In recent decades, robotics has attracted more and more attention from researchers since it has been widely used in scientific research and engineering applications, such as space exploration, underwater surveys, industrial and military industries, welding, painting and assembly, medical applications, and so on. Much effort has been spent on robotics, and different types of robot manipulators have thus been developed and investigated, such as serial manipulators consisting of redundant manipulators and mobile manipulators, parallel manipulators, and cable‐driven manipulators. A redundant manipulator is often designed as a series of links connected by motor‐actuated joints that extends from a fixed base to an end‐effector while a mobile manipulator is often designed as a robotic device composed of a mobile platform and a redundant manipulator fixed to the platform. Different from these serial manipulators, a parallel manipulator is a mechanical system that usually uses several serial chains to support a single platform, or end‐effector. Using these manipulators to save labor and increase accuracy is becoming common practice in various industrial fields. As a consequence, many approaches have been proposed, investigated and employed for the control of robot manipulators. Among them, thanks to the many advantages in parallel distributed structure, nonlinear mapping, ability to learn from examples, high generalization performance, and capability to approximate an arbitrary function with sufficient number of neurons, the neural‐network‐based approach is a competitive way to control movements of robot manipulators.

In this book, focusing on robot arm control aided with neural networks, we present and investigate different methods and schemes for the control of robot arms. The idea for this book on the redundancy resolution of robot manipulators via different methods and schemes was conceived during research discussion in the laboratory and at international scientific meetings. Most of the material of this book is derived from the authors' papers published in journals and proceedings of international conferences. In fact, in recent decades, the field of robotics has undergone phases of exponential growth, generating many new theoretical concepts and applications (including those of the authors). Our first priority is thus to cover each central topic in enough detail to make the material clear and coherent; in other words, each part (and even each chapter) is written in a relatively self‐contained manner.

This book contains 10 chapters which are classified into the following three parts.

• Part I: Neural Networks for Serial Robot Arm Control (Chapter 1 through Chapter 6).
• Part II: Neural Networks for Parallel Robot Control (Chapter 7 and Chapter 8).
• Part III: Neural Networks for Cooperative Control (Chapter 9 and Chapter 10).

Chapter 1 – This chapter breaks these limitations by proposing zeroing neural network (ZNN) models, allowing nonconvex sets for projection operations in activation functions and incorporating new techniques for handing inequality constraint arising in optimizations. Theoretical analyses reveal that the presented ZNN models are of global stability with timely convergence. Finally, illustrative simulation examples are provided and analyzed to substantiate the efficacy and superiority of the presented ZNN models for real‐time dynamic quadratic programming subject to equality and inequality constraints.

Chapter 2 – Variable structure strategy is widely used for the control of sensor‐actuator systems modeled by Euler–Lagrange equations. However, accurate knowledge on the model structure and model parameters are often required for the control design. In this chapter, we consider model‐free variable structure control of a class of sensor–actuator systems, where only the online input and output of the system are available while the mathematic model of the system is unknown. The problem is formulated from an optimal control perspective and the implicit form of the control law is analytically obtained by using the principle of optimality. The control law and the optimal cost function are explicitly solved iteratively. Simulations demonstrate the effectiveness and the efficiency of the proposed method.

Chapter 3 – This chapter identifies two limitations of existing recurrent neural network solutions for manipulator control, i.e., position error accumulation and the convex restriction on the projection set, and overcomes them by proposing two modified neural network models. Similar to the model presented in Chapter 1, the method investigated in this chapter allows nonconvex sets for projection operations, and control error does not accumulate over time in the presence of noise. Unlike most works in which recurrent neural networks are used to process time sequences, the presented approach is model‐based and training‐free, which makes it possible to achieve fast tracking of reference signals with superior robustness and accuracy. Theoretical analysis reveals the global stability of a system under the control of the presented neural networks. Simulation results confirm the effectiveness of the presented control method in both the position regulation and tracking control of redundant PUMA 560 manipulators.

Chapter 4 – In this chapter, we propose a novel model‐free dual neural network, which is able to address the learning and control of manipulators simultaneously in a unified framework. Different from pure learning problems, the interplay of the control part and the learning part allows us to inject an additive noise into the control channel to increase the richness of signals for the purpose of efficient learning. Due to a deliberate design, the learning error is guaranteed for convergence to zero despite the existence of additive noise for stimulation. Theoretical analysis reveals the global stability of the proposed neural network control system. Simulation results verify the effectiveness of the proposed control scheme for redundancy resolution of a PUMA 560 manipulator.

