Mechatronic design of strongly nonlinear systems on a basis of three wheeled mobile platform

Mechanical Systems and Signal Processing 52-53 (2015) 700–721

Contents lists available at ScienceDirect

Mechanical Systems and Signal Processing journal homepage: www.elsevier.com/locate/ymssp

Review

Mechatronic design of strongly nonlinear systems on a basis of three wheeled mobile platform Krzysztof J. Kaliński 1, Cezary Buchholz n Gdansk University of Technology, Faculty of Mechanical Engineering, ul. G. Narutowicza 11/12, 80-233 Gdańsk, Poland

a r t i c l e in f o

abstract

Article history: Received 15 April 2014 Received in revised form 5 June 2014 Accepted 10 June 2014 Available online 20 August 2014

Remarkable grow in demand both of mobile platform operability performance and reduction of project leading time development encourage to apply modern algorithms and reliable engineering tools for the design process. The paper discusses the mechatronic design applied for the surveillance system based on the energy performance index algorithm. The exploited mechatronic techniques i.e. virtual prototyping, Hardware-In-the-Loop Simulation (HILS) and rapid prototyping on target object, supported by the LabVIEW, allowed for integration of the developed control system and strongly nonlinear mobile platform, built simultaneously for the research purposes. Mathematical complexity of on-line algorithm and sophisticated model description affected all the process design. In order to boost mobile platform performance and handle its real time motion surveillance the authors implemented the Real Time controller. The presented design approach allowed authors to achieve the highest level of a mobile platform performance and increased probability of the final concept success. & 2014 Elsevier Ltd. All rights reserved.

Keywords: Mechatronic design Mobile platform Nonlinear systems Energy performance index Mechatronic techniques LabVIEW

Contents 1. 2.

3.

4. 5.

n

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 701 Design approach of real time surveillance system for the platform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 702 2.1. Design methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 702 2.2. Algorithm improvement. Correction velocities. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 705 2.3. Mobile platform improvement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 709 Mechatronic approach in the design of three-wheeled mobile platform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 713 3.1. Virtual prototyping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 713 3.2. Hardware in the loop simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 715 3.3. Rapid prototyping on target object. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 717 Mechatronic design. Enhanced performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 719 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 720 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 720

Corresponding author. Tel.: þ47 46429097; fax: þ 48 58 347 21 51. E-mail addresses: [email protected] (K.J. Kaliński), [email protected] (C. Buchholz). 1 Tel.: þ 48 58 347 14 96.

http://dx.doi.org/10.1016/j.ymssp.2014.06.016 0888-3270/& 2014 Elsevier Ltd. All rights reserved.

K.J. Kaliński, C. Buchholz / Mechanical Systems and Signal Processing 52-53 (2015) 700–721

701

1. Introduction Mobile robots, operating in rough surroundings, like terrain or extraterrestrial planets, seabed and during demanding enterprises are inherently multidisciplinary [1–4]. Designers often employ a subsystem-partitioning approach for their analysis and synthesis [5,6] to develop robot system not only withstanding risky operations while guarantying the highest possible performance. But also precision, continuous motion, high operability and low power consumption are the core and crucial design factors. Effective power management system with real time control algorithms leads to reduction of overall energy consumption, increases mobility performance and distributes wheels' speeds and torques in an optimal way [7,8]. Increasing computation ability of processors, parallel processing architectures, FPGA (Field Programmable Gate Array), hybrid processor deployments and accurate sensors provide the opportunity for improvement of control performance. They also reduce faults of tolerance and simplify implementation of complex hardware and software design. Significant advantages while utilizing embedded real time systems together with sufficient computing capabilities allow implementing algorithms where online model updating possibilities are incorporated. On-line algorithms applied to surveillance of the sophisticated nonlinear dynamic model (in this case, mobile platform) result remarkable (against PID controller [9]) increase of control motion performance, achieving successfully design constrains. However, significant increase of control motion efficiency requires often undertaking optimisation process within applied processors (real time and/or FPGA) [10,11]. For this reason, highest (optimal) control system performance is achievable predominantly by choice of the Δt integration step. Reduction of this step allows decreasing time when mobile platform is out of surveillance. The discussed strategy affects for control command, which can be generated more frequently without position deviation. Three-wheeled mobile platform structure is nonlinear dynamic system, in which matrices M (of inertia) and L (of damping) are generated for time instant t, instead of time tþΔt, as it happens for control command u. Also in this case, the reduction of integration step Δt has a positive effect for surveillance efficiency of the mobile platform. However, step Δt is a consumable factor of controller performance (CPU, memory) and influences considerably real time implementation. Therefore, due to the limited capacity of applied control unit, architecture of system has to be optimized, and the length of Δt has to be balanced. On the other hand, in order to achieve robust mobile platform allowing facing various missions, optimal and careful mechanical design strategies should be carried out. Weight limitation, strength and design constrains of the robot contribute mainly in this part of study. Although close interaction between dependent subsystems which are developed as a whole common system, still considerably large number of the design variables influence on complexity of the design methodology and multidisciplinary objective functions, have to be optimised. For the current study several substantial aspects of the design had to be consulted and resolved. Even if, it can be mentioned about resolving issues related with avoidance of the wheels slip while the mobile platform is moving, proper weight balance assures the expected speed conveyance and propulsion system, which had to be based on the difference system. In the traditional, serial attitude towards the design, when an embedded system to control mobile platform is developed, a wide range of experts, such as hardware digital designers, hardware analogue designers, software developers, are required. Additionally, there should be mechanical engineers acquiring expertise in scope of machine control domain. In this design approach, first the conceptual development, and subsequently implied design methodology will be carried out. After the main concept solution is acquired, and then the tasks will be decomposed into mechanics, electronics and software (control) part, which will be further proceeded concurrently without reciprocal interactions. Finally each part of the performed design will be assembled, integrated and validated. Existing feedbacks in the loop design process will eliminate in interactive way the system misstatements [12–14]. Within the software design, there are many steps and techniques for developing a real-time control application to execute the applied on-line algorithm. There subsist several different software platforms and hardware architectures to implement the control strategy and develop all aspects of the design. In addition, several attributes to accommodate the design requirements have to be defined. Contemporary software development requires expertise for low-level tasks, such as real-time, FPGA, device driver development, control algorithm development, system optimisation, drivers, networking and so on. As can be seen, such serial approach requires a large team of dedicated specialists for a complex system design. A substitution option to the traditional, serial design is to implement mechatronic attitude towards the system development. For the present design approach it should first follow the functional modelling to perform the conceptual and detailed engineering design (electronics, mechanics and software). Herein, discipline coexistence and interaction are prevailing successful design factors. Software design is normally the top development cost of solution. However, deployment of the embedded controller reduces the needed number of software developers, which helps to cover lower development costs and creates a more efficient design process. Smaller teams can iterate on designs more quickly and get final prototypes and products developed much faster. Moreover, the appropriate simulation to verify the feasibility of the whole design is performed, and at final integration of all subsystems (controller and mechanics) into a complete product, is done [15–20]. Uppermost outcome for mechatronic approach is achievable while the combined development system is applied. In following research, National Instruments (NI) provides LabVIEW, the graphical system design platform, which includes off-the-shelf hardware with the fully integrated graphical software. The authors, using graphical system design tools, had proven that they could use off-the-shelf tools to develop strongly nonlinear mechatronic system. Having system level

702

K.J. Kaliński, C. Buchholz / Mechanical Systems and Signal Processing 52-53 (2015) 700–721

