Time-Optimal Path Tracking for Robots: A Convex Optimization Approach

Abstract

This paper focuses on time-optimal path-constrained trajectory planning, a subproblem in time-optimal motion planning 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 transcription 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.Index Terms-time-optimal trajectory planning, time-optimal control, convex optimal control, path tracking, trajectory planning, convex optimization, second-order cone program, direct transcription.

Fast Interpolation and Time-Optimization on Implicit Contact Submanifolds

“…The classical method integrates the time scaling variable along dynamic limits [2], but as identified in [9,13], this method was found to suffer from numerical instability issues at dynamic singularities. Recent work formulated a more robust convex optimization approach that casts time optimization as a second-order cone program (SOCP) [15]. This paper presents a simpler convex formulation that can be solved via sequential linear program (SLP), for which fast and robust implementations are widely available.…”

“…Scalability to very high-DOF robots is improved by quickly pruning irrelevant constraints. As a result the method solves 100D problems about as quickly as the prior authors [15] solved a 6D one.…”

Convex Optimization approach for Time-Optimal Path Tracking of Robots with Speed Dependent Constraints

“…The decoupled approach is composed of two stages: path planning and path tracking. The path planning stage is concerned with geometric constraints and obstacle avoidance (Nyström and Norrlöf, 2003), whereas dynamic aspects such as manipulator constraints are concerns of the path tracking stage (Verscheure et al, 2009). …”

“…To achieve this it is necessary to have a complete model of the manipulator and the actuator constraints (Shin and McKay, 1985, Bobrow et al, 1985, Shin and McKay, 1986, Pfeiffer and Johanni, 1987, Slotine and Yang, 1989, Tarkiainen and Shiller, 1993, Constantinescu and Croft, 2000. As shown in (Verscheure et al, 2009) it is straightforward to do the optimization with respect to energy instead of cycle time or a combination of both time and energy. In this paper the result in (Verscheure et al, 2009) is extended to cover speed dependent constraints, such as viscous friction in the model.…”

“…As shown in (Verscheure et al, 2009) it is straightforward to do the optimization with respect to energy instead of cycle time or a combination of both time and energy. In this paper the result in (Verscheure et al, 2009) is extended to cover speed dependent constraints, such as viscous friction in the model. In Section 2 the theory from (Verscheure et al, 2009), on which this paper is based, is briefly discussed.…”