Nash Bargaining Solution-Based Multi-Objective Model Predictive Control for Constrained Interactive Robots

Abstract

Dear Editor, This letter proposes a novel Nash bargaining solution-based multi-objective model predictive control (MPC) scheme to deal with the interaction force control and the path-following problem of the constrained interactive robot. Considering the elastic interaction force model, a mechanical trade-off always exists between the interaction force and position, which means that neither force nor path following can satisfy their desired demands completely. Based on this consideration, two irreconcilable control specifications, the force object function and the position track object function, are proposed, and a new multi-objective MPC scheme is then designed. At each sampling interval, the control action is chosen automatically among the set of Pareto optimal solutions with the Nash bargaining solution from the cooperative game theory. Furthermore, we set state and control constraints to consider physical limitations. The proposed controller's efficacy is demonstrated through simulations on a constrained interactive robot.