Is There a Closed-Loop Lagrangian for Hierarchical Motion Control?

Yes. In this paper, we prove that the closedloop Lagrangian in hierarchical motion control is an Euler-Lagrange system with symmetry, which additionally has geodesic invariance along the symmetry. The proposed theory enables a hierarchical control synthesis, in which the energetic behaviour is prescribed in advance. Using this approach, we derive a hierarchical control for the Floating-base Robotic Mechanisms, which has an inherent Lagrangian symmetry.