Topological duality in humanoid robot dynamics (Q2762253)

This paper develops an abstract framework for the study of humanoid robot dynamics. The authors view a humanoid robot system as a collection of segments coupled at rotational joints that are represented geometrically by constrained rotational Lie groups. They construct and analyze dual invariant topological structures on finite dimensional manifolds associated with humanoid motions. The authors investigate both cohomology and homology structures on tangent and cotangent bundles of the humanoid motion configuration manifold. The latter is represented as a toral Lie group. The authors demonstrate that both cohomology and homology groups, acting on momentum -- as well as velocity-phase space manifolds of humanoid motion, provide essentially the same description of humanoid dynamics.