Abstract
Properties of solutions to the inverse dynamics problem of n-link, planar, flexible manipulator arms are analyzed. Conditions for the solution to be meaningful and usable as control commands are obtained. It is shown that, when a given trajectory to follow comprises the same frequency components as the extended natural frequencies of the arm structure, the solution to the inverse dynamics problem, which is provided as actuator torque commands, bocomes oscillatory and divergent with time. The divergence of actuator torque commands also occurs when any two of the extended natural frequencies are the same. Guidelines for the design of the flexible arm as well as the planning of the endpoint trajectory are then provided. Analytical results are verified through simulation.
