Time-optimal path following for robots with trajectory jerk constraints using sequential convex programming

Abstract

Time-optimal path following considers the problem of moving along a predetermined geometric path in minimum time. In the case of a robotic manipulator a convex reformulation of this optimal control problem has been derived previously [1]. However, the bang-bang nature of the time-optimal trajectories results in near-infinite jerks in joint space and operational (Cartesian) space. For systems with unmodeled flexibilities, this usually results in excitation of the resonant frequencies, hence in unwanted vibrations and acceleration peaks, contributing to a tracking error. These vibrations can be reduced by imposing jerk constraints on the trajectory [2]. However, these jerk constraints destroy the convexity of the time-optimal control problem. The present paper proposes an efficient sequential convex programming (SCP) approach to solve the corresponding non-convex optimal control problem by writing the non-convex jerk constraints as a difference of convex (DC) functions. We illustrate the developed approach by means of experiments with a seven d.o.f. robot. Furthermore, numerical simulations illustrate the fast convergence of the proposed method in only a few SCP iterations, confirming