The Near-Minimum-Time Control of Open-Loop Articulated Kinematic Chains

摘要

The time-optimal control of a system of rigid bodies connected in series by single-degree-of-freedom joints is studied. The dynamical equations of the system are highly nonlinear and a closed-form representation of the minimum-time feedback control is not possible. However, a suboptimal feedback control which provides a close approximation to the optimal control is developed. The suboptimal control is expressed in terms of switching curves for each of the system controls. These curves are obtained from the linearized equations of motion for the system. Approximations are made for the effects of gravity loads and angular velocity terms in the nonlinear equations of motion. Digital simulation is used to obtain a comparison of response of the optimal and suboptimal controls. The speed of response of the suboptimal control is found to compare quite favorably with the response speed of the optimal control. The analysis is applied to the control of three joints of a mechanical manipulator. Modifications of the suboptimal control for use in a sampled-data system are shown to result in good performance of a hydraulic manipulator under computer control. (Author)