Motion synthesis for humanoid robot behaviours is made difficult by the combination of task space, joint space and kinodynamic constraints that define readability. Solving these problems by general purpose methods such as sampling based motion planning has involved significant computational complexity, and has also required specialised heuristics to handle constraints. In this paper we propose an approach to incorporate specifications and constraints as a bias in the exploration process of such planning algorithms. We present a general approach to solving this problem wherein a subspace, of the configuration space and consisting of poses involved in a specific task, is identified in the form of a nonlinear manifold, which is in turn used to focus the exploration of a sampling based motion planning algorithm. This allows us to solve the motion planning problem so that we synthesize previously unseen paths for novel goals in a way that is strongly biased by known good or feasible paths, e.g., from human demonstration. We demonstrate this result with a simulated humanoid robot performing a number of bipedal tasks.
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