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Time-Optimal Path Parameterization (TOPP) is a well-studied problem inrobotics and has a wide range of applications. There are two main families ofmethods to address TOPP: Numerical Integration (NI) and Convex Optimization(CO). NI-based methods are fast but difficult to implement and suffer fromrobustness issues, while CO-based approaches are more robust but at the sametime significantly slower. Here we propose a new approach to TOPP based onReachability Analysis (RA). The key insight is to recursively compute reachableand controllable sets at discretized positions on the path by solving smallLinear Programs (LPs). The resulting algorithm is faster than NI-based methodsand as robust as CO-based ones (100% success rate), as confirmed by extensivenumerical evaluations. Moreover, the proposed approach offers unique additionalbenefits: Admissible Velocity Propagation and robustness to parametricuncertainty can be derived from it in a simple and natural way.

A New Approach to Time-Optimal Path Parameterization based on Reachability Analysis