Hierarchical Motion Planning in Topological Representations

Motion can be described in alternative representations, including joint configuration or endeffector spaces, but also more complex topological representations that imply a change of Voronoi bias, metric or topology of the motion space. In particular 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 motion synthesis in only a topological space is insufficient since it does not account for additional tasks and constraints in other representations. In this paper we propose methods to combine and exploit different representations for motion synthesis and generalization of motion to novel situations. Our motion synthesis approach is formulated in the framework of optimal control as an approximate inference problem. This 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 benefit 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. In real world we demonstrate the use of topological representations for online motion generalization in dynamic environments.