| Making robots perform point-to-point motions faster can make production lines run faster, and increase productivity. In practical applications, robot operation is affected by disturbances and vibrations produced by flexibility in the joints. This dissertation aims to develop methods 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. First a linear model predictive control (MPC) strategy is developed based on equations linearized about the open-loop optimal solution. When the disturbances are small enough, the results are encouraging. However, there are some limitations. To address these, a nonlinear model predictive control (NMPC) method is generated. The feedback is no longer based on an open-loop solution, but is computed in real-time aiming to make updates that are optimal based on the current measured state using nonlinear equations. 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. A formulation is developed that makes a smooth transition between the time optimal maneuver objective and the regulator objective after arrival at the endpoint. 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. 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. The solution approach is based on the direct multiple shooting method and a recently developed real-time iteration scheme. Numerical examples are investigated. The algorithm shows good feedback control performance. Finally, inverse dynamics is introduced to reduce the real-time computational effort, with the aim of making true optimal feedback control practical. |
