Intelligent mobile manipulator navigation using hybrid adaptive-fuzzy controller

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Intelligent mobile manipulator navigation using hybrid adaptive-fuzzy controller ✩ Amal Karray∗, Malek Njah, Moez Feki, Mohamed Jallouli Energy Management Laboratory (CEMLab), University of Sfax, Sfax Engineering School, BP 1073, 3038 Sfax, Tunisia

a r t i c l e

i n f o

Article history: Received 14 October 2015 Revised 5 September 2016 Accepted 6 September 2016 Available online xxx Keywords: Intelligent navigation Mobile manipulator Adaptive control Fuzzy control Collision avoidance

a b s t r a c t Intelligent navigation, path following and obstacle avoidance are necessary features for mobile robots to permit the navigation in a dynamic environment and to train intelligent robots. In this context, this paper examines a dynamic feedback control design, firstly to treat the trajectory tracking control of a mobile manipulator with model uncertainties and external disturbances and secondly to avoid collision with obstacles during the navigation to add more functionality to mobile robots. In order to overcome the unknown perturbation effects and uncertainties, we use an adaptive estimator such that the mobile manipulator velocity converges to the desired trajectory. Furthermore, we apply a fuzzy controller to avoid collision. The contribution of this work is that the mobile manipulator executes two acts together which are the tracking of the desired trajectory despite of the uncertainties and disturbances, and the avoiding of obstacles during the trajectory tracking. Simulation results are given to illustrate the efficiency of the proposed adaptive-fuzzy controller. © 2016 Elsevier Ltd. All rights reserved.

1. Introduction The trajectory tracking control of mobile robots has been the item of various research work [1,2]. As a matter of fact, in industrial applications the mobile robot comes in contact with the environment, so that the state of the system is intended to converge to the desired path in spite of the presence of perturbations and model uncertainties [3]. The control of mobile manipulators with uncertainties is important in different applications, unusually when the force of the manipulator should be considered. To manipulate unknown dynamic parameters of mechanical systems and external disturbances, adaptive controls have been investigated to solve these problems. In [4], an adaptive tracking controller using neural network is presented for a mobile robot with kinematic constraints and unknown dynamic model, in addition to that a neural network sliding mode control is used for the tracking control of a two-links robot manipulator with large uncertainties [5]. To guarantee the rejection of disturbances, a generalized proportional integral observer based controller was used for the trajectory tracking tasks in [6]. Moreover, in [7], an adaptive fuzzy sliding mode control is proposed to stabilize the robotic manipulator to a desired trajectory. To evaluate the unknown position of a mobile manipulator with parameter uncertainties, an adaptive hybrid force-position controller is employed in [8].

✩ ∗

Reviews processed and recommended for publication to the Editor-in-Chief by Guest Editor Dr. A. Bhojan. Corresponding author. E-mail address: [email protected] (A. Karray).

http://dx.doi.org/10.1016/j.compeleceng.2016.09.007 0045-7906/© 2016 Elsevier Ltd. All rights reserved.

Please cite this article as: A. Karray et al., Intelligent mobile manipulator navigation using hybrid adaptive-fuzzy controller, Computers and Electrical Engineering (2016), http://dx.doi.org/10.1016/j.compeleceng.2016.09.007

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Fig. 1. Schematic of the mobile manipulator.

