Adaptive Feedback Optimal Control for Robot Manipulators

Robotic systems are essentially dynamical systems. In the cases of slow motion and mechanical configuration with weakly coupled subsystems, it is not necessary to solve the control task dynamically[1]. However, in the cases of faster motion and mechanical configuration with strongly coupled sub-systems, the dynamic effects such as inertia, coriolis, centrifugal and gravity moments are not negligible. In the other hand the performance of a manipulator is related to both its speed in executing tasks, as well as its precision and reliability, hence driving robotic manipulators as fast as possible is highly desirable. In this paper the problem of the adaptive optimal time control of a six degrees of freedom manipulator is considered, it is shown that the opimal time control is essentially of the bang-bang type in the acceleration work zone. In the uniform work zone the optimal control is given for the singular arcs by considering an extention of the Kelly optimal singular arcs control [5]. This type of control, however is too sensitive to frequent switchs of the actuators between their limits leading to deviations exeeding the tolerance desired in the final speed and position precisions. In the other hand this scheme of control is not adaptable to the environment (sensor and workspace) evolution, a fact which is important to the robot versatility and reliability.