SCTOMP: Spatially Constrained Time-Optimal Motion Planning

TL;DR

This paper introduces a novel two-stage motion planning approach for spatial time-optimal trajectories that does not require a collision-free geometric reference, relying only on environment representation and goal location.

Contribution

It presents a new method that combines obstacle-free spline computation with a spatially reformulated optimization to achieve time-optimal motion planning without predefined geometric references.

Findings

Successfully benchmarks the approach on a planar example.

Validates applicability in complex spatial systems.

Guarantees time-optimality through environment-based spline extension.

Abstract

This paper focuses on spatial time-optimal motion planning, a generalization of the exact time-optimal path following problem that allows the system to plan within a predefined space. In contrast to state-of-the-art methods, we drop the assumption that a collision-free geometric reference is given. Instead, we present a two-stage motion planning method that solely relies on a goal location and a geometric representation of the environment to compute a time-optimal trajectory that is compliant with system dynamics and constraints. To do so, the proposed scheme first computes an obstacle-free Pythagorean Hodograph parametric spline, and second solves a spatially reformulated minimum-time optimization problem. The spline obtained in the first stage is not a geometric reference, but an extension of the environment representation, and thus, time-optimality of the solution is guaranteed. The efficacy of the proposed approach is benchmarked by a known planar example and validated in a more complex spatial system, illustrating its versatility and applicability.