software tools for programming hardware with built-in processors, FPGAs, and I/O, smaller teams can accomplish a task that traditionally would have required twice as many people. The result is decrease in hardware and software development expenses that typically are the top expenses for an embedded design. On average, NI customers have reported that they can get to market 50 per cent faster using 20 per cent fewer engineering resources with off-the-shelf graphical system design tools [21]. The applications that fit NI tools the best are custom monitoring and control applications that involve specialized analogue and digital I/O as well as advanced control that require custom signal processing or tailored and exquisite control algorithms. Considerable beneficial of applying mechatronic design can be Embraer Company, which applied mechatronic techniques to develop Legacy 500 Iron Bird Jet. To perform electronic systems integration testing, Embraer developed an iron-bird simulator in which the complete electrical system of the aircraft is connected to simulation of the rest of the plane in order to perform the simulated flight tests which accurately exercise the electronics and the software. The Embraer's attitude significantly reduced development efforts. Get up and run of jet was decreased by 12 months [22]. Other example comes from the Process Automation Company, where crucial cost reduction was obtained by utilizing the HILS technique. Their customer asked them to implement a new control system to retrofit their aircraft arrestor system. The new embedded control device is the part of a hydraulic control system, which adjusts dynamically the resistance of a cable that is caught by the tail hook of the aircraft when landing. In order to test these systems, they used test facility where they could accelerate a mass down a run-way to replicate the effect of a plane landing. It costs $50,000 per day to use the test facility and the last time these control systems were updated required 20 days of the field testing. To reduce the number of real system level test necessary to validate the new controllers, Process Automation implemented a HILS test system, which allowed them to begin identifying issues before they went to the airfield. Thanks to the deployed technique, it was possible to reduce total testing cost by more than $740,000 [23]. This paper discusses the mechatronic development process applied during the design of the surveillance system based on energy performance index for the mobile platform i.e. built for the research purposes. Exploited mechatronic techniques (i.e. Virtual Prototyping, Hardware-In-the-Loop Simulations and Rapid Prototyping on target object) were supported by the LabVIEW environment [24–26]. The latter is applied for control of system software and mobile robot development. In the presented study, the researchers focused mainly their attention on ensuring the appropriate algorithm execution conditions. Fulfilment of real-time during control signal generation was essential due to final successful integration surveillance system of the mobile platform. Required output from the presented research and also contemporary modern design process enforces multidisciplinary approach in understanding the effects of dynamic model of the platform and usage of comprehensive mechatronic development environment giving the possibility to prototype, design, simulate and integrate with the dedicated hardware. Developed and tailored control algorithm was deployed into real-time embedded controller cRIO-9076 powered also by LabVIEW and finally integrated with mobile platform (built for experimental purposes). The presented research object allowed authors to verify responses (for optimal control commands generated by controller) of the mobile platform while moving on three different trajectories (here the “sine” trajectory is presented). This paper is organized as follows. Nonlinear dynamic mobile platform model and control algorithm are treated in Section 2. In addition mechatronic approach and research challenges are also discoursed. Section 3 presents both mechatronic techniques and optimisation process applied during the research. Partial experimental results are depicted in Section 4. Conclusions are given in Section 5. 2. Design approach of real time surveillance system for the platform Development approach of mechatronic system results separates description of controller (embedded), mechanical and software subsystems, but the principles of common interactions should be incorporated. Mobile platform is strongly nonlinear system, which changes significantly its dynamics while conveying. This also amends control system conditions respectively, which are reflected in the algorithm formula architecture. For succeeding the project, the authors implemented the adaptable to mobile platform dynamics algorithm, which required involving the on-line feature update based real-time controller. 2.1. Design methodology Design of mechatronic system affects separate description of controller (embedded system with control software) and mechanic subsystems, but under the principle of common interaction. For these subsystems, it is imperative to deliver on schedule to prevent delaying overall project development. On the other hand, market requires delivering increasingly more and more complex and innovative systems. At the same time, product quality continues to be a substantial issue. It is highly expected to control any kind of system or process, even though the dynamics of the above is strongly nonlinear. The accuracy and robustness have to be met or exceeded with fewer system prototypes (lower costs) while maintaining enough flexibility to adapt to any last-minute requirement changes. Applying traditional development methods, the design was performed early in the development process, but implementation of the embedded control systems and system validation had to wait until late in the process.

K.J. Kaliński, C. Buchholz / Mechanical Systems and Signal Processing 52-53 (2015) 700–721

703

Fig. 1. General overview of mechatronic techniques applied during the research.

This delay was directly tied to the availability of production prototypes for testing the control software, a critical step in revealing errors in the embedded software behaviour. Because the initial integration of systems (controller with mechanical subsystem) occurred so late in the development cycle, the discovery of errors and final debugging often resulted in production delays, as well as additional expenses related to control system updates and mechanical modifications. Often, due to serious changes which seemingly had to be introduced forced that the whole concept had to be sacrificed [27–30]. Nowadays, mechatronics as a new approach and more often the LabVIEW as tool for the development of systems are applied. Real-time environment (software and hardware) is now deployed throughout the design cycle for system model description, simulation (virtual simulation), system developing and prototyping (HILS and Rapid prototyping), performing tests and implementations earlier in the development cycle, so the potential bugs can be identified faster and reduce considerably inadvisable risk [31]. Moreover, it is not without significance for the development process and successful results of the design that LabVIEW can be easily coupled with real-time hardware (here cRIO), supplementing traditional off-line simulation with real-world testing [32,33]. In this paper the authors demonstrate (Fig. 1) mechatronic and open design platform (LabVIEW supported in early stage by Maple), particularly suitable for research purposes, which has brought advantages from the early stage of mobile platform design to the successful validation of the physical prototype. As it was highlighted previously, the authors utilized three mechatronic techniques: Virtual prototyping, Hardware-In-the-Loop Simulations and Rapid Prototyping on the target object. The design phase of mobile platform begins with elaboration of mathematical model and analysis of the system requirements. Nonlinear differential equations are solved by supportive software Maple [34,35] so the solutions can be implemented into LabVIEW, achieving finally virtual model of mobile platform. Further, by the software implementation, the authors accomplished the design of virtual controller. Then, prior to moving to developing the system design, first mechatronic technique (i.e. virtual prototyping) for system evaluation was adopted. The technique allows creating a testable prototype without the need for real hardware, which provides a documented method for verifying and validating the design against requirements. An emulated model of the system also provides a possibility that can be iterated quickly during the transition from project specifications to design stages. Shorter iterations earlier in the design process provide also reduced the cost and time. Real-time computing is essential component of a surveillance system for nonlinear mobile platform. It allows implementing on-line control algorithm and generating timely reaction events while the platform moves (in this case dynamics depends significantly on time, position and velocity). Furthermore real-time computing concept is also applied in real-time tests, to preserve the dynamic fidelity of the test by integrating the physical and numerical components in reality.

704

K.J. Kaliński, C. Buchholz / Mechanical Systems and Signal Processing 52-53 (2015) 700–721

Such design attitude implemented for development of mechatronic strategy brings expected proceeds. The system, especially nonlinear, can be improved, and compatibility with design assumption is corroborated before the prototype is build. The authors utilized two applicable real-time mechatronic techniques development for testing nonlinear design, i.e. Hardware-In-the-Loop Simulations (HILS) and rapid prototyping on the target object. For making an appropriate test, the LabVIEW, having the real-time module, was included. In the HILS testing, the emulated mobile platform was simulated in real-time environment without the need of the physical object's existence. Virtual platform moves in accordance to real-time signals generated by standalone embedded controller (cRIO). Responses of nonlinear model dynamics were exploited for controller development and platform parameters optimisation against the Virtual Prototyping technique results. The HILS technique reduced seemingly developing time and failure cost. For the authors, this testing phase was essential to workout architecture of the system design and complete functionality of the controller. System integration, when the controller is incorporated into nonlinear target object yields several opportunities finalizing the development process. With rapid prototyping, the target control code generation step command is passing directly from graphical system design (i.e. LabVIEW), usually in the form of a prepared software specification, to the embedded controller. LabVIEW provides possibilities to automatically generate both prototype and production code directly from the control design models. The design model serves as the specification and design for the generated and compiled code, so that all design changes automatically flow through to final embedded implementation. This process results in significant time and cost savings due to the inherent reproducibility and testability of the generated code, on-line compilation and communication errors exclusion. Finally, as the mobile platform chassis is combined with controller and control software implemented, so the system design can be validated to ensure that the original design requirements are met. Usually, during the first test, appropriate parameters of the controller have to be finely tuned in this phase to meet original design requirements. Although the rapid prototyping technique process can be time consuming while all the drawbacks should be expelled, it offers several opportunities to reduce the amount of tests that will be required prior to the release of the final system. It should be recalled about software recurrence likewise, fast process debugging together with on-line compiling.

Fig. 2. Mechatronic design process diagram.

K.J. Kaliński, C. Buchholz / Mechanical Systems and Signal Processing 52-53 (2015) 700–721

705

Table 1 The scope of optimisation for each mechatronic design technique. Nr Optimisation

Goal function

1

Energy of control system

2

Algorithm execution

Error in the movement of the Length of the integration step platform relative to the desired trajectory Usage of the CPU real-time controller Premises of algorithm execution: CPU/FPGA and memory

3

Algorithm

4

Computation model of mobile platform Systems integration

5

Decision variable

Generating control signal in accordance with the applied monitoring strategy Movement of mobile platform without slips

Length of the programme code compilation process, the size of the output file; compilation errors Geometric and mechanical parameters of the proposed mobile platform

Systems integrated according to research specification

R and Q matrices coefficients; gain selection and settings of DC motor drivers: NI-9505 (for wave PWM)

Limitation Time determinism condition and controller performance Operating frequency of the CPU, and the number of FPGA logic unit Computer processing power (compiler), the size of operational memory Engine type cooperating with the module NI – 9505 Systems are integrated and mobile platform is built

As it was addressed previously, for the following study where the main challenge was designated, developing surveillance system of strongly nonlinear object had significant meaning in the design approach. The authors have coupled together mechatronic techniques to provide time and cost-effective approach for development of nonlinear systems. Associated control system faces extreme complex dynamics of the object. Formidable nonlinearity was contrived by implementation of the economical control strategy complying with both mobile robot dynamics and operation environment. To address the aforementioned challenge, the authors study and propose the on-line tailored algorithm. The proposed strategy is capable to control nonlinear object with the acknowledged precision and applicable research criteria. While the control signal and dynamics of the nonlinear mobile platform is performed in real-time, the embedded system is striving significantly for the CPU computing power. In this stage, time extended mobile platform operability (electrical power), together with error movement level and controller performance, should be equilibrated. Consequently the mechatronic attitude incorporated into the presented development methodology is complemented with optimisation design loops, facilitating the balanced design. It is portrayed a complementary perspective of the design flow (Fig. 2). Segregated stages of the adopted mechatronic process merge optimisation feedback loops, enabling during iterative cycles for the optimal system design. The detailed overview of the applied optimisation loops in following study was summarized in Table 1.