Generally the aim of research is to allow autonomous systems, equipped with sensors and actuators, to execute complex tasks in unknown and uncertain environments, especially the mobile manipulator which has been considered as an efficient robot. Franzé used a predictive control scheme for ground vehicles operating in uncertain environments to avoid obstacles [9]. In [10], authors allow the robot to move in an environment with obstacles and to use dynamic programming to find optimal path by minimizing energy and avoiding obstacle collision. In [11] authors deal with the problem of navigation (path-following, wheel slippage and skid) and design a controller based on the proposed side friction model and skid check condition. Fangquin [12] proposed a fuzzy controller to drive a vehicle with obstacle avoidance. This type of controller is also used in the work of M. Njah and M. Jallouli [13] for electric wheelchair navigation in an indoor environment containing obstacles. There is a huge motivation for research in assistance technology to permit more autonomy [14], in this context Fredriksson outfitted the MICA wheelchair with camera and laser scanner in order to follow the desired path and to facilitate its navigation [15]. The difference between this work and the work of other authors [16–18] consists not only in avoiding collision with obstacles and join the target point, but our goal is also, during its motion the mobile manipulator must achieve convergence to the proposed trajectory in presence of the uncertainties of dynamic parameters and external disturbances. In this paper we try to solve the problem of uncertainties in system model, external disturbances and avoiding collision during the navigation of the mobile manipulator. Tackling cited problems allows to the mobile robot to be autonomous and let to meet the performance level required by applications in order to achieve fast, precise and quality production. Our paper is organized as follows. In Section 2, the system model is presented. Then we explain the global control system used to converge to the desired trajectory without any collision in Section 3. In the fourth section, the torque controller design is presented. Section 5 is devoted to the fuzzy controller synthesis. In Section 6, simulation results are given to show the efficiency of the proposed controller. And finally, Section 7 contains the concluding remarks. 2. Model of a non holonomic mobile manipulator The mobile manipulator shown in Fig 1 is composed of two subsystems which are a mobile platform and an end effector (see [19]). The robot parameters are presented by a vector q:



q = xOb

yOb

φ

θr

θl

θ1

θ2

T

(1)

The dynamic model of the studied system [20] subject to non holonomic constraints is given by the following equation (see [19]):

H υ˙ + C υ + g = τ¯ + τ¯d

(2)

where H = C= g= τ¯ = and τ¯d = vector time function υ (t ) ∈ Rn−m such that, for all t we have : ST MS,

ST MS˙ ,

ST V,

ST E τ

ST E τd .

S(q) is a

Rn×(n−m )

q˙ = S(q )υ (t )

full rank matrix and v(t) is a velocity

(3)

The following assumptions are pertaining to many systems of practical interest. Assumption 1. System (2) is linearly parameterizable (LP), i.e.,

H (q )υ˙ + C (q, q˙ )υ + g(q, q˙ ) = Y (q, q˙ , υ , υ˙ )

(4)

Please cite this article as: A. Karray et al., Intelligent mobile manipulator navigation using hybrid adaptive-fuzzy controller, Computers and Electrical Engineering (2016), http://dx.doi.org/10.1016/j.compeleceng.2016.09.007

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3

Fig. 2. Block diagram of the designed control.

where  is a ρ dimensional vector of unknown parameters and Y ∈ R(n−m )×ρ is a matrix of known functions. Assumption 2. The external disturbance τ¯d = F1 τs with τ s satisfies the dynamics τ˙ s = F2 τs in which F2 and F1 are known matrices. Moreover, assume that there exists a known positive definite matrix P such that P F2 + F2T P ≤ 0.

3. Global control system of the mobile manipulator The global control system shown in Fig 2 explains how the mobile manipulator follows the desired trajectory in the presence of a fixed obstacle. So that, in the absence of obstacle an adaptive controller is used to estimate the parameters of dynamic model, to eliminate the effects of external disturbances and to allow the mobile robot to follow the desired path (see [19]). The designed control is based on the feedback of information from the displacement and distance sensors. The current position is determined using the robot’s model, and according to this position we can determine the distance between the robot and the obstacle. If the distances dl and dr are higher than the safety distance (absence of obstacle), the digital switcher selects the adaptive controller for the desired trajectory tracking, therefore, the speeds of the base (υl and υr ) and the speeds of the arm (υ1 and υ2 ) will be generated. If dr and dl are less than the safety distance (presence of obstacle), the control algorithm generates a virtual target point located on the desired path. To move away from the obstacle we used two fuzzy controllers for obstacle avoidance and joining target, in this case only the speeds υl and υr will be calculated and the arm stays fixed. When the virtual target is reached the adaptive controller is activated again to achieve the rest of the desired trajectory.

