Peter Werner, Alexandre Amice, Tobia Marcucci, Daniela Rus, and Russ Tedrake
Many computations in robotics can be dramatically accelerated if the robot configuration space is described as a collection of simple sets. For example, recently developed motion planners rely on a convex decomposition of the free space to design collision-free trajectories using fast convex optimization.
In this work, we present an efficient method for approximately covering complex configuration spaces with a small number of polytopes. The approach constructs a visibility graph using sampling and generates a clique cover of this graph to find clusters of samples that have mutual line of sight. These clusters are then inflated into large, full-dimensional, polytopes.
We evaluate our method on a variety of robotic systems and show that it consistently covers larger portions of free configuration space, with fewer polytopes, and in a fraction of the time compared to previous methods.
The collision-free configuration space of a simple robot is decomposed into 7 polytopes, achieving around 92% coverage. Left: Robot with with 3 revolute joints q1 to q3. Center: Visualization of the full collision-free configurationspace Cfree , given by the interior of the green mesh. Right: Approximate convex cover of Cfree generated with the proposed method.
This work was supported in part by Amazon.com PO#2D-06310236, Air Force Research Laboratory FA8750-19-2-1000, Office of Naval Research (ONR), Awards No. N00014-22-1-2121 and N00014-18-1-2830, and the Toyota Research Institute (TRI).