from the compliance rule base for each recorded end-effector force set was combined with the generated neuro-fuzzy compensator output to generate an approximation of how the system would have performed had the learning algorithm been present. An example of a comparison of the compliant positions generated by: (a) the fuzzy compliance rule base; (b) the compliance rule base combined with the fuzzy compensator to form the fuzzy trajectory generator; and (c) the neuro-fuzzy trajectory generator is shown in Fig. 5(a) and (b) when applied to a linear trajectory along the manipulator x-axis. The results clearly show that the error between the generated compliant position and the desired compliant position can be reduced by the incorporation of learning into the fuzzy trajectory generator. As expected, without the neuro-fuzzy scheme, the manually-tuned fuzzy compensator merely adds an additional offset to the output from the compliance rule base as a function of the measured force without any regard for the desired compliant position. The complete hybrid neuro-fuzzy system, however, is able to provide the offset necessary to match the desired compliance regardless of the measured forces at the end-effector. The flat lines that are shown in the response of the compliance rule base and fuzzy compensator are likely a result of either missing data in the compliance rule base, or problems with the manual tuning of the fuzzy compensator. This highlights that potential for the additional learning algorithm to adjust the compliance to match the reference data much better than the manually tuned compensator despite errors in the rule base. Overall, the addition of a learning component into the fuzzy trajectory generator significantly improved the performance of the system offline, providing a firm basis for the implementation of a real-time neurofuzzy trajectory generator.
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Fig. 4. X -axis, Y -axis comparative compliance for the lead mode circular trajectory. The top profiles represent the measured human lead interaction, while the bottom profiles represent the replicated interaction between the human and robot.
Fig. 5. (a) Learning algorithm applied to: X -axis rule base, (b) Y -axis rule base with multiple branches for a linear X -axis trajectory.
4.3. Neuro-fuzzy implementation results Once the potential for the application of a hybrid neuro-fuzzy scheme was established, the neuro-fuzzy trajectory generator was implemented as a real-time module on the Epson E2L853 manipulator shown in Fig. 9. The system was tested using the linear trajectories, which showed the most consistent results in preliminary testing, in order to generate a reliable comparison between the reference data, fuzzy rule base, and complete neurofuzzy trajectory generator. On average, the complete neuro-fuzzy algorithm was able to generate the next compliant trajectory point in 3.3 ms while simultaneously tuning the dynamics of the interaction using the compensator. This was well within the computational bounds outlined for the algorithm. The performance of the neuro-fuzzy trajectory generator while leading the patient along an x-axis trajectory is evaluated in Fig. 6(a) and (b). The results clearly indicate that the ability of the neuro-fuzzy algorithm to better replicate the human–robot interaction, shown in the preliminary testing, was confirmed. According to the results shown in Fig. 6(a), the manually-tuned fuzzy compensator actually had a negative effect on the performance of the system, in some cases driving the magnitude of the compliant position far higher than the desired position. To determine the influence of multiple compliant trends for the same force profiles, or ‘‘branches’’, the experiment was repeated with a refined reference
dataset. The additional results are shown in Fig. 7(a) and (b). Table 1 indicates that the refined reference dataset somewhat negatively affected the performance of the system along both axes, reinforcing the need for a comprehensive reference database outlined in Section 2.1. It should be noted that the additional ‘‘branches’’ were not removed from the compliance rule base, which likely influenced the deviation in the compliance trend between 5 N and 10 N in Fig. 7(a). Though the performance of the system was detrimentally affected by the removal of multiple branches from the compliance rule base, these results indicate that the neuro-fuzzy system is able to adapt a complete rule base to a specific implementation or experiment. The specialization of the system using a general purpose rule base highlights the further potential for development of a library of generic fuzzy rule bases for a variety of diseases or levels of impairment. The results of the implementation of a linear y-axis trajectory are shown in Fig. 8(a) and (b). The y-axis was also implemented using a ‘‘single branch’’ training set, to overcome some conflicts in the training set as outlined in Section 2.1, and to further investigate the potential for generic rule bases with specialized on-line neuro-fuzzy tuning. The performance of the x-axis component of the neuro-fuzzy system is significantly better than both the fuzzy rule base and the manually-tuned system in this case, further confirming the effectiveness of the learning algorithm.
