Trajectory planning and control of kinematically redundant robotic manipulators

摘要

This dissertation dealt with the development of trajectory planning schemes and advanced control schemes for kinematically redundant robotic manipulators (KRRM), classified as manipulators whose number of joints is greater than the dimension of the workspace. A globally optimal joint trajectory planning scheme was developed by applying the Pontryagin's Minimum Principle. This is an off-line optimization scheme which employed the shooting method to numerically solve the associated two point boundary value problem, and thereby to optimally resolve the KRRM redundancy. KRRM joint limits were taken into account by two considered methods, the penalty function method and the state space augmentation method. Using the above methods, the singularity avoidance, joint limit avoidance and motion conservativity at position/joint level were achieved simultaneously on the resultant optimal joint trajectories. The output of the optimal trajectory planning scheme is a set of desired joint control points satisfying the trajectory optimalities. An error-based direct adaptive control scheme was developed in order to deal with considerable uncertainties in KRRM dynamic model, including highly non-linear and coupled dynamic equations, joint frictions, gear backlashes, sudden payload changes and other external disturbances. The adaptation scheme is obtained using the Lyapunov Theorem and the concept of model reference adaptive control. This control scheme was developed in joint space and consists of a proportional feedback term, a derivative feedback term and a feedforward compensator. The developed scheme is very computationally efficient as compared to existing model-based adaptive control schemes because it does not require the manipulator dynamics. In order to evaluate the above developed trajectory planning and adaptive control schemes, intensive computer simulations were performed on a three degree-of-freedom planar KRRM model considered for two-dimensional tasks. Several study cases were conducted with the desired joint trajectories generated by the optimal trajectory planning scheme, serving as the reference inputs to the adaptive control scheme. Computer simulation results showed that conservative trajectories avoiding joint limits and singularities were generated by the globally optimal trajectory planner. Simulation results also manifested that the developed adaptive control scheme was able to successfully react to sudden change in payload, dynamic uncertainties and time-varying manipulator parameters.