Two robots’ exact collision-free paths solved for optimal movement
A complete analytical characterization of optimal collision-free motion for two robots
Robotics
Summary
Getting two robots to move without bumping into each other is hard. This paper figures out the exact best ways two robots can move from one spot to another without collisions, starting and stopping smoothly. The authors show there are eight kinds of ideal paths and explain which path fits each situation. They also make a method to find these paths quickly, which can help make robots work together better.
What this means in practice
- •For industrial robot operators: Coordinate two robots’ movements precisely in manufacturing to avoid collisions and optimize energy use by following analytically derived paths.
- •For drone fleet managers: Plan energy-efficient, collision-free flight paths for two drones starting and ending at rest, improving coordination in aerial shows or operations.
Authors
Jan Kamm, Antonio Terpin, Raffaello D'Andrea
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 driven the development of exclusively numerical methods. We derive a complete analytical characterization of the optimal trajectories for two robots that start and end at rest, under double-integrator dynamics and a squared-acceleration objective. We prove that these trajectories belong to eight distinct contact families and determine which family applies for each configuration of initial and final positions. We 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.