Determination of robot trajectories satisfying joint limit and interference constraints using an optimization method

Abstract

An important problem in robotics research is the automatic off-line planning of optimal robot trajectories to perform specified tasks while satisfying physical constraints. This thesis proposes a method for finding an optimal geometric robot trajectory subject to the constraints of joint displacement limits and interference avoidance. A geometric method for calculating the distance between convex polyhedra is presented, and the method is implemented in two dimensions for the calculation of interference. Point-to-point trajectory planning is posed as a two-point boundary value problem in the calculus of variations. The kinematic constraints are formulated as exterior penalty functions and are combined with other optimization criteria to form a cost functional. The problem is solved by discretizing the problem and numerically minimizing the cost functional by using a steepest-descent approach to iteratively modify the trajectory. Any starting trajectory which satisfies the boundary conditions is acceptable, but different starting trajectories may converge to different locally optimal final trajectories. The method has been implemented for the two-dimensional case by an interactive FORTRAN program running on a VAX 11/750 computer. Successful results were obtained for a number of test cases, and further work has been identified to allow application of the method to a wide range of problems.