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

Abstract

Finding the Time-Optimal Parameterization of a given Path (TOPP) subject to kinodynamic constraints is an essential component in many robotic theories and applications. The objective of this article is to provide a general, fast and robust implementation of this component. For this, we give a complete solution to the issue of dynamic singularities, which are the main cause of failure in existing implementations. We then present an open-source implementation of the algorithm in C++/Python and demonstrate its robustness and speed in various robotics settings.

Asymptotic Optimality of a Time Optimal Path Parametrization Algorithm

“…The proof that h satisfies Condition (4) is ommitted since it can be derived analogously. (1) and (2) of Theorem 3, so we turn to deriving Condition (3). As in part (a), the proof of Condition (4) is ommitted as it can be derived analogously.…”

Time-Optimal Path Parameterization of Rigid-Body Motions: Applications to Spacecraft Reorientation

“…then efficient methods and implementations allow finding the timeoptimal parameterization st (see, e.g., [9]). Consider now a rigid body with three independent actuations, such as a rigid spacecraft whose equation of motion is [2][3][4] I _ ω ω × Iω τ (11) in which I is the 3 × 3 inertia matrix of the spacecraft, and τ the 3-D torque vectors.…”

“…Regarding steps 2 and 3, the crucial requirement is the ability to optimally time parameterize a given path in SO(3) under kinodynamic constraints. We do so by extending the classical [7][8][9] time-optimal path parameterization (TOPP) algorithm to the case of SO(3), which constitutes the main contribution of this note. We show that, overall, the method we propose can find fast maneuvers for a satellite model in a cluttered environment in less than 10 s. We also present an extension to the space of three-dimensional (3-D) rigid-body motions, SE(3).…”

Dynamic non-prehensile object transportation

“…Next, the geometric and kinodynamic constraints of the robot can be expressed as functions of path parameter s. In the sequel, an inequality constraint is said to be in the Bobrow form [7] if it is expressed as…”