4. Adaptive control of the mobile manipulator We consider the following system model:

q˙ = Sυ

(5)

υ˙ = H −1 [τ¯ + τ¯d − C υ − g]

(6)

The aim of this section was to get a control law υ ∗ such that all state variables of the Eq. (5) satisfy the desired output position. Please cite this article as: A. Karray et al., Intelligent mobile manipulator navigation using hybrid adaptive-fuzzy controller, Computers and Electrical Engineering (2016), http://dx.doi.org/10.1016/j.compeleceng.2016.09.007

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Fig. 3. Membership function of the left distance.

4.1. The velocity control By defining y = h(q ) as the output of the system, we use a vector υ ∗ to achieve the output tracking of the desired position and velocity given by the following form:

υ ∗ = −1 (y˙ d + Kp ey )

(7)

where  is the decoupling matrix and ey represents the error between y and

yd

(see [19]).

4.2. The torque controller Previously, the velocity controller (7) denoted by υ ∗ was suggested to achieve the tracking problem y(t) → yd (t), subsequently, the system (6) is considered to compute the torque controller. So that, the proposed controller is given in the following form ([19]):

ˆ − F1 τˆs − K p1 (υ − υ ∗ ) τ¯ = Y (q, q˙ , υ ∗ , υ˙ ∗ )

(8)

υ˙ = H −1 [τ¯ + τ¯d − C υ − g]

(9)

ˆ˙ = −( T )−1Y T (q, q˙ , υ ∗ , υ˙ ∗ )(υ − υ ∗ ) 

(10)

τˆ˙ s = F2 τˆs + P−1 F1T (υ − υ ∗ )

(11)

where Y ∈ R(n−m )×ρ is a matrix of known functions and



 = mb

mw

Ib

Iw

m1

m2

I1

I2

T

 is the vector of unknown parameters.

with mb , mw , m1 , m2 , Ib , Iw , I1 and I2 are respectively the masses and the inertia of the base, the wheels and the two links of the manipulator. F2 and F1 are known matrices, P is a known positive definite matrix and Kp1 a positive definite matrix. 5. Fuzzy controller synthesis The avoidance of obstacle is an essential behavior for mobile robots because it facilitates their navigation in a dynamic environment and gives them more autonomy during their motions [21,22]. Fuzzy logic control is one of the efficient methods that guarantees this basic behavior. In this section, we used firstly a fuzzy controller to keep away from collision with obstacle located on the desired path, and secondly to join a virtual target point in order to permit the return of the mobile manipulator to the desired trajectory where the adaptive tracking control will be activated again to continue the navigation to the end. The type of inference mechanism for the used fuzzy controller is Takagi-Sugeno of the order 0. •

Fuzzy controller for obstacle avoidance: We supposed that the base of the mobile manipulator is equipped with ultrasonic sensors and two encoders. The input variables of the fuzzy controller for obstacle avoidance are the left and the right distance generated by the sensors and the output variables are the left and the right velocity of the left and right wheels. Figs. 3 and 4 show the triangular membership functions used for the fuzzy quantification of the left distance dl and right distance dr . The fuzzy inference tables of velocity of the left and right wheels are manually constructed following several simulations (Table 1) where υr and υl are respectively the right and the left velocity, SD: Short Distance, ID: Intermediate Distance, TD: Tall Distance, LV: Low Velocity, MV: Medium Velocity, HV: High Velocity. Fig. 5 shows the output membership functions for the left and right wheel velocities for the two different fuzzy controllers (for obstacle avoidance and joining the virtual target).

Please cite this article as: A. Karray et al., Intelligent mobile manipulator navigation using hybrid adaptive-fuzzy controller, Computers and Electrical Engineering (2016), http://dx.doi.org/10.1016/j.compeleceng.2016.09.007

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5

Fig. 4. Membership function of the right distance. Table 1 Fuzzy inference table of the right and left velocity. dl

SD

SD

SD

ID

ID

ID

TD

TD

TD

dr

SD LV HV

ID LV HV

TD LV HV

SD HV LV

ID MV HV

TD MV HV

SD HV LV

ID HV MV

TD MV HV

υr υl

Table 2 Linguistic inference table for the left velocity .

