A trajectory planner for a one-flexible-link manipulator is presented. The approach is based on the solution to the inverse dynamic problem for flexible manipulators in the frequency domain. The problem is mathematically formulated as an optimization of the settling time subject to maximum torque and high frequency content constraints. A cubic-rectangular acceleration profile is proposed as a generic input to be used in the optimization process, and the general optimization procedure is established. The application of the approach to a particular case shows the operativeness of the proposed methodology and the possibility of an intelligent election of trajectories for flexible manipulators.>

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.>

A technique is presented for the solution of the inverse dynamics of open-chain flexible robots. The proposed method finds the joint torques necessary to produce a specified end-effector motion. The formulation includes all the nonlinear terms due to the large rotation of the links, together with Timoshenko beam theory to model their elastic characteristics. The finite-element method is used to discretize the equations of motion. The performance and capabilities of this technique are tested through a simulation analysis. Results show the potential of the method not only for feedforward control, but also for incorporation in feedback control strategies.>