Flexible Arms

The adoption of lightweight mechanical structures may improve the performance of today's massive industrial robots. In order to exploit the potential offered by lightweight robot arms, one must consider the effects of structural link flexibility and deal with active and/or passive suppression of vibrations. A finite-order dynamic model can be obtained by combining the Lagrangian formulation with the assumed modes method for modelling deflections, with the aid of symbolic manipulation languages. Explicit models have been derived for one- and two-link planar arms with bending deformations. A model reference adaptive control approach has initially been proposed for the one-link case. More promising results, applicable to multilink arms, have been obtained by adopting a singular perturbation technique with approximate two-time scale control; in this context, the problem of lack of full state measurements has been solved by designing optimal output feedback dynamic compensators of fixed order. An alternative nonlinear dynamic decoupling approach has been followed to design exact trajectory controllers; for the single link case it has been shown that reproduction of joint trajectories is always possible while reproduction of link trajectories may lead to internal unstable behavior. Extension to the multilink case has been worked out; to the purpose, a complete, explicit, accurate dynamic model has been derived in closed-form with special concern to the issue of time-varying mass boundary conditions. A robust controller with observer has been designed which is particularly effective in the case of low structural damping. The regulation problem of flexible arms under gravity has been solved by designing a stable PD joint control with compensation of gravity at the desired equilibrium configuration. End-effector position regulation can be achieved by using a suitable Jacobian transpose inverse kinematics scheme to compute the desired joint and deflection set points. The problem has been extended to the case of end-effector contact with a rigid and a compliant environment.