Hierarchical Motion Planning in Topological Representations

Motion can be described in alternative represen- tations, including joint configuration or end-effector spaces, but also more complex topological representations that imply a change of Voronoi bias, metric or topology of the motion space. Certain types of robot interaction problems, e.g. wrapping around an object, can suitably be described by so-called writhe and interaction mesh representations. However, considering mo- tion synthesis solely in topological spaces is insufficient since it does not cater for additional tasks and constraints in other representations. In this paper we propose methods to combine and exploit different representations for motion synthesis, with specific emphasis on generalization of motion to novel situations. Our approach is formulated in the framework of optimal con- trol as an approximate inference problem, which allows for a direct extension of the graphical model to incorporate multiple representations. Motion generalization is similarly performed by projecting motion from topological to joint configuration space. We demonstrate the benefits of our methods on problems where direct path finding in joint configuration space is extremely hard whereas local optimal control exploiting a representation with different topology can efficiently find optimal trajectories. Further, we illustrate the successful online motion generalization to dynamic environments on challenging, real world problems.