Motion planning and irreducible trajectories

We introduce a novel notion for lowering the dimensionality of motion planning problems: Irreducibility. Irreducibility of a configuration space trajectory τ means: We cannot find another configuration space trajectory τ', such that the swept volume of τ' is included in the swept volume of τ. The main contribution of our work is twofold: First, we show that motion planning in the space of irreducible trajectories is complete. Second, we show that we can construct reducible subspaces by reasoning about the inherent hierarchical structure of open kinematic chains. Using those theoretical results, we proceed by analytically defining a 7-dimensional irreducible configuration subspace for the humanoid robot HRP-2 under some assumptions. To show its practical importance, we solve a high-dimensional pin-hole problem for HRP-2 from the scratch.