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

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 un-modeled 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 the efficiency and practicality of the proposed framework.