2.2. Algorithm improvement. Correction velocities There are several not commonly used features that distinguish the presented mobile platform design among the other constructions of the same type. Propulsion is given by electrical motor coupled on the same shaft with differential fitted into mobile platform chassis. Solution neutralizes wheel slips phenomena and secures existence of non-holonomic constraints. Not widespread solution (however, it can be lastly noted a considerable augmentation of such application) was applied on the control side of the system, where embedded controller cRIO, powered by the LabVIEW, was implemented. For the mechanical part of the design, it is worth indicating the maximum speed, which is achievable while the quality of surveillance system is guaranteed. The value 0.31 m/s was obtained as speed limit. This value was first verified successfully during the virtual tests (bearing in mind mainly capabilities of equipment and study requirements) and subsequently within validation process. An assumed model taken into consideration is presented (Fig. 3). Mobile platform is composed of following main parts: chassis 5, driving system ZN and control system ZK. The driving system consists of two wheels 1 and 2, which thanks to differential mechanism are driven by one electric motor. Wheels rotate about their axes, whose positions are unchangeable relatively to the chassis. Components of the control system are: wheel 3 embedded in steering unit 6, which is driven by the other electric motor 4. Coordinates α1, α2 and α3 are the rotation angles of three mobile platform wheels 1, 2 and 3 respectively. The angle of the wheel 3 plane is denoted by φ. Angle β is the rotation angle between the platform frame and fixed coordinate axis x. Point H belongs to the plane of wheel 3. Angle θ defines instantaneous rotation of a mobile platform on a circular trajectory of point H. Point A is a point of intersection of the frame longitudinal symmetry plane with the axis of rotation of wheels 1 and 2. The mobile platform is fully described by a set of coordinates x, y, β, φ, θ, α1, α2, α3. Mathematical modelling of the mobile platform is essential step in modelling of a control system. It has considerable impact on accuracy of simulation of the real system. Real mobile platforms have driving systems with restricted moments, as well as—are characterized by the latency and joint limits that must be modelled in order to produce sufficient simulation of how the vehicle will respond to its commands.

706

K.J. Kaliński, C. Buchholz / Mechanical Systems and Signal Processing 52-53 (2015) 700–721

Fig. 3. Three-wheeled mobile platform's geometry and kinematics.

During the movement of point H of a mobile platform on the circular track of radius R and centre K, velocity vector vA of point A (of the chassis) is restricted by non-holonomic constraints. A thorough study yields that the generalized velocities' vector can be expressed as matrix Eq. (1) 2 3 2 3 vA U cos β β_ 6 7 6 7 q_ ¼ 4 φ_ 5 ¼ Jk 1 ðqÞ U 4 vA U sin β 5; vA Utg φ θ_

ð1Þ

where: 2

l1 sin β þ l3 sin ðβ þφÞ

6 Jk ¼ 4  l1 cos β  l3 cos ðβ þ φÞ l1

l3 sin ðβ þ φÞ  l3 cos ðβ þφÞ 0

R cos θ

3

R sin θ 7 5 0

Jacobian matrix for kinematics. For applicable study and generally for the mechanical systems with numerous movement functions, dynamic computational model of the controlled object is usually nonlinear. Nonlinearity of the model may be contrived by:

 Computed model parameters being variable, not only as functions of time, but also as functions of generalized displacement and their derivatives [36],

 The mechanical system restricted by non-holonomic constraints (unilateral or bilateral), which are not integrable. Considerable movement of the mechanical system causes intensive change of kinetic energy (due to the variation of the generalized velocities). Changes of the potential energy of elastic forces can be neglected. The same concerns potential energy of the gravity forces, if the system is moving on the roughly flat surface. During the research, the authors decided to use the Lagrange equations [36] of the second kind for description of the motion. In case of a non-holonomic system, motion of the mobile platform (neglecting influence of the potential energy of the system) can be expressed by following equation [36]:   _ qÞ _ qÞ d ∂Tðt; q; ∂Tðt; q; _ qÞ þ Bu ðt; q; _ qÞu þ JT ðq; _ qÞ λ;  ¼ fðt; q; dt ∂q_ ∂q

ð2Þ

where q ¼ ½ψ; φ; xA ; yA ; β; αT —vector of generalized coordinates, ψ—rotational angle of substitutive wheel, instead of wheels 1 and 2, whose position is at point A, xA, yA—Cartesian coordinates of point A of the chassis, α¼α3—rotational angle of _ qÞ—kinetic energy, fðt; q; _ qÞ—vector of generalized forces of the uncontrolled system, Bu ðt; q; _ qÞ—control wheel 3, Tðt; q;

K.J. Kaliński, C. Buchholz / Mechanical Systems and Signal Processing 52-53 (2015) 700–721

707

matrix, u—vector of control commands, λ—vector of Lagrange multipliers, 2 3  r cos β 0 1 0 0 0 6 7 0 0 6  r sin β 0 0 1 7 7 _ qÞ ¼ 6 Jðq; 6 7 sin β  r cos ðβ þ φÞ 0 0 1 0  l 1 4 5  r sin ðβ þ φÞ 0 0 0 1 l1 cos β —Jacobian matrix for dynamics, r—radius of the substitutive wheel and wheel 3. The presented equation makes possible to solve both forward and inverse dynamic problem of the mobile platform and calculate the Lagrange multipliers. Algorithms, whose parameters are not updated during control process, demonstrate considerable inefficiency for nonlinear systems. Utilized broadly and willingly the PID controllers, which apart for irrefutable advantages, can be replaced by more energy economical control strategies complying with both mobile platform dynamics and operation environment. In opposition to such inadaptable controllers, it is highly recommended to deploy on-line control methods where dynamic model and its nonlinearity are reflected. For this study, in order to obtain sufficient motion control strategy (i.e. determination of proper commands) firstly dynamics of mobile platform was identified. For matrix description of the platform's motion, Lagrange equations of the second kind were proposed. Dynamics of controlled nonlinear system can be described in discrete time domain [36] Mt q€ t þ Δt þ Lt q_ t þ Δt þ Kt qt þ Δt ¼ f t þBu;t ut þ Δt ;

ð3Þ

_ qÞ, Lt ¼ Lðt; q; _ qÞ, Kt ¼ Kðt; q; _ qÞ, Bu;t ¼ Bu ðt; q; _ qÞ, f t ¼ fðt; q; _ qÞ;ut þ Δt and qt þ Δt denote respectively matrices where Mt ¼ Mðt; q; of inertia, damping, stiffness, control, and vector of generalized forces for time instant t, and also vectors of generalized displacements and control commands of the system for time instant t þΔt. Eq. (3) reveals that all matrices are functions of the generalized velocities, generalized displacements and time. As a result, the dynamics of system changes with every moment of the motion. Effective control strategy has to comply with model changes and reflect the current state of the system. Defined certain features of such algorithm impose implementation of real-time system where the timing is controlled (i.e. control system time must be equal with actual time). After transformation of Eq. (3) we obtain the state Eq. (4) of unsteady controlled system in the form [36] ( x_ ¼ Ax þ Dzþ Bu ; ð4Þ y ¼ Cx þw h where x ¼ q_

q

i

T

" —vector of state coordinates, A ¼ "

M  1 Bu

#

 M  1L

M  1 K

I

0

"

# —state matrix of the system, D ¼

M1 0

# —

—matrix of inputs, C—matrix of outputs, z  f—vector of disturbances, y—vector of 0 output whose component are the registered system's responses, w—vector of the measured noise. The solution of the first equation of the system (4) by the state transition method can be written as [36] Z t Φðt; τÞ ½BðτÞ uðτÞ þ DðτÞ zðτÞ dτ; ð5Þ xðtÞ ¼ Φðt; t 0 Þxðt 0 Þ þ

matrix of disturbances, B ¼

t0

where Φ(t, t0) is solution of homogeneous differential equation x_ ¼ AðtÞx;

xðt 0 Þ ¼ I:

ð6Þ

Further, it is possible to define energy performance index, which takes into account changing in time kinetic and potential energy of the system, with respect to trajectory of the desired motion. The latter is represented by state coordinates vector x. Thus we obtain 1 1 JðtÞ ¼ ðx  xÞT Q ðx  xÞ þ uT Ru; 2 2 where

"

Q¼ x ¼ ½q_

Q 1M

0

0

Q 2K

T

ð7Þ

# ;

qT T :

Q1, Q2—dimensionless matrices of influences of kinetic and potential energy, R—matrix of the control command's effect. Variation of energy performance index Eq. (7) can be written as 1 1 δJ ¼ ðx  xÞT ðQ þQ T Þ δðx  xÞ þ uT ðR þ RT Þ δu: 2 2

ð8Þ

708

K.J. Kaliński, C. Buchholz / Mechanical Systems and Signal Processing 52-53 (2015) 700–721

Fig. 4. Control flow diagram.

