Practical Time-Optimal Trajectory Planning for Robots: a Convex Optimization Approach

Abstract

This paper focuses on time-optimal path-constrained trajectory planning, a subproblem in time-optimal motion plan- ning of robot systems. Through a nonlinear change of variables, the time-optimal trajectory planning is transformed here into a convex optimal control problem with a single state. Various convexity-preserving extensions are introduced, resulting in a versatile approach for optimal trajectory planning. A direct tran- scription method is presented that reduces finding the globally optimal trajectory to solving a second-order cone program using robust numerical algorithms that are freely available. Validation against known examples and application to a more complex example illustrate the versatility and practicality of the new method.