Leveraging Distance Information to Compute Collision-Free Volumes in Robot Configuration Space
While traditional sampling-based path planning approaches for robotic manipulators, such as RRT (Rapidly-Exploring Random Trees) and PRM (Probabilistic Roadmaps), provide feasible solution paths, convex optimization-based techniques offer some additional features. Some of these methods unfortunately require a representation of the manipulator’s configuration space as a set of convex volumes, which can be challenging to obtain due to the high dimensionality and complexity of the configuration space. This work presents an algorithm for computing convex volumes in the manipulator’s configuration space, called GBur-IRIS. The algorithm combines the structure known as the generalized bur of free C-space with the convex volume-inflating algorithm IRIS (Iterative Regional Inflation by Semidefinite Programming). It follows a simple iterative procedure. First, it computes a generalized bur. Then, it encloses the bur in an ellipsoid. Finally, it uses this ellipsoid to initialize the IRIS algorithm. The paper provides a detailed description of the algorithm and shows an extensive simulation study. This study is conducted on several robotic manipulators and environments, and the results are discussed and compared with existing approaches from the literature.