Taking into account the variation of expression (5) and comparing Eq. (8) to zero, the variation of energy performance index is   Z t 1 1 δJ ¼ ðx xÞT ðQ þ Q T Þ Φðt; τÞΒðτÞ dτ þ uT ðR þ RT Þ δu ¼ 0: ð9Þ 2 2 t0 Finally, optimal control command can be obtained, as follows Z t u ¼  ðR þ RT Þ  1 BT ðτÞΦT ðt; τÞdτ U ðQ þ Q T Þ Uðx  xÞ ¼ KR ðtÞ U ðx xÞ: t0 |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}

ð10Þ

KR ðtÞ

It is a time-varying function of the controller gain KR(t) and the coordinates of the state vector x. Determination of the on-line control during the process performance does not require investigation of the system controllability. Suitable block diagram (Fig. 4) allows understanding of the relationships between objects, and the nature of signals' interaction in the context of the inclusion of the proposed optimal control strategy applied in this research. Secondly, controller performance and surveillance efficiency have to be balanced and optimised. Implementation of the defined control command u(t)—Eq. (10), for the mobile platform is calculated on a basis of matrices M and L, whose values are generated for time instant t, while u(t) is computed for tþΔt. As it was mentioned in Section 1, representation of a step of integration Δt has considerable impact on the system energy efficiency on one side and surveillance process performance on the other side. A lack of control signal (during time period Δt) can cause significant deviations between actual and desired trajectory of the platform, and thus—disturbs energy system trade-off. Therefore, researchers had to perform optimisation process within the surveillance system. It became critical and essential operation for feasibility of the on-line algorithm execution, in order to secure real time implementation in the system. Representing a step of integration Δt is limited by CPU performance of the applied mobile platform controller (here is National Instruments cRIO-9076, 400 MHz, powered by LabVIEW). Common approach encourages decreasing to minimum time Δt (mainly by speed up of CPU clock frequency), and thus—find minimal energy losses (error level associated directly with computation of differential equations describing dynamics of mobile platform). In this study, limitations of the applied controller had to be considered. Fixed CPU clock and willingness to keep real-time application forced authors to find compromise between time Δt and error level occurrence. During the study, the authors investigated remedies for system balance and defined suitable correction velocities which were finally implemented into the optimal control command u(t). Defined correction velocities along axes x and y respectively, can be given as: xH  xH x_^ H ¼ ; k U Δt

y  yH y_^ H ¼ H : k U Δt

ð11Þ

where xH and yH —Cartesian coordinates describing desired position of characteristic point H of the platform in time t; xH and yH – Cartesian coordinates describing actual position of characteristic point H of the platform in time t; k—coefficient determined in a way of simulation. _ Bearing in mind the defined correction velocities, vector of correction states x can be calculated and optimal control command Eq. (10) can be modified as follows: u ¼ K ðtÞ Uðx  x _ xÞ: ð12Þ R

For sampling time Δt, where the time determinism is assured, the applied correction velocities can lead to elimination of the mobile platform error occurrence and improve considerably the system energy efficiency. Due to the nature of system development study (i.e. the mechatronic approach), type of control object (nonlinear) and implemented algorithm (on-line), as well as the situation when the embedded controller was held in a very early stage of

K.J. Kaliński, C. Buchholz / Mechanical Systems and Signal Processing 52-53 (2015) 700–721

709

Table 2 Determination of the Δt length study results. Only for Δt ¼0.005 s both controller determinism conditions and satisfactory error level are guaranteed. Integration step time [s]

Computation time [ms]

Average energy losses [Nm]

Errors OK?

Determinism

Trajectory “sine”–test 50 s 0.01 0.005 0.001 0.0005

7848 18985 91056 145843

0.026436 0.000686 0.0001018 0.0000834096

NO YES YES YES

YES YES NO NO

2350 5883 32057 63386

– 0.001652 0.00012 0.0000540326

NO YES YES YES

YES YES NO NO

9129 20227 167075 540690

– 0.000234256 0.0000675311 0.0000102256

NO YES YES YES

YES YES NO NO

Trajectory “parabolic”–test 72 s 0.01 0.005 0.001 0.0005 Trajectory “circle”–test 20 s 0.01 0.005 0.001 0.0005

the project, the elimination of local or non-optimal solutions became indispensable. For this reason, the authors were obliged to perform virtual prototyping techniques and optimise simultaneously system energetic performance (under the scope of HILS) i.e. determine the length of integration step (system command frequency) ensuring that the operation of the control system is executed in real-time at which the errors occurrence fulfils satisfactory level. Appropriate selection of integration step followed by a feedback loop: virtual prototyping technique—the HILS technique. The controller obeys real time performance if all the foreground processes (algorithm related) have been successfully executed before their stated critical time constraints. The authors, by the choice of step length Δt verified equalization of computation time (system time) with actual time. The considered optimisation loop was depicted in Fig. 2. Provisory input for step length analysis can flow in when the deviation levels measured between desired torque trajectories and trajectories obtained in the process of virtual prototyping technique are acceptable. During the virtual prototyping technique (first stage of this study), the authors explored the Δt step sets, but demanding computation process of on-line algorithm and real-time conditions (equalization between simulation and real time clock readings) of the HILS tests verified authors assumptions and final Δt had to be set for 0.005 s. Determined length of Δt guaranteed fulfilment of both controller determinism conditions, and satisfactory error level (Table 2). Furthermore, having ability to use the FPGA (integral part of applied controller), the authors decided to allocate there certain parts of the algorithm code (responsible for the PWM formation). In this level, considerable increase of the controller output level (decreasing of CPU and memory usage) was obtained. Complete outcomes from this partial study were included in Table 2. 2.3. Mobile platform improvement Prototyping technique enabled to achieve the initial system optimisation, and the target embedded controller could be elaborated. Further, selected controller was used primarily over the HILS test and finally—ntegrated with the real platform. Execution of last stage of the research brought possibilities to perform the decisive verification experimental process. Concurrently with rapid prototyping, the mobile platform was finally tuned and corroborated with established study premises. During the project, some decisions, such as choosing a way of steering wheel concept, had to be resolved quite early. The distinctive dynamic nature and requirement for mobile platform conveyance without slips, determined the geometrical structure and the adopted solutions for propulsion and steering systems. Finally, the developed mobile platform construction of the platform, and requirement for mobile platform conveyance without slips, determined the geometrical structure and the adopted solutions for propulsion and steering systems. Deployed algorithm, which tailors the architecture and fosters on-line in minimizing mobile platform displacement errors, as well as—very strong dynamic nonlinearity, imposed the need for highly efficient computing controller. Thereupon it was presented in a view of the designed platform (Fig. 5). As it was mentioned formerly, due to necessity of wheels slips exclusion, the differential system, connected centrally to electrical motor (Micromotors) had to be deployed. Electric line scheme was depicted (Fig. 6). The main component of developed system was based on the cRIO NI-9076 embedded controller powered by the LabVIEW. The ruggedness of cRIO controller concept by high-end and flexible architecture allows developing deterministic application both in real time processor and FPGA. The meaningful and decisive factor in the choice of mobile platform DC motors had incorporated separate driver module NI-9505, which beside PWM generation feature includes a built-in quadrature encoder interface. The authors, by customizing the FPGA logic in cRIO, were able to accurately control torque in addition to velocity and motor position. However, recommended by the manufacturer the PWM frequency (20 kHz) and maximum inrush current for this module, narrowed considerable motor

710

K.J. Kaliński, C. Buchholz / Mechanical Systems and Signal Processing 52-53 (2015) 700–721

Fig. 5. Three-wheeled mobile platform.

