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 timeoptimal 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 the efficiency and practicality of the proposed framework.

Predictive path-accurate scaling of a sensor-based defined trajectory

“…Thus optimization methods as e.g. [1], [2], [3] are too slow. Instead, the computation time should be below 1 ms, even if this results in a sub-optimal trajectory.…”

A sequential log barrier method for solving convex-concave problems with applications in robotics

“…The proposed algorithm is a sequential convex programming (SCP) method which sequentially linearizes the concave parts of the inequality constraints while preserving the convex parts. This method is both theoretically and practically appealing: theoretically it ensures that a stationary point of the non-convex problem is attained [9] and in practice fast convergence in only a few iterations is observed for typical applications [3], [10].…”

Successive dynamic programming and subsequent spline optimization for smooth time optimal robot path tracking

“…Smooth trajectories can be achieved by taking jerk or torque rate restrictions into account. In Constantinescu and Croft (2000) and Oberherber et al (2014) methods to consider them in phase space are presented, while Debrouwere et al (2013) proposes a sequential convex scheme to solve a nonlinear program. However, for standard six axis industrial robots and long geometric paths the calculation effort is enormous due to the high number of optimization variables and restrictions.…”