SOFTCOMPUTINGTECHNIQUES FORROBUST CONTROLLER DESIGN OF STEWART PLATFORM MANIPULATORS

Abstract

In the last few decades, there has been an increasing interest in model based robust controllers because of two main factors. The first one is technological advances and the other is due to challenges such as demand for higher level of automation to reduce lifecycle costs, issues such as maintenance on demand, zero standstill, and fault tolerance. Due to these challenges linear and decoupled control algorithms have proved to be rather inefficient. On the other hand advances in the fields of microprocessors, microcontrollers, digital signal processors and communication have made implementation of complex and advanced control algorithms very much easier and practical and hence have given an impetus to the field. Added to this, economic and social factors like market competition and increase in demand for high quality products have boosted the need for model based robust and adaptive controllers. This is especially true in control of robotic systems as they are the main workforce in industrial manufacturing and the quest is to achieve improved interaction of robotic systems with humans, to design controllers for efficient task coordination between multiple robots and to design high precision robots having improved rigidity and stiffness. The latter one can be achieved by using parallel robots such as the Stewart platform manipulators and utilizing soft computing techniques for their robust control. Stewart platform manipulators are six DOF parallel robots having fixed base and movable platform joined by six extensible legs. They have high structural rigidity and stiffness and are preferred over serial robots for applications such as precision machining, robotic surgery and so on. However the absence of robust controllers, which are able to compensate their nonlinear dynamics and uncertainties due to model inaccuracies, parameter variations, and external disturbances, has limited the real application of the manipulators to low speed motion simulators only. Presently, only single input single output PID controllers are in practical use and these controllers have a number of drawbacks including lack of synchronization and low performance. To tackle these problems, some researchers have proposed various robust and adaptive controllers which are based on hard computing. Nevertheless results have shown that the controllers were unable to tolerate the uncertainties and their performance degrades when the manipulator moves at high speeds. Therefore using soft computing techniques for the design of a robust controller for Stewart platform manipulators is expected to result in a better and effective controller. Soft computing is a word coined by L.A. Zadeh and refers to a methodology which tends to fuse synergyically the different aspects of fuzzy logic, neural network, genetic algorithm and other evolutionary algorithms to achieve a system that is tolerant of imprecision, uncertainty, partial truth and approximation. Researches in the last few decades have witnessed the successful applications of soft computing to aerospace industry, communication systems, consumer appliances, electric power systems and manufacturing automation including serial robots. However, the application of this important tool for the control of parallel robots has not been investigated. This thesis is a step in this direction. To this end, the thesis tries to systematically combine and pull together three important areas: nonlinear robust control, with emphasis on sliding mode control, soft computing and Stewart platform manipulator control. The thesis begins by presenting a state of the art literature review on sliding mode control, on Stewart platform manipulator modeling and control and on application of soft computing techniques for robust control. Then five important applications ofsoft computing techniques for robust control are proposed and implemented through simulations. The first application discussed in the thesis is solving forward kinematics problem ofthe manipulator. Forward kinematics is the computation ofend-effector/platform position and orientation from given leg length values and is necessary to close the feedback loop in task space control of the manipulator. Nonetheless, unlike serial manipulators, in Stewart platform manipulator its mathematical formulation is highly nonlinear and coupled making computation highly complex and time taking. To solve this problem, the thesis deals with exhaustive comparison between the performance oftwo estimation methods, the hard computing Newton Raphson numerical method and the soft computing neural networks method. The performance metrics used for the comparison are: estimation error for position and orientation and average time taken, tolerance to external disturbances and uncertainties present in the manipulator. The methods are compared using various trajectories. Simulation results showed that, the numerical algorithm, irrespective of initial conditions taken, always has more estimation error than neural network. Moreover, it was found that numerical algorithm takes longer average time while neural network takes less average time with uniform estimation error for all trajectories. Hence wefound that using neural network improves control performance. The second application of soft computing techniques dealt in the thesis is improving robustness of existing controllers. In Stewart platform manipulator, there are two basic approaches used for controller design, namely joint space approach and task space approach. In the joint space approach, the controller is a collection of single input single output (SISO) systems implemented using local information on each actuator length only and the coupling between legs is ignored or is considered as a disturbance. The most important and practically used joint space SISO controller is PID control. The advantage of this approach is that local information required for feedback is obtained easily using simple sensors and the control algorithm is easy for parallel implementation. Due to this, the control algorithm is able to execute reasonably fast. But the performance of such controllers quickly degrades when the manipulator speed is increased. In the thesis, a solution to this problem is proposed using fuzzy logic, where the three gain parameters of the PID controller are tuned using fuzzy logic system. Though using fuzzy logic to tune PID controllers has been proposed by earlier researchers for other systems, it has not been used for Stewart platform. Moreover, in our proposed controller, the fuzzy logic system has additional advantage of achieving synchronization. Hence in our proposal, like the joint space PID control, each leg is controlled by a PID controller but the gains are varied by a fuzzy logic system. The input to each fuzzy logic system is a weighted sum of errors in all legs and the rate of change of the weighted sum of errors. The weight factor is taken based on intuition and it enables to minimize the coupling error between the legs, which is drawback of independent leg PID control. Simulation results showed that the controller has better performance than simple PID controller in terms of tracking accuracy and robustness against parameter uncertainty. The third application of soft computing techniques discussed in the thesis is in the design of three types of sliding mode controllers. These are: task space fuzzy sliding mode controller (TFSMC), fuzzy sliding mode controller with integral loop (FSMCPI) and hybrid sliding mode controller with synchronization error. The FSMC presented utilizes the full dynamics of the manipulator and fuzzy logic is used as switching controller. Task space HI position and velocity errors are used as inputs to the fuzzy logic system and their universe of discourse is selected based on disturbance bounds. Simulation results have shown that it performs better than joint space PID but it has small control signal chattering which is the usual problem of sliding mode controllers. To solve this problem, external PI loop is used to enhance the performance ofthe controller. The assumption taken is that the PI loop serves as along time average calculator and minimizes chattering. Simulation results have shown that the FSMCPI performs better than both independent PID controller and fuzzy sliding mode controller. However, a better result is obtained by using hybrid implementation. The hybrid sliding mode controller is a combination of task space and joint space approaches. The switching controller part of the sliding mode controller is implemented in joint space and the model based equivalent control part is implemented in task space. The hybrid structure makes the controller easier to implement and avoids the need for forward kinematics estimation. Moreover the controller uses a newly proposed sliding surface which helps to drive synchronization error to zero and the controller achieves high performance in task space. The fourth application of soft computing used in this thesis is evolutionary computing technique of genetic algorithm. In this thesis, it is used to solve an important design problem, viz., design of integral sliding mode controller for systems having unmatched uncertainty. There are various methods proposed to solve the basic drawbacks of classical sliding mode controller. These include: higher order sliding modes, boundary layer methods and integral sliding mode control. Integral sliding mode control (ISMC) is an improvement over conventional SMC and uses a nonlinear sliding surface having an integral term. It is able to remove reaching phase problem of conventional sliding mode by using a sliding surface which is designed to constrain the system states to be on sliding mode from initial time. Moreover, the sliding surface of ISMC improves the stability of sliding dynamics and it attempts to enhance robustness against unmatched uncertainties. Nonetheless the design of sliding surface of ISMC is not a simple task and has no formal methods, especially for nonlinear systems with unmatched uncertainty. To solve this problem, the design of integral sliding mode controller is formulated as optimization problem and genetic algorithm is used for its solution. The application of the method to SISO and MMO systems is discussed using examples. Finally genetic algorithm based multi-objective optimization is proposed as a

