Calculation of time-optimal motion primitives for systems exhibiting oscillatory internal dynamics

TL;DR

This paper introduces a fast, reliable numerical method for calculating time-optimal motion primitives in systems with oscillatory internal dynamics, enabling near real-time trajectory planning without relying on traditional optimization algorithms.

Contribution

It presents a novel numerical calculation approach that explicitly evaluates optimality conditions and reduces the problem to a line-search, ensuring constant computation time and practical implementation.

Findings

The method guarantees a fixed number of computational steps for solutions.

It enables real-time trajectory planning for oscillatory systems.

Experimental validation was performed on a laboratory system.

Abstract

An algorithm for planning near time-optimal trajectories for systems with an oscillatory internal dynamics has been developed in previous work. It is based on assembling a complete trajectory from motion primitives called jerk segments, which are the time-optimal solution to an optimization problem. To achieve the shortest overall transition time, it is advantageous to recompute these segments for different acceleration levels within the motion planning procedure. This publication presents a numerical calculation method enabling fast and reliable calculation. This is achieved by explicitly evaluating the optimality conditions that arise for the problem, and further by reducing the evaluation of these conditions to a line-search problem on a bounded interval. This reduction guarantees, that a valid solution if found after a fixed number of computational steps, making the calculation time constant and predictable. Furthermore, the algorithm does not rely on optimisation algorithms, which allowed its implementation on a laboratory system for measurements with the purpose of validating the approach.