Topology-based Representations for Motion Planning and Generalisation in Dynamic Environments with Interactions

Motion can be described in several alternative representations, including joint configuration or end-effector spaces, but also more complex topology-based 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 motion synthesis solely in a topology-based 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 synthesis and generalization of motion in dynamic environments. Our motion synthesis approach is formulated in the framework of optimal control as an approximate inference problem. This allows for consistent combination of multiple representations (e.g., across task, end-effector and joint space). Motion generalization to novel situations and kinematics is similarly performed by projecting motion from topologybased 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 demonstrations, we highlight the benefits of using topology-based representations for online motion generalization in dynamic environments.