υl

DT

ϕ

SDT MDT LDT

NBA

NMA

ZA

PMA

PBA

HV HV HV

MV MV HV

LV MV HV

LV LV LV

LV LV LV

Table 3 Linguistic inference table for the right velocity.

υr

DT

ϕ

SDT MDT LDT

NBA

NMA

ZA

PMA

PBA

LV LV LV

LV LV LV

LV MV HV

MV MV HV

HV HV HV

where NBA: Negative Big Angle, NMA: Negative Middle Angle, ZA: Zero angle, PMA: Positive Middle Angle, PBA: Positive Big Angle, are the fuzzy subsets given for the angle ϕ .

Fig. 5. Output membership Functions for the left and right wheel velocities.

•

Fuzzy controller to joint virtual target This controller has two inputs which are the distance DT and the angle ϕ , where DT is the distance between actual position and virtual target point and ϕ is the angle between the mobile manipulator orientation and the target. The output variables are the left and the right velocity of wheels (Tables 2 and 3). The triangular membership functions of the distance (DT) and angle (ϕ ) are described by Figs. 6 and 7.

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Fig. 6. Membership function of the distance DT.

Fig. 7. Membership function of the angle ϕ . Table 4 Parameters of the mobile manipulator. Parameters (unit)

Platform

Manipulator

Dimension (m)

b = 0.182 r = 0.0508 La = 0.1

L1 = 0.514 L2 = 0.362 Lcm1 = 0.252 Lcm2 = 0.243

Mass (kg)

mb = 17.25 mw = 0.159

m1 = 2.56 m2 = 1.07

inertia (kg.m2 )

Ib = 0.297 Iw = 0.0 0 02

I1 = 0.148 I2 = 0.0228

The developed fuzzy controller is composed by two controllers: the first for obstacle avoidance and the second is used to achieve a virtual target point placed on the path to follow. When the obstacle avoidance task is completed the adaptive controller will be activated to follow the rest of desired trajectory. In the next section we will detail the simulation results obtained by the navigation controller.

6. Simulation results We present simulation results of the mobile manipulator under the action of the proposed controller. The robot parameters are stated in Table (4). To show the robustness of the proposed controller, we suggest here to apply it to the mobile system that needs to track a desired path in the presence of an obstacle. Two different trajectories have been planned, the first is a circular trajectory Please cite this article as: A. Karray et al., Intelligent mobile manipulator navigation using hybrid adaptive-fuzzy controller, Computers and Electrical Engineering (2016), http://dx.doi.org/10.1016/j.compeleceng.2016.09.007

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Desired path for the base

3.5 3

7

Obstacle

virtual target point

Desired path for the manipulator

2.5

Y(m)

2 1.5 1 0.5 0

trajectory achieved by the base

trajectory achieved by the manipulator

−0.5 −1 −3

−2

−1

0 X(m)

1

2

3

Fig. 8. Mobile Manipulator tracking the circular trajectory.

Fig. 9. Required speeds to achieve the circular trajectory tracking.

for both the end effector and the base of the robot, however, the second desired trajectory is rectilinear for the base and sinusoidal for the end effector. •

1st trajectory (circular):

•

2nd trajectory (sinusoidal):

⎧ d x = 1.2 sin(0.1π t ) ⎪ ⎨ ed ye = 1.6 − 1.2 cos(0.1π t ) ⎪xdb = 1.6 sin(0.1π t ) ⎩ ydb = 1.6 − 1.6 cos(0.1π t ) ⎧ d ⎪ ⎨xed = 0.2t + 0.3

ye = 2 + 0.25 sin(0.2π t )

d ⎪ ⎩xed = 0.2t + 0.3

ye = 1.5

Figs. 8 and 11 demonstrate the motion trajectory of the mobile manipulator when the robotic arm and the base are moving along the desired trajectories in the presence of a fixed obstacle. In the first simulation (Fig. 8), the starting position of the mobile manipulator is considered (x = 0, y = 0, ϕ = 0 ). In the beginning, the mobile robot navigates along the circular trajectory using the adaptive tracking controller. Once the obstacle is detected, the first fuzzy controller starts to avoid the collision with this obstacle until the distance between the base and the obstacle will be higher than 0.5m, at this moment the second fuzzy controller generates to the mobile robot a virtual target point placed on the desired path. If the obstacle avoidance is achieved and the base joined the virtual target, the adaptive controller activates again to finish the Please cite this article as: A. Karray et al., Intelligent mobile manipulator navigation using hybrid adaptive-fuzzy controller, Computers and Electrical Engineering (2016), http://dx.doi.org/10.1016/j.compeleceng.2016.09.007

