Velocity Obstacle for Polytopic Collision Avoidance for Distributed Multi-Robot Systems

Obstacle avoidance for multi-robot navigation with polytopic shapes is challenging. Existing works simplify the system dynamics or consider it as a convex non-convex optimization problem positive distance constraints between robots, which limits real-time performance and scalability. Additionally, generating collision-free behavior polytopic-shaped robots harder due to implicit non-differentiable functions polytopes. In this letter, we extend concept of velocity obstacle (VO) principle propose novel approach construct VO in function vertex coordinates other robot's states. Compared existing work about our much more computationally efficient proposed construction polytopes optimization-free. Based on representation shapes, later distributed systems. We validate multiple challenging scenarios including large-scale randomized tests, outperforms state art many evaluation metrics, completion rate, deadlock average travel distance.