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

Yes. In this letter, we prove that the closed-loop 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 frm, which have an inherent Lagrangian symmetry.