Incremental Model Predictive Control Exploiting Time-Delay Estimation for a Robot Manipulator

Abstract

This article proposes a new incremental model predictive control (IMPC) strategy, which allows for constrained control of a robot manipulator, while the resulting incremental model is derived without a concrete mathematical system model. First, to reduce dependence on the nominal model of robot manipulators, the continuous-time nonlinear system model is approximated by an incremental system using the time-delay estimation (TDE). Then, based on the incremental system, the tracking IMPC is designed in the framework of MPC without terminal ingredients. Thus, compared with existing MPC methods, the nominal mathematical model is not required. Moreover, we investigate reachable reference trajectories and confirm the local input-to-state stability (ISS) of IMPC, considering the bounded TDE error as the disturbance of the incremental system. For reachable reference trajectories, the local ISS of IMPC is analyzed using the continuity of the value function, and the cumulative error bound is not overconservative. Finally, several real-time experiments are conducted to verify the effectiveness of IMPC. Experimental results show that the system can achieve optimal control performance while guaranteeing that input and state constraints are not violated.