Real-Time-Feasible Collision-Free Motion Planning For Ellipsoidal Objects

TL;DR

This paper introduces a novel, efficient collision avoidance method for ellipsoidal objects using differentiable Minkowski sum constraints, enabling real-time motion planning in robotics and autonomous vehicles.

Contribution

It presents a new collision avoidance constraint formulation based on a parametric over-approximation of the Minkowski sum, improving computational efficiency and real-time applicability.

Findings

Minkowski sum formulation is more efficient than separating hyperplane approach.

Pre-determined over-approximation parameters cause minimal suboptimality.

Method successfully demonstrated in real-world, real-time experiments.

Abstract

Online planning of collision-free trajectories is a fundamental task for robotics and self-driving car applications. This paper revisits collision avoidance between ellipsoidal objects using differentiable constraints. Two ellipsoids do not overlap if and only if the endpoint of the vector between the center points of the ellipsoids does not lie in the interior of the Minkowski sum of the ellipsoids. This condition is formulated using a parametric over-approximation of the Minkowski sum, which can be made tight in any given direction. The resulting collision avoidance constraint is included in an optimal control problem (OCP) and evaluated in comparison to the separating-hyperplane approach. Not only do we observe that the Minkowski-sum formulation is computationally more efficient in our experiments, but also that using pre-determined over-approximation parameters based on warm-start trajectories leads to a very limited increase in suboptimality. This gives rise to a novel real-time scheme for collision-free motion planning with model predictive control (MPC). Both the real-time feasibility and the effectiveness of the constraint formulation are demonstrated in challenging real-world experiments.