Nonlinear Model Predictive Control of Robots Using Real-time Optimization

Abstract

This paper is one in a series of papers that address practical issues making near time optimal control of robots into something that can be practical in applications. This work emphasizes the issue of how to create feedback that is consistent with the near time optimal objective. In a previous work, iterative learning control was used to learn to make commercial feedback controllers actually track a computed open loop optimal trajectory, but the feedback is still classical and unrelated to the optimality criterion. Another work used linear model predictive control (MPC) based on equations linearized about the open loop solution. The present work goes one step further and uses nonlinear model predictive control (NMPC). The feedback is no longer based on an open loop solution, but is computed real time aiming to make updates that are optimal based on the current measured state. The approach addresses the issue of vibrations in the robot harmonic drives by limiting the bandwidth of the control action, similar to classical design approaches. Standard time optimal control formulations for moving from one state to another do not address the fact that in robot maneuvers, one is normally interested in staying at the endpoint after arrival. A formulation is developed that makes a smooth transition between the time optimal maneuver objective and the regulator objective after arrival. This is accomplished with both a time optimal term and a regulator term in the cost, appropriately weighted so that time optimality dominates at the start, and in addition a free time horizon is used that converts to fixed time as the endpoint is approached, thus disabling the time optimal term in the cost. Issues of terminal penalty or final state constraints are addressed for producing stability of the feedback control. Numerical examples are presented that examine the tuning needed to develop good feedback control performance.