choice possibilities. The authors, in order to ensure proper operation of the engines and safe operation of the motor driver module, equipped NI-9505 modules with power amplifier NI-9931, which raised the permissible level of continuous load current from 5 A to 7.3 A and inrush current up to 12 A. Lastly, 12V DC as a voltage standard across the system was adopted. Initial selection of components defined upper mass limit (10 kg). At this stage, applicable development feedback loop allowed the selection of a suitable differential system, with respect to the mass of platform. The authors deployed the system, which derived from the weighing 15 kg remote-controlled car (Off Road Buggy petrol type). Due to project conditions imposing a requirement for platform movement without slips (securing the minimal energy usage), the development process had to encompass an analysis of Lagrange multipliers. Although the Lagrange multipliers have only an abstract meaning, so indeed there are special nonlinear mechanical construction, restricted by non-holonomic constraints (like three-wheeled mobile platform) where multipliers can be traced to their particular physical interpretation. For the portrayed study, the multipliers were associated with dry friction forces. Analysis of Lagrange multipliers was performed during virtual prototyping stage. The main objective for the discussed study at this stage was to reckon the change of dry friction forces at the points of contact platform wheels with the road and then to estimate whether current changes in the friction force do not exceed the limit values. Verification process was performed within optimisation feedback loops (see Table 1) during which a final concept (computation model) of the mobile platform was able to mature. In order to assess temporary values of Lagrange multipliers, the authors simplified the notation, of dynamic Eq. (3) and obtained: Mq€ þ Lq_ ¼ f þBu u þ JT λ

ð13Þ

K.J. Kaliński, C. Buchholz / Mechanical Systems and Signal Processing 52-53 (2015) 700–721

711

Fig. 6. Mobile platform electric scheme.

The equation of non-holonomic constraints can be given as [36] " # h i q_ i Ji J ¼0 ð14Þ d q_ d h i T  T where q_ i ¼ ψ_ φ_ ; q_ d ¼ x_ A y_ A β_ α_ —vectors of generalized velocities respectively in independent and dependent motion, 2 3 2 3 1 0 0 0  r cos β 0 6 7 6  r sin β 0 7 0 0 60 1 7 6 7 7: Ji ¼ 6 7; Jd ¼ 6 6 7 sin β  r cos ðβ þφÞ 1 0 l 4 0 05 1 4 5  r sin ðβ þφÞ 0 1 l1 cos β 0 0 A prerequisite for unequivocal relationship between generalized velocities in depended motion and generalized velocities in independent motion is non-singularity of matrix Jd. Then, the constraints' Eq. (14) is converted into the form q_ d ¼  Jd 1 Ji q_ i ¼ Jn q_ i |fflfflfflffl{zfflfflfflffl}

ð15Þ

Jn

and, after differentiating it with respect to time, the authors obtained n

q€ d ¼ _J q_ i þ Jn q€ i :

ð16Þ

Complying Eq. (13) with Eqs. (14)–(16), it is possible to separate subsystems corresponding with dependent and independent coordinates of the motion (velocities and accelerations). Then " #" # " #" # " # " # " T# q_ i Mii Mid Lii Lid Bui Ji q€ i fi þ ¼ þ uþ T λ ð17Þ q_ d Mdi Mdd Ldi Ldd Bud q€ d fd Jd Eq. (17) can be expressed as a set of two matrix equations Mii q€ i þ Mid q€ d þ Lii q_ i þ Lid q_ d ¼ f i þ Bui u þ JTi λ; Mdi q€ i þMdd q€ d þLdi q_ i þ Ldd q_ d ¼ f d þBud u þ JTd λ:

ð18Þ

After expelling Lagrange multipliers λ from the first equation of set Eq. (18), the authors acquired n

n

n

n

n n T n Mn q€ þ L q_ ¼ f þ Bu u; Mdi q€ þ Mdd q€ d þLdi q_ þ Ldd q_ d ¼ f d þ Bud u þ Jd λ;

where: qn  qi ; Mn ¼ Mii þ Mid Jn  JTi Jd T Mdi JTi Jd T Mdd Jn ;

ð19Þ

712

K.J. Kaliński, C. Buchholz / Mechanical Systems and Signal Processing 52-53 (2015) 700–721 n n Ln ¼ Lii þ Lid Jn  JTi Jd T Ldi  JTi Jd T Ldd Jn þMid _J  JTi Jd T Mdd _J ;

Bnu ¼ Bui  JTi Jd T Bud ; f ¼ f i JTi Jd T f d : n

The  second of matrix equations' set (19) provides a possibility for analysis of the Lagrange multipliers, because T λ ¼ λ1 λ2 λ3 λ4 ; signs λ1 and λ3/λ2 and λ4 denote respectively friction force components in the direction of axes x/y of Cartesian coordinates' system. For resolving the investigated equation the Maple symbolic environment was applied. Solutions were implemented in the LabVIEW, where the detailed survey of multipliers was carried out. The changes in time of dry friction forces were verified only for the “sine” type trajectory as the mostly demanding while the mobile platform is conveying. There are demonstrated graphical solutions of the Lagrange multipliers (Fig. 7). Total values of the friction forces TN and TM, acting on appropriate wheels respectively, i.e. on steering wheel and abstractive substitutive wheel used for computation modelling of mobile platform (Fig. 3) can be determined using formula qffiffiffiffiffiffiffiffiffiffiffiffiffiffi qffiffiffiffiffiffiffiffiffiffiffiffiffiffi T N ¼ λ21 þ λ22 ; T M ¼ λ23 þλ24 : ð20Þ However, the limit forces for several wheels are defined by relationships: T N max ¼ μN U ðN 1 þN 2 Þ; T Mmax ¼ μN U N3 :

ð21Þ

where mN, mM—dry friction coefficients for steering and substitutive wheel respectively, N1, N2 and N3—normal reaction forces for wheel 1, 2 and 3. On the basis of the instantaneous values of the Lagrange multipliers, by using Eq. (20), the authors defined total friction forces acting on the appropriate wheels, which lastly were compared with the limit values Eq. (21). The obtained results of this analysis are shown (Fig. 8). Results of the Lagrange multipliers analysis confirm that specific (instantaneous total friction force for each wheel of the platform is about 5.5 times lower than the limit one) optimised parameters of the platform secure motion along the presented trajectory without slips, and thus—with a balanced energy expenditure; any slip could result in loss of controllability, and thus—move the wrong track on the platform.

Fig. 7. Instantaneous values of the Lagrange multipliers for the “sine” type trajectory.

K.J. Kaliński, C. Buchholz / Mechanical Systems and Signal Processing 52-53 (2015) 700–721

713

Fig. 8. An instantaneous value of the friction force (continuous line) and the limit value (dotted line) for steering wheel (left) and substitutive wheel (right) for the “sine” type trajectory.

3. Mechatronic approach in the design of three-wheeled mobile platform Predominant challenge of controlling mechatronic systems is associated with nonlinearity of dynamic model. Nonlinear analysis and control must be researched and solved in order to improve the steady-state and dynamic characteristics of the object. The authors performed intensive research in the system development to secure assumed performance of motion control. Nonlinearity of the mobile platform, which was portrayed by Eq. (3) considerably, substantiated dynamic matrices dependency on generalized velocity vector, generalized displacement and time. In this case it will be highly inefficient to deploy controllers, where the changeable effect of dynamics is not reflected. Recognizing the potential difficulties associated with ignoring dynamic nonlinearities and constraints in algorithm ordinary (like PID) architectures, the research focused on full integration of dynamic model into control system design, guaranteeing the validity of analytical, numerical, and experimental outgrowths. In particular, mechatronic development methodology was incorporated in analysis and design. Additionally, features in motion control of mechatronic system aroused, resulting computational and algorithm implementation difficulties. Due to outstanding research tasks, the embedded control system in development process was included. The task of designing embedded controller was based on two fundamental mechanisms, namely operations associated with securing real-time execution across the system and algorithm deployment reflecting on-line changes of mobile platform dynamics while conveying. Real time system conditions could be guaranteed after optimisation process performed during the research (see, Section 2). The architecture of algorithm was tailored by dynamic model of mobile platform, reflecting system interactions, behavioural and components functions knowledge. Accomplishment of all discussed aspects of a design methodology is requisite, which helps not only to fulfil research objectives, but also to succeed the project within limited time and budget. The presented model in Section 2 was developed to assist especially in interdisciplinary design process by implementing mechatronic techniques supported by optimisation feedback loops. In traditional sequential development approach design, mechanical subsystem has to be “frozen” before proceeding to the design of control software. There are few interactions and common interferences. This approach usually does not succeed in balanced design, since it does not properly address the interaction among mechanical, electronic and control subsystems. The authors applied concurrent developing approach with several milestones put across incorporated mechatronic techniques. Evaluation of the design and eventually necessary actions minimizing deviations can be performed on every stage (while mechatronic technique is performed) of the whole development process. Such strategy, where partial design freeze is based on multi-disciplinary objective and constraints evaluation are divided along research flow diagram leads to expected outcomes while the probability of breakdown, leading time and cost are reduced. 3.1. Virtual prototyping The idea of virtual prototyping [37] is to create a computational model of investigated solution (resembling real object upon agreed accuracy), which in the virtual space (computer environment) is actuated by external (to the object) signals or forces. Test results are gathered and analysed also in virtual space. In this research, the authors applied virtual prototyping technique, whose block diagram is presented (Fig. 9). The main contrivance of virtual prototyping deployment, conducted

714

K.J. Kaliński, C. Buchholz / Mechanical Systems and Signal Processing 52-53 (2015) 700–721

Fig. 9. General concept of virtual prototyping.