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Fig. 10. Required torques to achieve the circular trajectory tracking.

Fig. 11. Mobile Manipulator tracking the sinusoidal trajectory.

Fig. 12. Required speeds to achieve the sinusoidal trajectory tracking.

desired trajectory. For the simulation of sinusoidal path (Fig. 11) the starting position of the mobile manipulator is taken ( x = 0, y = 1.5, ϕ = 0 ). We can see that the actual trajectories are almost superposed on the desired trajectories and the distance between the mobile robot and the obstacle is acceptable for no collision. So that, the objective is accomplished and the good tracking performance demonstrates the effectiveness of the proposed controller. Figs. 9 and 12 depict the right and the left speeds of the wheels, vR and vL respectively, during the navigation of the two desired trajectories. The sampling period is taken 0.002. Figs. 10 and 13 show the torques required by the robot to achieve different desired paths (τ R : right torque and τ L : left torque). In these figures we see three phases, the first when the robot follows the desired path, the second is the period of obstacle avoidance, and in the third phase the robot continues the tracking of the desired trajectory. If we want to discuss the general case we must take into account two necessary data which are the equations for the different parts of the desired trajectory and the dimensions of obstacles when the environment is known. When the robot detects an obstacle, firstly, the navigation algorithm creates a target point which is the intersection between the desired Please cite this article as: A. Karray et al., Intelligent mobile manipulator navigation using hybrid adaptive-fuzzy controller, Computers and Electrical Engineering (2016), http://dx.doi.org/10.1016/j.compeleceng.2016.09.007

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Fig. 13. Required torques to achieve the sinusoidal trajectory tracking.

