Nonlinear adaptive motion control for the Tau platform with friction

This dissertation addresses the development of a model-based control algorithm for Tau platform joint space trajectory tracking in the presence of strong friction affections. The tracking performance of model-based control schemes depends heavily on the model used in the control design. The rigid body dynamic model of the Tau platform is derived using Euler-Lagrange equations. Because the friction torques can not be neglected in the Tau platform, the LuGre friction model is included in the Tau platform dynamic model. The parameters of the rigid body dynamic and friction models are identified using a nonlinear optimization procedure based on experimental data obtained from the Tau platform. Sequential or step-by-step identification procedures are used to reduce the parameter sets for optimization in order to avoid, if possible, local minimum that can occur when using nonlinear optimization algorithms. What's more, dedicated experiments are designed to obtain better initial parameter values to increase the quality of the results obtained from the nonlinear optimization procedures. Experiments show that the identified model captures the major dynamic properties of the Tau platform. The identified dynamic model of the Tau platform is then used to design a model-based control scheme to achieve high performance trajectory tracking in the joint space of the robot. State observers are constructed to estimate the unmeasured states of the LuGre friction model in order to compensate for the friction torques. A model-based control scheme, using a combined passivity-based controller and observer design method, is proposed. Global asymptotic tracking in the joint space is proven via Lyapunov analysis. Under a mild condition on the desired velocities, the observer errors are proven to go to zero asymptotically. Because parameter uncertainties always exist in real applications, an adaptive control scheme is presented in this thesis to deal with parameter uncertainties of both the rigid body dynamic model and the friction model. Global asymptotic tracking in the joint space is also proven for the adaptive control scheme.; Simulation results verify the theoretical results given in the thesis, that is, global asymptotic trajectory tracking is achieved for the Tau platform in the presence of friction. The tracking performance of the adaptive control scheme is compared statistically with that of the nonadaptive control scheme when parameter uncertainties exist. The simulation results show that the adaptive control scheme is superior to its nonadaptive counterpart. Robustness of the adaptive control scheme to unmodeled uncertainties is also studied using simulations.