A General, Fast, and Robust Implementation of the Time-Optimal Path Parameterization Algorithm

Finding the Time-Optimal Parameterization of a given Path(TOPP) subject to kinodynamic constraints is an essential component inmany robotic theories and applications. The objective of this article isto provide a general, fast and robust implementation of this component.For this, we first derive a general formulation of the TOPP problemand show how diverse robot dynamics and constraints can be castinto this formulation. Next, we give a complete solution to the issueof dynamic singularities, which are the main cause of failure in existingimplementations. Based on these two contributions, we provide an open-source implementation of the algorithm in C++/Python and demonstrate its efficiency in some complex kinodynamic planning problems.