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

2009/09/24 by Diederik Verscheure, D. Verscheure, Bram Demeulenaere +7 · 542 citations
Computer Science · Engineering · Mathematics · #Artificial intelligence #Computer science #Control (management) #Control theory (sociology) #Convex optimization #Convexity #Guidance and Control Systems #Mathematical optimization #Mathematics #Motion planning #Nonlinear system #Optimal control #Path (computing) #Regular polygon #Robot #Robotic Mechanisms and Dynamics #Robotic Path Planning Algorithms #Tracking (education) #Trajectory

paper · open access · doi:10.1109/tac.2009.2028959

published in IEEE Transactions on Automatic Control 54(10), 2318-2327 (Institute of Electrical and Electronics Engineers)

openalex publication_date 2009/09/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29

Abstract

This paper focuses on time-optimal path tracking, a subproblem in time-optimal motion planning of robot systems. Through a nonlinear change of variables, the time-optimal path tracking problem is transformed here into a convex optimal control problem with a single state. Various convexity-preserving extension are introduced, resulting in a versatile approach for optimal path tracking. 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.

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