Deterministic and Stochastic Robustness of the Computed Torque Scheme

Stability robustness of robot controllers using computed torque (inverse dynamics) scheme is investigated. It is assumed that the only unknowns are the exact values of the equivalent masses of links. First, unknown masses are treated as deterministic structured perturbation and bounds are found on the degree of uncertainty that can be tolerated by the design using Lyapunov´s second method. Then, masses are modelled as random structured perturbations which results in a description of the manipulator by a nonlinear stochastic vector differential equation. In this case, we find bounds on uncertainty variances which guarantee sample path boundedness and asymptotic stability of the manipulator. The theoretical bounds obtained are examined using the solution of the Lyapunov equation associated with the globally linearized computed torque model. Numerical results are obtained for the case of a 2-degree-of-freedom anthropomorphic manipulator and their usefulness in assessing design robustness is demonstrated.