Exploiting structure in humanoid motion planning

If humanoid robots should work along with humans and should be able to solve repetitive tasks, we need to enable them with a skill to autonomously plan motions. Motion planning is a longstanding core problem in robotics, and while its algorithmic foundation has been studied in depth, motion planning is still an NP-hard problem lacking efficient solutions. We want to open up a new perspective on the problem by highlighting its structure: the behavior of the robot, the mechanical system of the robot, and the environment of the robot. We will investigate the hypothesis that each structural component can be exploited to create more efficient motion planning algorithms. We present three algorithms exploiting structure, based on geometrical and topological arguments: first, we exploit the behavior of a walking robot by studying the feasibility of footstep transitions. The resulting algorithm is able to plan footsteps avoiding up to 60 objects on a 6 square meters planar surface. Second, we exploit the mechanical system of a humanoid robot by studying the linear linkage structures of its arms and legs. We introduce the concept of an irreducible motion, which is a completeness-preserving dimensionality reduction technique. The resulting algorithm is able to find motions in narrow environments, where previous sampling-based methods could not be applied. Third, we exploit the environment by reasoning about the topological structure of contact transitions. We show that analyzing the environment is an efficient method to precompute relevant information for efficient motion planning. Based on those results, we come to the conclusion that exploiting structure is an essential component of efficient motion planning. It follows that any humanoid robot, who wants to act efficiently in the real world, needs to be able to understand and to exploit structure