Robot kinematics is the study of the geometric relationships and motions of the links and joints of manipulators, without considering the forces and torques being applied to produce these motions. The relation of motion to torques and forces is the domain of dynamics. Direct kinematics concerns the computation of the positions and motions of the robot end effector, given the motion at the joints (where the motors are located). Inverse kinematics has to do with the computation of joint motions required to produce desired displacements or velocities in the Cartesian work space of the end-effector.
This research monograph provides an exhaustive treatment of robot kinematics, both direct and inverse. The emphasis is on the development of symbolic solutions for the direct kinematics problem. A rule-based Prolog program is developed for symbolic generation of the direct kinematics solution and the Jacobian matrix for a robot with given link parameters. The book suffers from two problems: (1) it concentrates entirely on kinematics, although much contemporary work in robotics is concerned with problems of dynamics; and (2) development of the symbolic solutions in Prolog does not take advantage of available tools such as Macsyma or Mathematica, which can dramatically simplify the process.
The book contains a significant amount of original material. In addition to the Prolog-based solution of the direct kinematic problem, it presents a new algorithm for deriving the manipulator Jacobian matrix and efficient iterative algorithms for solution of inverse kinematic problems. While it includes substantial discussion of visualization of the kinematic mechanisms and formulation of mathematical models, this book is clearly for specialists. It assumes significant familiarity with vectors, matrices, and basic mechanisms, as well as some background in robotics.
Chapter 1 is basically a statement of the objectives for the research that formed the basis for the book. Chapter 2 is a cursory review of the literature, which can only be followed by readers with a substantial background in the field. Chapter 3 begins with some mathematical background and then presents the development of a mathematical model of the geometric relationships between joints and links, and its direct kinematic solution. Basically, the resulting equations can be used to control the position of the robot end effector. The following chapter deals with differential motions, thus making possible the derivation of a speed control model, which relates differential end point motion with the corresponding joint motions.
Chapter 5, extracted from a paper published by the authors, presents a symbolic solution of the direct kinematics problem and its implementation in Turbo Prolog. Chapter 6 is devoted entirely to three approaches to the inverse kinematics problem. The first two yield symbolic closed-form solutions under certain conditions; the third, which is more general, yields an iterative approach to numerical solutions. Finally, chapter 7 presents numerical applications to two commercial robots. Appendices provide listings of the symbolically automated program for direct kinematics (written in Prolog) and of the “arm-wrist partitioned synthesis” method for inverse kinematics (written in Turbo C).
The book is not suitable as a textbook, since it contains no exercises and the writing style is more appropriate to a doctoral dissertation. I recommend it for specialists in robotics who are interested in computational approaches to kinematic problems.
