Estimation of external forces acting on the legs of a quadruped robot using two nonlinear disturbance observers

This paper addresses the sensor-less estimation of external forces exerted on the legs of a quadruped from the environment, with the use of the data provided from the angular position and velocity sensors at the joints of the legs. For this purpose, two nonlinear disturbance observers have been used. The first disturbance observer, estimates the torques applied to the legs through the legs' couplings with the body, while the second one uses the data from this observer to derive an estimation of the external torques applied to the tips of the robot legs. The external torque estimations are then converted to force estimations with the use of a Jacobian matrix. The proposed disturbance observers are shown to be able to derive an accurate estimation of the torques, with the estimation errors converging exponentially to zero, when the torques' changes with time are not too fast, which is not a restricting condition, considering the interactions between a quadruped robot and its environment. On the other hand, when the variation rates of the external torques are fast, the proposed disturbance observer still provides an acceptable estimation of the torques and the estimation error dynamics is globally uniformly ultimately bounded. The proposed method has been simulated on the model of the TMUBot quadruped. The results of the simulation, have been compared with the results derived from another disturbance observer. These results show the efficiency of the proposed estimation method.