A complete analytical characterization of optimal collision-free motion for two robots
Overview
This paper presents a complete analytical characterization of optimal collision-free trajectories for two robots starting and ending at rest under double-integrator dynamics with a squared-acceleration objective. The authors prove that these trajectories belong to eight distinct contact families, determine which family applies for each configuration of initial and final positions, analyze the geometrical properties of the optimal trajectories, provide a numerical algorithm for computing them, and discuss how these insights may improve the performance of existing numerical trajectory optimizers.
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“arXiv:2610.41558v1 Announce Type: new Abstract: Collision-free motion planning for multi-agent robotic systems remains an active research area because of the complexity of coordinating robot trajectories, with applications ranging from coordinated drone shows to autonomous operations on land, in the air, and on water. Importantly, the analytical difficulty of nonconvex collision-avoidance constraints has so far drive”
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- arXiv Robotics — research abstractsSignalA complete analytical characterization of optimal collision-free motion for two robots
This paper presents a complete analytical characterization of optimal collision-free trajectories for two robots starting and ending at rest under double-integrator dynamics with a squared-acceleration objective. The authors prove that these trajectories belong to eight distinct contact families, determine which family applies for each configuration of initial and final positions, analyze the geometrical properties of the optimal trajectories, provide a numerical algorithm for computing them, and discuss how these insights may improve the performance of existing numerical trajectory optimizers.
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