Technology Category
Planning, Routing, and Scheduling: Replanning and Plan RepairSearch and Optimization: Sampling/Simulation-based SearchIntelligent Robots: Motion and Path Planning
Real-Time-Feasible Collision-Free Motion Planning For Ellipsoidal Objects
🤖 AI Summary
Real-time, collision-free trajectory planning for ellipsoidal objects—such as vehicle bounding volumes or uncertainty ellipsoids—in robotic and autonomous driving applications remains computationally challenging due to the high cost of exact geometric collision checking.
Method: This paper proposes a differentiable motion planning framework that embeds geometric constraints into an optimal control problem (OCP) solved within a model predictive control (MPC) architecture. Its core innovation is the first integration of direction-adaptive Minkowski sums with tight over-approximations into differentiable collision constraints, circumventing the computational overhead of classical separating hyperplane methods. A warm-started parameterization strategy further accelerates convergence.
Contribution/Results: The method achieves millisecond-scale online replanning on real-world hardware while maintaining low suboptimality and high obstacle avoidance success rates. It establishes a new paradigm for safe, real-time navigation of ellipsoidal agents in dynamic environments.
Technology Category
Application Category
📝 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.
Problem
Research questions and friction points this paper is trying to address.
Online collision-free trajectory planning for ellipsoidal objects
Differentiable Minkowski-sum constraints for collision avoidance
Real-time MPC-based motion planning with efficient computation
Innovation
Methods, ideas, or system contributions that make the work stand out.
Uses Minkowski sum for ellipsoid collision avoidance
Integrates collision constraints into optimal control
Enables real-time planning with model predictive control
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