Fig. 10. Steering wheel torque (left) and propulsion torque (right).

during the system development process was to analyse the responses (in the block “visualization of results”) of the deployed computational model of the mobile platform. Key element of virtual prototyping is proper selection of the software development environment (in this case the authors used LabVIEW), which has a substantial impact on the quality of the design, and secures important flexibility on this stage of study. Emulated model of the controller was created based on an algorithm architecture description Eq. (12). Kinematics and Lagrange differential equations of the second kind, arising directly from the imposed non-holonomic constraints, were used for mobile platform model formulation. The virtual prototyping technique was conducted for three specified trajectories, applicable in the whole demonstrated research (here only the results for “sine” type trajectory are presented). Reference values for the system optimisation and development were desired trajectories of the platform conveyance. Graphical solutions of optimal control signals, as well as being the consequence of the response of mobile platform, confirm the correctness of the implementation of the proposed control algorithm. The authors achieved such system configuration, which guaranteed for optimal control signals (motor torques) barely 5% deviation from desired trajectories (Fig. 10), the “sine” type trajectory. Further, kinematic responses were verified and the system could be optimised. In Fig. 11 are demonstrated wheels' speed plots α_ 1 , α_ 2 , α_ 3 tracked throughout the mobile platform conveyance (on “sine” type trajectory). Despite strong nonlinearity of the system, for all type of trajectories the platform was moving; the authors could not observe any local symptoms that might had indicated a loss of stability or adhesion (wheel slip effect). The presented figures depict that the mobile platform was moving faster than expected but higher values of the speed could be omitted due to controller tuning process performed on later stage of the study. Similar test results were obtained for remaining kinematic parameters (i.e. β, φ). Due to the cumbersome system description, the calculation process of nonlinear equations, implemented the LabVIEW algorithm, absorbs significant computer resources (during the calculations the processor is loaded with approximately 100%). Therefore, in order to achieve feasible solution within equipment available performance (the type of available controller was known before the main phase of study), there was extremely important to perform optimisation process

K.J. Kaliński, C. Buchholz / Mechanical Systems and Signal Processing 52-53 (2015) 700–721

715

Fig. 11. Wheel speeds (virtual prototyping).

(i.e. surveillance system energy optimisation, Fig. 2). It should be noted that the system optimisation was obtained during iteration processes. The optimisation process is:

 associated with code architecture of deployed algorithm, and the place of its execution to secure request for controller 

performance (it was decided to separate the part of algorithm executed in the Real-Time processor and the part executed in the FPGA unit), energetic (the most noticeable) from a point of view of the control system (i.e. the choice of integration step).

The applied virtual prototyping technique lowered considerably the risks associated with the design, by improving understanding of the system requirements. Many variants and system set-ups could be verified and analysed before building physical prototype, while speeding up the design process, reducing costs and streamlining debugging. The mechanical concept of mobile platform was approached giving design parameters inputs for controller type choice. The authors performed debugging of algorithm and narrowed the scope of searching the matrix (i.e. R and Q) elements choice. 3.2. Hardware in the loop simulation Due to increasing complexity of mechatronic systems and the accompanied lack of opportunities to build prototypes (caused by limited access to the resources, budget and timeframe of the project), and also—due to the increasing computational power of computers and appropriate test environments increasing popularity of design techniques, an emulated model closely resembled the real object (or part of the system) actuated by real signals. Development process supplemented by the HILS technique considerably increases the probability for appropriate decisions approaching final successful system design. Frequently, important factor while using HILS technique is to avoid the loss of expensive equipment, caused by testing different control strategies and the stability of the solution. In addition, significant advantage for HILS is test contingency of algorithms, where the number of controlled variables (I/O) can be unreservedly deployed, tailored and optimised [38–46]. The necessary element to achieving these advantages is implementing real-time conditions that can execute models efficiently and connect it to the real world using hardware I/O with the appropriate accuracy and performance. Picture of the HILS test facility and an overview of the HILS block diagram architecture, are shown respectively in Fig. 12 and 13. Created computational model of three-wheeled mobile platform (the same one which was used in the technique of virtual prototyping) emulates a real object. At the same time, the embedded real-time controller cRIO generates optimal control signals. When the controller is deployed on physical mobile platform, the generated commands (optimal torques) control DC motors of the propulsion and steering system. In this case, for the emulated platform and computed torques (cRIO signals) the forward dynamics and kinematics problems are solved (relevant transformations made in the Maple environment, which then were modelled in the LabVIEW). Emulated computational model of the platform is a real-time standalone application running on PC with LabVIEW Real Time (emulated model platform block is accommodated into Control System and Design loop and is synchronized internally with real-time loop). Fulfilment of the determinism requirements during the flow of signals between the controller and

716

K.J. Kaliński, C. Buchholz / Mechanical Systems and Signal Processing 52-53 (2015) 700–721

Fig. 12. Block diagram of the HILS test.

Fig. 13. Overall concept of the HILS arrangement.

emulated model is assured by the real-time global variables of a FIFO queues type, which are transported over Ethernet with RCP/UDP/IP. According to Fig. 12 the analysis of forward dynamics and kinematics problems allowed designating motion parameters of the emulated platform, which were resulted by optimal torques. For controller and emulated mobile platform the integration step was set to 0.005 s, which guaranteed, as authors mentioned before, fulfilment of the system energy balance (providing real time conditions while error occurrence has an acceptable level). The HILS test results for wheels' speeds α_ 1 ; α_ 2 ; α_ 3 are illustrated (Fig. 14). Due to the specific setup of the HILS test, which adopts virtual computational model of the mobile platform, there were differences between the model responses and desired trajectories. Apparent deviation occurrence is associated mainly with finite precision of computers (numerical errors), while the differential equations were solved. It should be noted that the final results of the HILS test are subjected to several (i.e. differential and integral) transformations, both in the controller and while responses in the emulated platform model are computed.

717

speed [rad/s]

K.J. Kaliński, C. Buchholz / Mechanical Systems and Signal Processing 52-53 (2015) 700–721

time [s] Fig. 14. Wheel speeds (HILS).

Furthermore, the fact of controlling highly nonlinear system (matrix of inertia and damping depend on angle φ) significantly adversely affects the results of these tests. Small deviations of steering angle φ with respect to the desired values influence considerable discrepancies in final trajectories appearance. Performing simulation in real time using the embedded controller acknowledged the correctness of control algorithm deployment, and the choice of hardware architecture. The authors could preserve the dynamic fidelity of the test by integrating the physical and numerical components in real-time. Extremely valuable (as it turned out later in also necessary for system energy optimisation) element of the tests was the ability to verify the length of the integration step. Carrying out the HILS test enabled authors to optimise the code of the control algorithm. Part of the code has been placed in separate loops, and the data blocks were grouped into sub-functions. The applied optimisation process significantly improved the signal flow within the control system, which caused a significant reduction of memory usage in the cRIO controller. Nevertheless, execution of implemented control strategy in real-time enlarges the CPU (mainly ALU) significantly. Despite number of efforts tending to CPU load reduction, still algorithm execution absorbs around 95% of the processor's performance. Finally, applying the HILS technique in the presented mechatronic development allowed to comprehensive approach for validation of the system reliability, and to avoid building a prototype. The authors evaluated the design tradeoffs and achieved the reduced cost while the increased system energy efficiency. In addition, control system performance could be evaluated across a wide range of test set-ups. 3.3. Rapid prototyping on target object One of the main motivations of this research was to design nonlinear system facilitated by the mechatronic development process. Proposed methodology emphasizes efforts for using mechatronic techniques, which allows to approach in stages the system's solution. In this way, the proposed tailored algorithm to control nonlinear object was deployed into embedded controller, and three-wheeled mobile platform was constructed. The final stage of the presented design (described in earlier chapters of the paper) that verified the assumptions and deployed technical solutions (through the validation process, where integrated platform conveyed desired trajectories) was rapid prototyping on target object technique. The use of the rapid prototyping technique entered in a new field of research and development for mechatronic systems (mobile robots). In this way, the rapid prototyping of these systems is associated not only with the design approach of the physical system, but mainly focusing on experimental implementations of obtained design hardware and software systems. When the system or the object exists and in the same time there is still a need to implement new (machine or one of the parts will be automated) or upgrade the old control system (e.g. new functionality was introduced), rapid prototyping on the target object can be applied. In classical approach, the software of the embedded control system can be elaborated on dedicated real time hardware (i.e. dSPACE). After being developed and tested the specification for controller is worked out and the software in accordance to requirements can be implemented to physical system.