Chapter 5 – In this chapter, we propose a novel recurrent neural network to resolve the redundancy of manipulators for efficient kinematic control in the presence of noises in a polynomial type. Leveraging the high‐order derivative properties of polynomial noises, a deliberately devised neural network is presented to eliminate the impact of noises and recover the accurate tracking of desired trajectories in workspace. Rigorous analysis shows that the presented neural law stabilizes the system dynamics and the position tracking error converges to zero in the presence of noises. Extensive simulations verify the theoretical results. Numerical comparisons show that existing dual neural solutions lose stability when exposed to large constant noises or time‐varying noises. In contrast, the presented approach works well and has a low tracking error comparable with noise‐free situations.

Chapter 6 – In this chapter, we make progress on real‐time manipulability optimization by establishing a dynamic neural network for recurrent calculation of manipulability‐maximal control actions for redundant manipulators under physical constraints in an inverse‐free manner. By expressing position tracking and matrix inversion as equality constraints, physical limits as inequality constraints, and velocity‐level manipulability measure, which is affine to the joint velocities, as the objective function, the manipulability optimization scheme is further formulated as a constrained quadratic program. Then, a dynamic neural network with rigorously provable convergence is constructed to solve such a problem online. Computer simulations are conducted and show that, compared with the existing methods, the proposed scheme can raise the manipulability almost 40% on average, which substantiates the efficacy, accuracy and superiority of the proposed manipulability optimization scheme.

Chapter 7 – In this chapter, the kinematic control problem of Stewart platforms is formulated to a constrained quadratic programming. The Karush–Kuhn–Tucker conditions of the problem are obtained by considering the problem in its dual space, and then a dynamic neural network is designed to solve the optimization problem recurrently. Theoretical analysis reveals the global convergence of the employed dynamic neural network to the optimal solution in terms of the defined criteria. Simulation results verify the effectiveness in the tracking control of the Stewart platform for dynamic motions.

Chapter 8 – In this chapter, we establish a model‐free dual neural network to control the end‐effector of a Stewart platform for the tracking of a desired spatial trajectory, at the same time as learning the unknown time‐varying parameters. The proposed model is purely data driven. It does not rely on the system parameters as a priori and provides a new solution for stabilization of the self motion of Stewart platforms. Theoretical analysis and results show that we can achieve a globally convergent neural model in this chapter. It is also shown to be optimal per the model‐free criterion. In this chapter, numerical simulations are those which highlight and illustrate relatable performance capability in terms of model‐free optimization. Simulation results provided verify the tracking control of the end‐effector efficiently while controlling the dynamic motion of the Stewart platform.

Chapter 9 – In this chapter, a distributed scheme is proposed for the cooperative motion generation in a distributed network of multiple redundant manipulators. The proposed scheme can simultaneously achieve the specified primary task to reach global cooperation under limited communications among manipulators and optimality in terms of a specified optimization index of redundant robot manipulators. The proposed distributed scheme is reformulated as a quadratic program (QP). To inherently suppress noises originating from communication interferences or computational errors, a noise‐tolerant zeroing neural network (NTZNN) is constructed to solve the QP problem online. Then, theoretical analyses show that, without noise, the proposed distributed scheme is able to execute a given task with exponentially convergent position errors. Moreover, in the presence of noise, the proposed distributed scheme with the aid of the NTZNN model has a satisfactory performance. Furthermore, simulations and comparisons based on PUMA 560 redundant robot manipulators substantiate the effectiveness and accuracy of the proposed distributed scheme with the aid of the NTZNN model.

Chapter 10 – This chapter investigates the distributed motion planning of multiple robot arms with limited communications in the presence of noises. To do this, a nonlinearly activated noise‐tolerant zeroing neural network (NANTZNN) is designed and presented for the first time for solving the presented distributed scheme online. Theoretical analyses and simulation results show the effectiveness and accuracy of the presented distributed scheme with the aid of the NANTZNN model.

This book is written for academic and industrial researchers as well as graduate students studying in the developing fields of robotics, numerical algorithms, and neural networks. It provides a comprehensive view of the combined research of these fields, in addition to the accomplishments, potentials, and perspectives. We hope that this book will generate curiosity and interest for those wishing to learn more, and that it will provide new challenges to seek new theoretical tools and practical applications. Without doubt, this book can be extended. Any comments or suggestions are welcome. The authors can be contacted via e‐mail: [email protected]; [email protected]; and [email protected].