Robot trajectory generation for paths with kinematic singularities

Abstract

This thesis considers the problem of trajectory generation for robot manipulators along fixed Cartesian paths which contain, or pass near, kinematic singularities. Following a path near singularities can cause very large velocities and accelerations in the robot's joints. Results are presented in this thesis to help understand and cope with this problem. Attention is focused on Cartesian paths which are piecewise analytic. First, it is shown that the joint solutions for such paths can always be expressed, in the neighborhood of a singularity, by means of a fractional power series. This implies a way to smoothly reparameterize the joint solution in the vicinity of a singularity. Second, the Optimal Admissible Timing (OAT) algorithm is presented, which utilizes this reparameterization to generate a minimum-time trajectory along a prescribed path, subject to fixed bounds on the velocities and accelerations of the robot's joints. Finally, an approximate implementation, called the Discrete Admissible OAT (DAO) algorithm, is presented, which works by specifying path velocities at a discrete set of knot points within the path interval. Experimental results are shown for the planar 2R robot and the PUMA robot.