718

K.J. Kaliński, C. Buchholz / Mechanical Systems and Signal Processing 52-53 (2015) 700–721

Fig. 15. Rapid prototyping on real object, block diagram.

Fig. 16. Test trajectory for mobile platform.

In this study, the HILS technique facilitated to accomplish optimal architecture of the embedded control system and based on acknowledged model, the mobile platform was created. As it was mentioned before, the authors decided to use the cRIO controller as hardware platform for control motion of the mobile platform. Existing both, object and control hardware encouraged the authors to modify current survey (technique) and connect prototyping process with the final implementation and validation. A concept of rapid prototyping test setup is shown (Fig. 15). The iterative development process was organized as follows. 1. Algorithm compilation and deployment to controller (Real Time and FPGA) [47]. 2. Mobile platform validation while moving on desired trajectories (verification of algorithm performance). 3. Algorithm debugging and control system adjustments (R and Q matrices, PWM).

Checking procedure of the system performance was executed by measuring deviation between real position of the platform and point 0 of the Cartesian coordinate system 0xy located on the desired trajectory. For each trajectory, the authors established several places where the measurements were taken. The “sine” test trajectory, with check-points, is presented (Fig. 16). In Fig. 17 (left) the authors demonstrated result for the last point of the obtained trajectory when the mobile platform moved with 0.17 m/s. In Fig. 17 (right) are presented results for the same check-point, but speed of the platform was 0.31 m/s (90% of max. speed). The test results for both applied speeds confirm sufficiently good performance of the proposed method to control strongly nonlinear object. During the test, the mobile platform reached the final destination with demanding repeatability. Small errors' occurrence (maximum error within 80 mm for both applied speeds) can be avoidable by comparison with the complexity of the trajectory and the conveyance distance to the size of the object. Numeric errors should be also contemplated.

K.J. Kaliński, C. Buchholz / Mechanical Systems and Signal Processing 52-53 (2015) 700–721

719

Fig. 17. Experimental results.

In the context of this study, rapid prototyping on target object provided opportunities for iterative closing tuning process and successful validation of the designed system [48]. 4. Mechatronic design. Enhanced performance The results of the performed experiments demonstrate the robustness and effectiveness of the deployed control strategy. Provided features of the embedded real-time system with tailored on-line algorithm allow sufficient and accurate motion control of strongly nonlinear three-wheeled mobile platform. The adopted methodology for the research development, where mechatronic techniques were utilized, confirms its unquestionable beneficial impact on quality and economics of the system design. Conducted virtual prototyping, subsequent HILS tests and finally—rapid prototyping on target object, allowed to accomplish the optimal system design and performance. Especially, positive results obtained during the movement speed are the pronounced exponent of the ability to control nonlinear object with the proposed optimal strategy, likewise sufficient acknowledgement of achieving both the optimum control system and the mechanical structure. Furthermore, the authors by implementing multi-variant test trajectories ascertained the employment of submitted control method with the option of considerable extensibility. The latter allowed, in the usage of other type of embedded hardware, to control sophisticated and more advanced mechatronic systems. Substantial challenge in the whole portrayed research was the test performance and the conveyance on the “sine” type trajectory. Despite the exigent conditions of motion, the mobile platform did not suffer significant deviations disqualifying the adopted control algorithm. In this study, the average deviation for “sine” type trajectory did not exceed 40 mm. In addition, for all types of the tested trajectories, the authors obtained good repeatability of the results. Errors occurrence can be excused mostly by nonlinearity of dynamics equations, whose real-time numerical solution became problematic and hardware-demanding. The optimising process carried out throughout the mechatronic development study (especially with the use of HILS technology) approached the tradeoff between the numerical errors occurrence, and the fulfilment of real-time condition. Moreover, the beneficial outcome from the performed optimisation process had resulted in possibilities to control nonlinear object with preconceived numerical error, causing position misalignment from desired trajectory while conveying. However, there were other meaning factors influencing the moving quality. The authors pointed out the precision of mechanical components predominantly impacting platform deviation. Finally, the average error for all completed trajectory is small, but future research may engage more efforts for its successive elimination from the design. The latter can be performed mainly by increasing the Real Time processor performance (in order of increasing frequency of the generated optimal control signal) or by implementation of the algorithm in the FPGA. It will be also applicable choosing high-end equipment. Although implementation of complicated algorithms caused difficulties, it was managed to attain the opportunity to immune control method for varying mobile platform poles while conveying. This unfounded advantage is not utilized while nonlinear object is moving according to the PID controller, which had been studied and proved in [19]. In contrast to traditional sequential design process, the parameters needed for an integrated mechatronic design are identified and moved to the mechatronic development architecture with common interactions and interrelations. Software environment to support such an approach is necessary. The applied development

720

K.J. Kaliński, C. Buchholz / Mechanical Systems and Signal Processing 52-53 (2015) 700–721

methodology was supported by mechatronic techniques providing unexceptional advantage in the presented study. It allowed the models to be set up in a way suitable to achieve an optimal result with respect to the mechatronic context. The mechatronic attitude can be favourable in a widespread construction and development areas, facilitating the development process and balancing economical paradigms. 5. Conclusion The presented concept in this paper of the system design was established as a result of mechatronic techniques deployment and applied supporting optimisation feedback loops. Subsequently, the results analysis of experimental tests (validation of the system during the conveyance of the object on the designated trajectory of motion) empowers to conclude draw on the research achievements and effectiveness of the proposed method. The derived conclusions from the author's experience of the conducted research reflect the current trends towards utilization of the mechatronic techniques as a basis for parallel development system method. In addition, it is worth mentioning about the LabVIEW environment, impacting on the ultimate success of the study completion.

 The study shows that the use of three-wheeled mobile platform due to the strong nonlinearity (matrices M and L

 









depending on the steering angle) is difficult to control. However, the adopted development methodology, based on the use of mechatronic design techniques with the significant participation of LabVIEW, proved its effectiveness in the implementation of the surveillance system, and influenced the final success of the research. The authors achieved an optimised energy, real-time system, and effective control of the mobile platform motion. The applied mechatronic methodology enabled to reduce the duration time of the project. The effectiveness of the proposed surveillance strategy to control nonlinear system was verified experimentally. The three-wheeled mobile platform demonstrated high accuracy and repeatability during the conveyance on the desired trajectories. The use of virtual prototyping technique enabled an initial verification of the implemented control algorithm and the concepts of the system architecture. Architecture of the algorithm could be optimised by the errors elimination, and increasing the flow of internal signals. In addition, the authors were able to narrow the search space of the R and Q matrices components. Particular results were obtained using technique HILS, where real-time test conditions were incorporated. Configuration of the test facilitated, by verifying the time determinism, with determination of optimal frequency signal generation. By eliminating errors and reorganization algorithm execution (execution of the algorithm responsible for the formation of PWM, DC motor driver support and encoders assigned to FPGA) further optimisation of the system architecture was accomplished. The integration process of the surveillance system with mobile platform, and later—the final validation, was conducted by use of rapid prototyping on target object technique. Validation process of integrated system confirmed the possibility to control nonlinear object by the proposed method. Features of the deployed on-line algorithm (energy performance index), enabled controlling (in real-time) the strongly nonlinear object during its motion along various trajectories and at different conveyance speeds. Especially, the positive results obtained during the movement at the higher speed are the exponents of the algorithm applicability. The applied mechatronic design techniques, as well as—a series of experimental tests allowed to optimise the system and to develop a methodology for its use. The energy optimisation condition was achieved by the selection of step integration time of differential equations (the generation of optimal control signal) for which the real-time system guarantees the errors occurrence on satisfactory level. Mechatronic selection of the integration step proved to be an essential element in the construction of nonlinear object surveillance system. Optimisation of integration step (a compromise between common errors, and the CPU performance controller) and the deployment of correction velocities improved control performance and energy efficiency of the system. The process of mechatronic design was supported by the LabVIEW package. The utilized development environment, together with dedicated software modules, allowed successful realization of the research system concept.

References [1] M.A. Erbil, S.D. Prior, M. Karamanoglu, S. Odedra, C. Barlow, D. Lewis: Reconfigurable unmanned aerial vehicles, in: Proceedings of the International Conference on Manufacturing and Engineering Systems, 2009, pp. 392–6. [2] A. Puri, A survey of Unmanned Aerial Vehicles (UAV) for traffic surveillance, Department of Computer Science and Engineering, University of South Florida, USA, 2005. [3] B. Coifman, M. Mccord, M. Mishalani, K. Redmill: Surface transportation surveillance from unmanned aerial vehicles, in: Proceedings of the 83rd Annual Meeting of the Transportation Research Board, 2004. [4] D.W. Murphy: The Air Mobile Ground Security and Surveillance System(AMGSSS), in: Proceedings of the 10th annual ADPA security technology symposium, September 2005. [5] C.H. Robin, M.R. Ememi, A holistic concurrent design approach to robotics using hardware-in-the-loop simulation, Mechatronics (2013) 335–34523 (2013) 335–345.

