Irreducible Motion Planning by Exploiting Linear Linkage Structures

Andreas Orthey (1) , Olivier Roussel (1) , Olivier Stasse (1) , Michel Taïx (1)

1 LAAS-GEPETTO - Équipe Mouvement des Systèmes Anthropomorphes

Irreducibility is a theoretical framework for completeness-preserving dimensionality reduction in motion planning. While classical motion planning searches the full space of continuous trajectories, irreducible motion planning searches the space of minimal swept volume trajectories, called the irreducible trajectory space. We prove that planning in the irreducible trajectory space preserves completeness. We then apply this theoretical result to linear linkage structures, which can be found in several mechanical systems, among them humanoid robots. Our main result establishes that we can reduce the dimensionality of linear linkages in the case where the first link moves on curvature-constrained curves. We further develop a curvature projection method, which can be shown to be curvature-complete, a weaker version of general completeness. As an application, we consider the simplification of humanoid motion planning by considering the arms and legs as linear linkages.

Mots clés: Motion Planning; Irreducible Trajectories; Linear Linkages; Swept Volume; Humanoid Robots

Domaines: Robotique [cs.RO]

Andreas Orthey, Olivier Roussel, Olivier Stasse, Michel Taïx. Irreducible Motion Planning by Exploiting Linear Linkage Structures. 2015. ⟨hal-01163259⟩