Causal approximate inversion for control of structurally flexible manipulators using nonlinear inner-outer factorization

A control scheme for flexible-link manipulators is advanced which is based on the notion of nonlinear inner–outer factorization. It is well known that the inverse of the forward dynamics map from joint torques to manipulator tip motion is noncausal and cannot be implemented in conjunction with real-time path planning. The methods used here determine causal approximations for the inverse dynamics using the inverse of the outer (stable and minimum phase) factor and a static approximation for the inverse of the inner (lossless but nonminimum phase) factor. The Hamilton–Jacobi equation that arises is approximated by a state-dependent Riccati equation at each time step. The factorization procedure yields the corresponding joint trajectories which can serve as reference trajectories for closing joint-based feedback loops. Experimental results from a planar three-link manipulator with two flexible links demonstrate the efficacy of the procedure. © 2001 John Wiley & Sons, Inc.