# Study provides complete analytical characterization of optimal collision-free motion for two robots

- Source: arXiv cs.RO
- Published: 2026-11-02T05:00:00.000Z
- RoboHot: https://robohot.news/en/items/ziiq2dnxmwfnj0gmbeisx229z
- Original: https://arxiv.org/abs/2610.41558

## Summary

The paper derives a complete analytical characterization of optimal collision-free trajectories for two robots moving from rest to rest under double-integrator dynamics and a squared-acceleration objective. It proves that these trajectories belong to eight contact families and gives the family determination for each combination of initial and final positions. The authors analyze the geometric properties of the optimal trajectories, provide a numerical computation algorithm, and discuss how these results can improve the performance of existing numerical trajectory optimizers.