Robust compliant motion for manipulators, part II: Design method

A controller design methodology to develop a robust compliant motion for robot manipulators is described. The achievement of the target dynamics (the target impedance is introduced in Part I) and preservation of stability robustness in the presence of bounded model uncertainties are the key issues in the design method. State-feedback and force-feedforward gains are chosen to guarantee the achievement of the target dynamics, while preserving stability in the presence of the model uncertainties. In general, the closed-loop behavior of a system cannot be shaped arbitrarily over an arbitrarily wide frequency range. It is proved that a special class of impedances that represent our set of performance specifications are mathematically achievable asymptotically through state-feedback and interaction-force feedforward as actuator bandwidths become large, and we offer a geometrical design method for achieving them in the presence of model uncertainties. The design method reveals a classical trade-off between a system's performance over a bounded frequency range and its stability relative to model uncertainties via multivariable Nyquits criteria. Two classes of such uncertainties are dealt with. While the first class of model uncertainties is formed from the uncertainties in the parameters of the modeled dynamics, the high-frequency unmodeled dynamics form the second class of model uncertainties. The multivariable Nyquist criterion is used to examine trade-offs in stability robustness against approximation of desired target impedances over bounded frequency ranges.