K.J. Kaliński, C. Buchholz / Mechanical Systems and Signal Processing 52-53 (2015) 700–721

721

[6] E. Cetinsoy, S. Dikyar, C. Hencer, K.T. Oner, E. Sirimoglu, M. Unel, M.F. Aksit, Design and construction of a novel quad tilt-wing UAV, Mechatronics 22 (2012) 723–745. [7] K. Kaliński, C. Buchholz: Trajectory optimal control of three-wheeled mobile platform at time changeable energy performance index, in Proceedings of the 10th Conference Active Noise and Vibration Control Methods, Cracow, Poland, 2011. [8] K. Kaliński, C. Buchholz: Error minimisation in orientation and localization by correction velocities for three-wheeled mobile platform at time changeable energy performance index, in: Proceeding of the 16th International Conference on Methods and Models in Automation and Robotics, Międzyzdroje, Poland, 2011. [9] M. Mazur, Motion surveillance of two-wheeled mobile platform with the use of optimal control at energy performance index (in Polish) (Ph.D. thesis.), University of Technology, Faculty of Mechanical Engineering, Gdańsk, 2010. [10] L.F. Melo, C.R.E. Lima, J.M. Rosario: A. Reconfigurable Control architecturefor mobile robots, in: Proceedings of 2nd Internacional Symposium on Mutibody and Mechatronics—MuSMe , september 2005., v. 1. pp. 1–8. [11] L.F. Melo, J.M. Rosario: A Proposal for a hybrid opened archtecture with hardware reconfigurable control applied in mobile robots, in: Proceedings of IEEE International Conference on Robotic and Bionemetics—ROBIO, October 2006, v. 1. pp. 1101–1106. [12] P. Hahenberger, F. Poltschak, K. Zeman, W. Amrhein, Hierarchical design models in the mechatronic product development process of synchronous machines, Mechatronics 20 (2010) 864–875. [13] F. Harashima, M. Tomizuka, T. Fukuda, Mechatronics—what is it, why, and how? IEEE/ASME Trans. Mechatron. 1 (1996) 1–4(1) 1 (1996) 1–4. [14] L. Wang, W. Shen, H. Xie, J. Neelamkavil, A. Pardasani, Collaborative conceptual design—state of the art and future trends, Comput. Aided 34 (2002) 981–996. [15] L. Ferrarini, E. Carpanzano, A structured methodology for the design and implementation of control and supervision systems for robotic applications, IEEE Trans. Control Syst. Technol. 10 (2) (2002) 272–279. [16] M. Tomizuka, Mechatronics: from the 20th to the 21st century, Control Eng. Pract. 10 (2002) 877–886. [17] J. Wikander, M. Torgren, M. Hanson, The science and education of mechatronics engineering, IEEE Robot. Autom. Mag. 8 (2) (2001) 20–26. [18] H.P. Schoner, Automotive mechatronics, Control Eng. Pract. 12 (2004) 1343–1351. [19] N. Mathur, Mechatronics—five design challenges and solutions for machine builders, Instrum. Newslett. 19 (2007) 6–7. [20] J. Van Amerongen, P. Breedveld, Modeling of physical systems for the design and control of mechatronic systems, Ann. Rev. Control 27 (2003) 87–117. [21] NI. Instrumentation newsletter: Build Versus Buy: Which Is the Best Choice for Your Embedded Design? 2011, Q2. [22] G. Seelander: EMBRAER Performs Full Airplane Simulation Using NI HIL Tools, 〈www.ni.com〉. [23] G. Sussman: HILS Testing Reduces CompactRIO Control System Development Cost, www.ni.com/. [24] A. Furtanato, A. Ascari, The virtual design of machining centers for HSM: towards new integrated tools, Mechatronics 23 (2013) 264–278. [25] Y. Altinatas, C. Brcher, M. Weck, S. Witt, Virtual machine tool., CIRP Annals—Manuf. Technol. 53 (2005) 619–642(2) 53 (2005) 619–642. [26] G. Bianchi, F.D.E.N. Paoullucci, P.V. Braembussche, H.V. Brussel, Towards virtual engineering in machine tool design, CIRP Ann—Manuf. Technol. 45 (1) (1996) 381–384. [27] J. Hewit, Mechatronics design—the key to performance enhancement, Robot Auton. Syst. 19 (1996) 135–142. [28] H.V. Brussel, P. Sas, I. Nemeth, P.D. Fonseca, P.V. Den Braembussche, Towards a mechatronic compiler, IEEE/ASME Trans. Mechatron. 6 (2001) 90–105 (1) 6 (2001) 90–105. [29] A.A. Cabrera, M.J. Foeken, O.A. Tekin, K. Woestenek, M.S. Erden, B. De Schuter, M.J.L. van Tooren, R. Babuska, F.J.A.M. Van Houten, T. Tomiyama, Towards automation of control software: a review of challenges in mechatronic design, Mechatronics 20 (2010) 876–886. [30] B. Heck, L. Wills, G. Vachtevanos, Software technology for implementing reusable, distributed control systems, IEEE Control Syst. Mag. 23 (1) (2003) 21–35. [31] W. Song, S. Dyke, Development of a cyber-physical experimental platform for real-time dynamic model updating, Mech. Syst. Signal Process. 37 (2013) 388–402. [32] K. Kaliński, C. Buchholz, Three-wheeled mobile platform powered by LabVIEW at energy performance index, Measurement Autom. Robot. 12 (2012) 69–75. [33] K. Kaliński, C. Buchholz, LABVIEW in mechatronic design of control system for three-wheeled mobile platform at time changeable performance index. Mechatronic design. Chosen problems, in: T. Uhl (Ed.), Chair of Robotics and Mechatronics AGH, Kraków, 2011, pp. 47–55. [34] D. Balint: Maple Manual for Engineering Mechanics: Dynamics. Thompson Engineering, 2007. [35] J.L. Meriam, Engineering Mechanics-dynamics: WITH Solving Dynamics Maple, John Wiley & Sons, Ohio, 2007. [36] K. Kaliński, A surveillance of dynamic processes in mechanical systems (in Polish), Gdansk University of Technology Publishers, Gdansk, 2012. [37] G. Ferretti, G.A. Magnani, P. Rocco, Virtual prototyping of mechatronic systems, Annu. Rev. Control 24 (2004) 192–206. [38] C.H. Chhabra Robin, M.R. Emami, A holistic concurrent design approach to robotics using hardware-in-the-loop simulation, Mechatronics 23 (2013) 335–345. [39] A. Castano, A. Behar, P.M. Will, The control modules for reconfigurable robots, IEEE/ASME Trans. Mechatron. 7 (2002) 403–409(4) 7 (2002) 403–409. [40] K.J. Kaliński, C. Buchholz, HILS for the design of three-wheeled mobile platform motion surveillance system with a use of energy performance index, Solid State Phenom. 198 (2013) 90–95. [41] D. Maclay, Simulation gets into the loop, IEE Revis. 43 (3) (1997) 109–112. [42] G. Cai, B.M. Chen, T.H. Lee, M. Dong, Design and implementation of a hardware-in the-loop simulation system for small-scale UAV helicopters, Mechatronics 19 (2009) 1057–1066. [43] M. Linjama, T. Virvalo, J. Gustafsson, J. Lintula, V. Aaltonen, M. Kivikoski, Hardware-in-the-loop environment for servo system controller design, tuning, and testing, Microprocess. Microsyst. 24 (1) (2000) 13–21. [44] G. Stoeppler, T. Menzel, S. Douglas, Hardware-in-the-loop simulation of machine tools and manufacturing systems, Comput. Control Eng. J. 16 (2005) 10–15(1) 16 (2005) 10–15. [45] D. Bullock, B. Johnson, R. Wells, M. Kyte, Z. Li, Hardware-in-the-loop simulation, Transp. Res. Part C 12 (2004) 73–89. [46] M. Karpenko, N. Sepehri, Hardware-in-the-loop simulator for research on fault tolerant control of electrohydraulic actuators in a flight control application, Mechatronics 19 (2009) 1067–1077. [47] S. Zschack, J. Klockner, I. Guschina, A. Amthor, C.H. Ament, W. Fengler, Control of nanopositioning and nanomeasuring machines with a modular FPGA based data processing system, Mechatronics 23 (2013) 257–263. [48] H.A. Thompson, D.N.F.U.J. Ramos Hernandes, L. Jiang, I. Choi, K. Cartladge, A flexible environment for rapid prototyping and analysis distributed realtime safety-critical systems, Control Eng. Pract. 15 (2007) 77–94.