path and a virtual straight, named safety distance or minimum distance between the mobile manipulator and the obstacle. Secondly, the fuzzy controller allows to avoid many obstacles and to reach the virtual target point. The obstacle avoidance in the general case is discussed in a previous publication [13], in which the robot can achieve a target point and avoid the collision with several obstacles, knowing that the equations of the desired path are given at the beginning. We note that the size of the obstacle does not influence on the functioning of the proposed method but there is a necessary condition is that the obstacle should not be located on the target point, if it is the case the robot will not stop and it may lose the path. In addition to that, we used a rectangular obstacle and the changing of the obstacle’s type requires a change in the calculation of the virtual target. However, when the browsing environment is unknown, it is necessary to add mapping methods [23–25] to determine the sides of the obstacles which subsequently allows creating a virtual target point in order to reach the desired trajectory. 7. Conclusion In this paper, we have attempted to solve the tracking problem of non holonomic mobile manipulator with model uncertainties and external disturbances in the presence of an obstacle located on the desired path. We presented a block diagram to describe the designed control. On the first hand, we have proposed an adaptive controller to minimize the effect of perturbations and model uncertainties in order to allow the mobile robot to track the desired trajectory. On the second hand, we used a fuzzy logic control to avoid the collision with the obstacle: firstly a fuzzy controller was used to keep the robot away from collision with the obstacle located on the desired path and secondly another fuzzy controller was employed to join a virtual target point in order to permit the return of the mobile manipulator to the desired trajectory, after that the adaptive tracking controller is activated again to continue the navigation to the end of the desired path. Using our approach, the mobile manipulator achieved to follow two different desired paths, the first is a circular trajectory for both the end effector and the base of the robot and the second desired trajectory is rectilinear for the base and sinusoidal for the end effector. Both paths were tracked without any collision which demonstrates the effectiveness of the proposed controller. References [1] Akli I, Bouzouia B, Achour N. Motion analysis of a mobile manipulator executing pick-up tasks. Comput Electr Eng 2015;43:269–75. [2] Hentout A, Messous MA, Bouzouia B. Fault-tolerant multi-agent control architecture for autonomous mobile manipulators: simulation results. Comput Electr Eng 2015;43:238–56. [3] F G Rossomando CS, Carelli R. Sliding mode neuro adaptive control in trajectory tracking for mobile robots. J Intell Rob Syst 2014;74:931–44. doi:10. 1007/s10846- 013- 9843- 5. [4] Petre E. An adaptive tracking controller for a mobile robot using neural networks. J Control Eng Appl Inf 2002;4(3):54–66. doi:10.1016/j.neucom.2011. 06.035. [5] Sefriti S, Boumhidiand J, Naoual R, Boumhidi I. Adaptive neural network sliding mode control for electrically driven robot manipulators. J Control Eng Appl Inf 2012;14(4):17–26. [6] Sira-Ramirez H, Lopez-Uribe C, Velasco-Villa M. Linear observer-based active disturbance rejection control of the omnidirectional mobile robot. Asian J Control 2013;15(1):51–63. [7] Lu X, Schwartz-Howard M. A revised adaptive fuzzy sliding mode controller for robotic manipulators. Int J Model Ident Control 2008:127–33. [8] Nganga-Kouya D, Saad M, Okou AF. A novel adaptive hybrid force-position control of a robotic manipulator. Int J Model Ident Control 2011;13:97–107. [9] Franz G, Lucia W. An obstacle avoidance model predictive control scheme for mobile robots subject to nonholonomic constraints: a sum of squares approach. J Franklin Inst 2015. [10] Roozegar M, Mahjoob M, Jahromi M. Dp-based path planning of a spherical mobile robot in an environment with obstacles. J Franklin Inst 2014;351(10):4923–38. [11] Khan KB, Iqbal, Zielinska T. Longitudinal and lateral slip control of auto-nomous wheeled mobile robot for trajectory tracking. Front Inf Technol Electr Eng 2015;16:166–72. [12] Fangqina L., Feng. M.. Fuzzy control of automatic automobile obstacle avoiding. IEEE Int Conf Intell Rob Syst :282–285.

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Amal Karray received the B.S and M.S degrees in Electrical Engineering from Engineering School of Sfax of Sfax University in Tunisia on 2008 and 2009, respectively. She obtained a Ph.D. degree the Engineering School of Sfax in 2014. Her research interests include control theory and its application to control robotic manipulators. Malek Njah received the B.S and M.S. degrees in Electrical Engineering from Engineering School of Sfax of Sfax University in Tunisia on 2006 and 2008, respectively. He obtained Ph.D. degree in electrical engineering from National School of Engineers of Sfax, in 2014. He is currently an assistant professor in ISIMG. His main research interests mobiles robotics, fuzzy control, localization and intelligent control system design applied for mobile robots. Moez Feki received his B.Sc. and an M.Sc. in Electrical and Electronics Engineering from Bilkent University, Turkey in 1995 and 1997. Next, he obtained a Ph.D. degree in Applied Mathematics from Université de Metz France in 2001. He is actually a Professor at the Ecole Supérieure des Science et Technologie de Hammam Sousse-Tunisia and carrying his research activities in the Research group CEMLab of the Engineering School of Sfax. Mohamed Jallouli received the D.E.A degree from University of Valencienne, France, in 1986 in Automatics and the Ph.D. from University Paris XII, France, in 1991, in Robotics engineering. In 1987, he joined French University in education activities. In April 1991, he joined the Tunisian University where he held different positions involved in both education and research activities. He is currently a professor of electric and computer engineering at ISSIG. His current interests include the implementation of intelligent methods in robotic and vision system.

Please cite this article as: A. Karray et al., Intelligent mobile manipulator navigation using hybrid adaptive-fuzzy controller, Computers and Electrical Engineering (2016), http://dx.doi.org/10.1016/j.compeleceng.2016.09.007