Safety control for a 2-DOF planar manipulator based on penalty Quadratic Program

This paper studies the safety control problem for 2-DOF planar robot manipulator. While quadratic program (QP) has proven to be a powerful tool to design the safety-critical controllers for nonlinear systems by combining control Lyapunov and control barrier functions (CLF and CBF), the application to robotic systems is not easy due to the complexity of the structure and multiple coupling constraints. In this paper, an alternative penalty QP is explored to address the safety controller synthesis process of the robot manipulator. First, backstepping approach is employed to derive the CLF constraint by taking into account the Euler-Lagrangian dynamics of the manipulator. Second, the energy-based CBF constraint is constructed to enforce safety of the controllers. Third, integrating the CLF constraint into the objective function as a penalty term formulates a safety QP with stability penalty. Finally, an automatically Lipschitz controller with a closed form expression is presented by solving the penalty-based QP problem. Simulations demonstrate our results.