Kinematics and trajectory synthesis of manipulation robots
This is the third text in the series 'Scientific Fundamentals of Robotics,' published by Springer-Verlag. The first two books dealt with the dynamics and control of manipulation robots respectively. The third book is mostly concerned with manipulator kinematics. Efficient methods for evaluating the symbolic kinematic models and the motion generation algorithms for nonredundant and redundant manipulators are presented. Roboticists who have read the research papers in the field of kinematics over the last decade by the authors will find much that is familiar in this text. Although the work is also intended to provide teaching material for postgraduate robotics courses, the monographic nature of the work and the mathematical notations make the text more suitable as a specialist reference text than as a recommendable reading in the general area of robot kinematics and trajectory synthesis. Similarly to the previous two books of the series, a great number of the references is either from the Eastern Block or by Vukobratovic and his co-authors. The book is organized into 6 chapters. Chapter 1 contains the basic kinematic relations to describe manipulator position and orientation. Two methods for kinematic modeling are outlined. The first method is based on Rodriguez' formula describing a finite rotation of a rigid body about a fixed axis, while the second approach uses the more widely adopted homogeneous transformations based on Denavit-Hartenberg kinematic notation. Cartesian, spherical and cylindrical coordinates are adopted to describe the end-effector position. Euler angles and Euler parameters are used for the end-effector orientation. Jacobian matrices relating linear and angular velocities of the end-effector to joint velocities are also derived. In chapter 2 a method for the automatic, computer-aided generation of the symbolic kinematic equations and of the Jacobian matrices for an arbitrary serial-link manipulator is presented. The goal is to obtain a minimal number of floating-point multiplications and additions. Backward and forward recursive relations are derived. A block-diagram of the program for the symbolic model generation, numerical aspects issues and application examples are finally provided. One of the hottest research topics in robotics, namely the inverse kinematic problem, is considered in chapter 3. Analytical solution methods are first derived; they are shown to be feasible only for kinematically simple manipulators. Some numerical solution methods are then illustrated and compared to each other on the basis of computational burden and occurrence of kinematic singularities. Methods for manipulator motion generation are presented in the following two chapters. Chapter 4 contains a review of the purely kinematic approach to motion generation. Continuity of position, velocity and acceleration is provided. Interpolated motion functions are derived both in the joint space and in the task space. On the other hand, the dynamic approach which is an important of the research work by the authors is the core of chapter 5. The system is considered as a dynamic system modeled by the complete, nonlinear dynamic model of the mechanism and the actuators. A short review of the methods for dynamic motion synthesis is given first. An algorithm for determining the energy optimal velocity distribution using dynamic programming is then presented. All such methods are intended for off-line motion generation. Thus a method for quasi-optimal nominal trajectory synthesis which is implementable in real time is illustrated. Some examples are provided. The interesting issue of motion generation for redundant manipulators is finally dealt with in chapter 6. A variety of kinematic methods for motion generation are treated first. The synthesis of nominal trajectories for redundant manipulators based on a new dynamic approach both in free workspace and in an obstacle-cluttered environment is proposed. In sum, many of the concepts in this text are treated in a detailed and thorough manner. This book is a valuable addition to the specialist texts on kinematics and trajectory synthesis for robotic manipulators.
scientific article; zbMATH DE number 3930804