Collision free motion planning on a wedge of circles
This work addresses a specific motion planning problem in robotics, but it is incremental as it focuses on a particular track geometry.
The paper tackled the problem of planning collision-free motion for two robots on a wedge-shaped track of three circles, and the result was an optimal algorithm requiring exactly 3 continuous instructions, matching the topological complexity of the configuration space.
We exhibit an algorithm with continuous instructions for two robots moving without collisions on a track shaped as a wedge of three circles. We show that the topological complexity of the configuration space associated with this problem is 3. The topological complexity is a homotopy invariant that can be thought of as the minimum number of continuous instructions required to describe the movement of the robots between any initial configuration to any final one without collisions. The algorithm presented is optimal in the sense that it requires exactly 3 continuous instructions.