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Fig. 6. (a) X -axis comparative results, (b) Y -axis comparative results using multiple branches for an X -axis linear trajectory.
Fig. 7. (a) X -axis comparative results, (b) Y -axis comparative results using single branches for an X -axis linear trajectory.
Fig. 8. (a) X -axis comparative results, (b) Y -axis comparative results using single branches for a Y -axis linear trajectory.
5. Conclusions The fundamental overarching objective of the proposed approach was to develop a framework for the application of hybrid neuro-fuzzy control systems design to the field of rehabilitation robotics. The human-in-the-loop nature of rehabilitation robotics
requires a fundamentally different approach to the design and development of manipulator control systems that emphasizes the interaction between the patient and the manipulator system. This human-centred approach to design is ideally suited for the application of soft-computing approaches including FCM clustering and neuro-fuzzy control. To this end, several real-time trajectory
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Fig. 9. Implementation of the proposed system on the Epson E2L853.
Table 1 Comparative lead mode mean-square error. Trajectory tested (result set) X axis line multiple branches (X -axis) X axis line multiple branches (Y -axis) X axis line single branches (X -axis) X axis line single branches (Y -axis) Y axis line single branches (X -axis) Y axis line single branches (Y -axis)
Compliance rule base
Fuzzy trajectory generator
Neuro-fuzzy trajectory generator
209.45
630.72
14.49
100.81
952.64
25.81
659.10
N/A
29.58
234.96
N/A
86.85
637.81
83.68
1855.3
121.98
1289.9 100.81
generator modules were developed to evaluate the effectiveness of a neuro-fuzzy approach to the challenges inherent to upper-limb rehabilitation therapy. The primary approach to physical therapy employed in conventional therapy training sessions involves guiding the affected limb along a series of predetermined position profiles. During training, the proposed trajectory generator regulates the interaction force to offer variable levels of compliance as they are led along the specified trajectories by the manipulator servo controller. The critical objective of the architecture was to show that a robotic manipulator is able to replicate the therapist behaviour by providing the prescribed level of compliance during a therapy action. Implementation results showed that the fuzzy trajectory generator was able to successfully replicate the recorded patient/therapist interaction, validating the proposed approach. The fuzzy compensator module was then integrated into a hybrid neuro-fuzzy structure to automate the tuning process on-line. The introduction of learning into the trajectory generator significantly improved the performance of the proposed system. Overall, the neuro-fuzzy trajectory generator fulfilled all expectations providing an efficient and effective framework for the replication of therapy actions on almost any robotic manipulator system. To provide a user-friendly interface for the customization of a wide variety of system parameters, a graphical user interface was developed and implemented. The interface was created as an offline software module for the visual and linguistic specification
of the system behaviour to easily customize the human–robot interaction. In the future, this non-technical approach to the specification of system parameters may prove instrumental in the adoption of the proposed system as a feasible clinical approach to robotic rehabilitation. At the outset of the design and development of the proposed approach to robotic rehabilitation, the overarching objective for the performance of the trajectory generator system was identified as: the flexibility to perform a diverse range of exercises with the adaptability to conform to different patients and a high level of usability to appeal directly to the needs of the therapists. The successful results of the implementation and testing of the proposed real-time neuro-fuzzy trajectory generator attest to the fulfilment of these fundamental objectives. The robotic rehabilitation system presented in this paper may one day contribute to the improvement of the effectiveness of physical therapy in reducing the longterm functional impairment in patients with upper-limb dysfunction due to neurological diseases. References [1] M. Lee, M. Rittenhouse, H.A. Abdullah, Design issues for therapeutic robot systems: results from a survey of physiotherapists, J. Intell. Robot. Syst. 42 (2005) 239–252. [2] P.S. Lum, C.G. Burgar, M. Van der Loos, P.C. Shor, M. Majmundar, R. Yap, MIME robotic device for upper-limb neurorehabilitation in subacute stroke subjects: a follow-up study, J. Rehabil. Res. Dev. 43 (5) (2006) 631–642. [3] L.E. Sucar, R. Ledger, J. Hernández, I. Sánchez, G. Azcárate, Clinical evaluation of a low-cost alternative for stroke rehabilitation, in: IEEE International Conference on Rehabilitation Robotics, June 2009, pp. 863–866. [4] M.S. Ju, C.K. Lin, D.H. Lin, I. Hwang, S.M. Chen, A rehabilitation robot with forceposition hybrid fuzzy controller: hybrid fuzzy control of rehabilitation robot, IEEE Trans. Neural Syst. Rehabil. Eng. 13 (2005) 349–358. [5] R. Riener, Robot-aided rehabilitation of neural function in the upper extremities, in: Operative Neuromodulation, Vol. 97, Springer, Vienna, 2007, pp. 465–471 (1). [6] S.P. Buerger, J.J. Palazzolo, H.I. Krebs, N. Hogan, Rehabilitation robotics: adapting robot behavior to suit patient needs and abilities, in: Proceedings of the American Control Conference, Vol. 4, June–July 2004, pp. 3239–3244. [7] S. Chen, W. Harwin, T. Rahman, The application of discrete-time adaptive impedance control to rehabilitation robot manipulators, in: IEEE International Conference on Robotics and Automation, vol. 1, 1994, pp. 636–642. [8] C. Ellsworth, J. Winters, An innovative system to enhance upper-extremity stroke rehabilitation, in: Proceedings of the Second Joint EMBS/BMES Conference, vol. 3, 2002, pp. 2367–2368. [9] H. Sun, L. Zhang, X. Hu, L. Tian, Experiment study of fuzzy impedance control on horizontal lower limbs rehabilitation robot, in: International Conference on Electronics, Communications and Control, 2011, pp. 2640–2643.
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[10] H. Ho, T. Chen, Hybrid CPM/CAM physiotherapy by use of the slide-mode fuzzy neural network control, in: International Conference on Innovative Computing Information and Control, June 2008, pp. 510–514. [11] M.R. Emami, I.B. Türksen, A.A. Goldenberg, Development of a systematic methodology of fuzzy logic modeling, IEEE Trans. Fuzzy Syst. 6 (3) (1998) 346–361. [12] M. Sugeno, T. Yasukawa, A fuzzy-logic-based approach to qualitative modeling, IEEE Trans. Fuzzy Syst. 1 (1) (1993). [13] F. Nagata, K. Watanabe, K. Izumi, Position-based impedance control using a fuzzy compensator, Knowl.-Based Intell. Inf. Eng. Syst. (1999) 125–128. [14] P. Martin, M.R. Emami, Real-time fuzzy trajectory generation for robotic rehabilitation therapy, in: IEEE International Conference on Rehabilitation Robotics, June 2009, pp. 354–359. [15] D. Surdilovic, Z. Cojbasic, Robust robot compliant motion control using intelligent adaptive impedance approach, in: Proceedings Robotics and Automation, vol. 3, 1999, pp. 2128–2133. [16] J.S.R. Jang, C.T. Sun, Neuro-fuzzy modeling and control, Proc. IEEE 83 (3) (1995) 378–406. [17] L.X. Wang, J.M. Mendel, Back-propagation fuzzy system as nonlinear dynamic system identifiers, in: IEEE International Conference on Fuzzy Systems, March 1992, pp. 1409–1418. [18] P. Martin, Real-time neuro-fuzzy trajectory generation for robotic rehabilitation therapy, University of Toronto, 2010. http://hdl.handle.net/1807/18909.
Peter Martin received a B.Sc. Eng. in Systems and Computer Engineering with a specialization in mechatronics from the University of Guelph in 2007. He then completed a M.A.Sc. in Mechatronics at the University of Toronto Institute for Aerospace Studies in 2009. Since completing his master’s degree, he has gone on to pursue a career in robotics and controls education. His research interests include soft computing, artificial intelligence and rehabilitation robotics.
M. Reza Emami, Ph.D. in robotics and mechatronics from the University of Toronto. He has been the Director of Aerospace Mechatronics group and the Coordinator of Aerospace and Design Laboratories at the University of Toronto Institute for Aerospace Studies since 2001. Prior to joining the academia as a faculty member, he worked in the industry as a project manager for several years. He is a professional engineer, and his research interests centre on the intelligent control design for robotic systems, as well as concurrent engineering of mechatronic systems such as space manipulators.