Safe Approximate Optimal Control of Nonzero-Sum Games for Modular Robot Manipulator Systems Based on Control Barrier Functions

Abstract

The article introduces an approximate optimal control strategy grounded in the control barrier function (CBF) to address the challenges of ensuring safety in modular robot manipulators (MRMs). The manipulator system’s dynamic model is derived using joint torque feedback (JTF) technology, which thoroughly considers the impact of interconnected dynamic couplings (IDC). The CBF is employed to confine the MRM system states within the safe region. The optimal tracking control problem for the MRM system is then reformulated as a nonzero-sum (NZS) game encompassing multiple interconnected subsystems. By applying the adaptive dynamic programming (ADP) method, the Hamilton-Jacobi (HJ) equation is solved using a cost function approximator constructed with a critic neural network (NN). Finally, Lyapunov theory is utilized to demonstrate that the tracking errors remain uniformly ultimately bounded (UUB), with experimental results validating the method’s effectiveness and benefits.