Safety-Critical Control of Euler-Lagrange Systems Subject to Position Constraints

This paper studies the safety-critical control problem for Euler-Lagrange (EL) systems subject to multiple position constraints. The major contribution lies in a new cascade design of safety-critical controllers. The outer-loop controller is developed based on quadratic programming (QP). A velocity-tracking controller is designed to form the inner loop. One major difficulty is caused by the possible non-Lipschitz continuity of the standard QP algorithm. To solve this problem, we propose a refined QP algorithm with reshaped feasible set and relaxation factor such that the outer-loop controller is locally Lipschitz. It is proved that the safety-critical control objective can be accomplished as long as the EL systems under consideration satisfy a mild initial condition. The proposed design is validated by simulation results on a 2-link planar manipulator.