Robustness of the Unscented Kalman filter for state and parameter estimation in an elastic transmission

The Unscented Kalman Filter (UKF) was applied to state and parameter estimation of a one degree of freedom robot link with an elastic, cable-driven transmission. Only motor encoder and command torque data was used as input to the filter. The UKF was used offline for joint state and model-parameter estimation, and online for state estimation. This paper presents an analysis of the robustness of the UKF to unknown/unmodeled variation in inertia, cable tension and contact forces, using experimental data collected with the robot. Using model parameters found offline the UKF successfully estimated motor and link angles and velocities online. Although the transmission was very stiff, and hence the motor and link states almost equal, information about the individual states was obtained. Irrespective of variation from nominal conditions the UKF link angle estimate was better than using motor position as an approximation (i.e. inelastic transmission assumption). The angle estimates were particularly robust to variation in operating conditions, velocity estimates less so. A near-linear relationship between contact forces and estimation errors suggested that contact forces might be estimated using this error information.