An efficient computation of the inverse dynamics of flexible manipulators in the time domain

The problem of controlling the endpoint motion of flexible arms is addressed. A finite-element discretization of the system is carried out to obtain a set of ordinary differential equations that describe the motion of the manipulator. Theoretical and numerical difficulties pertaining to the inverse dynamic problem for flexible arms in the time domain are exposed. A novel time domain algorithm, much more efficient than that in the frequency domain, is presented. It is shown that the algorithm leads to the desired noncausal solution, and it eliminates the instability problems that arise if a direct integration scheme is used. Since the impulse response function can be computed offline, the only online computational burden consists of calculating convolution integrals. These can be integrated in real time. Extensions to the multilink case are discussed