Safe Control with Control Barrier Function for Euler-Lagrange Systems Facing Position Constraint

This paper provides a control barrier function (CBF)-based control for general Euler-Lagrange (EL) systems to ensure safety. The objective is to guarantee the forward invariance of the safe set. In the presence of constraints, directly applying the nominal control may make the system violate constraints. It could deteriorate the system stability and cause hardware failure in the worst case. To address this problem, we propose a control scheme and formulate the corresponding control barrier function. Furthermore, we present control of constrained 2-DOF manipulators as an example to show how to implement our proposed solution to EL systems. The effectiveness of the proposed solution is demonstrated through simulations.