design method for design of integral sliding mode controller for Stewart platform manipulators. The simulation results of the controller designed using the proposed method shows that the method can effectively be used for the design of ISMC for MMO systems having unmatched uncertainty. In the last part ofthe thesis, as fifth application ofsoft computing technique, a new controller having a better robustness and performance is presented. The controller is a neuro-fuzzy sliding mode controller. The controller has two parts: fuzzy logic system and neural network. The fuzzy logic and neural network parts are used concurrently but each part is responsible for one phase ofsliding mode controller. The fuzzy logic system is utilized to control reaching phase dynamics and the feedforward neural network is employed to keep the system states on the sliding surface. The neural network is trained online using modified back propagation algorithm. When the controller is used in a closed loop system, initially the fuzzy logic system part ofthe controller is dominant and has bigger output but as the system moves from reaching phase to sliding phase, the neural network part becomes more active as it learns the dynamics of the system. This hybrid computing paradigm is effective to avoid chattering and to better handle uncertainties. The stability of the system is analyzed using Lyapunov's direct method. The proposed controller is implemented to regulate a second order nonlinear uncertain system and simulation results confirm that the proposed system reduces chattering and improves transient response. All in all, the thesis deals with the various ways of using soft computing techniques for robust and high performance control of Stewart platform manipulator. The stability of all ofthe robust controllers designed for Stewart platform manipulator have been analyzed using Lyapunov's method and were implemented using Simmechanics toolbox of MATLAB and simulink. The controllers have been checked by taking wide uncertainty limits to minimize challenges in practical implementation. All of the simulations have shown promising results. The controllers discussed in the thesis are not only useful for the advancement of the field of robotics control but also have wider contribution to the field of nonlinear system control.