Near optimum control of flexible robot arms on fixed paths

This paper presents the analysis and modification of near optimum trajectories for robotic manipulators moving along pre-defined paths. Modifications of trajectories are done such that the vibrations due to flexibility of arms and other components of the manipulator are minimized. Ultimately, the productivity of robotic manipulators depends on the speed of the task execution. Higher productivity requires higher speed of operation and in turn better control and trajectory generation algorithms. Today trajectory generation algorithms do not consider the dynamic characteristics of the manipulators. In order to utilize the available capability in the optimum manner the trajectory generation algorithms need to consider the dynamics of the manipulator, actuator constraints, nature of the task, and flexibility of arms and compliance of the joint connections. In the search for an optimal trajectory that will meet all of the above requirements while optimizing some criterion, some simplifying assumptions have to be made and/or some of the requirements have to be kept out of the formulation so that the defined problem can be solved or some feasible solutions obtained. Once the simplified problem is solved, one may consider modifying the original solution in such a way that the excluded requirements are also satisfied to some extent. In this paper the minimum time control solution of a two link flexible arm with actuator constraints is presented. We solved the minimum time problem with no constraints on the flexible modes and show the time improvement due to the use of light-weight arms. The objective is to modify the trajectory, such that flexible vibrations are bounded while changing the solution from the previous one as little as possible. Practical ways of trajectory modifications for flexible arms are discussed.