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

Abstract

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 times 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.

Optimization of Hybrid Systems with Known Paths

“…Trajectory planning has been an area of research since the early 1970s Kahn and Roth [1971], an excellent overview of the last three decades can be found in Gasparetto and Zanotto [2008].…”

Parallelism in Manipulator Dynamics

“…Uicker (1965) and Kahn (1969) derived an early formulation having an (! )(n4) time complexity and requiring 7.9 seconds on a PDP 11/45 for just one trajectory point .…”

Task Time Optimization of a Robot Manipulator using Artificial Neural Network and Genetic Algorithm

“…However, the highly non-linear multi-input dynamics of robot manipulators complicates the process of finding true minimum time [1]. Khan and Roth [2] used the linearization technique to introduce the time-optimal control of robotic manipulators for the first time. The first efficient algorithm for finding the optimal trajectory was developed independently in 1985 by Bobrow et al and Shin and McKay [3,4] based on the possibility of parameterising the path with a single scalar variable.…”