Control of a nonlinear underactuated system with adaptation, numerical stability verification, and the use of the LQR Trees algorithm

[摘要] Underactuated robotics, though surrounded by an established body of work, has certain limitations when nonlinear adaptive control principles are applied. This thesis applies a nonlinear adaptative controller that avoids many of these limitations using alterations inspired by the control of a similar underactuated system, the cart-pole. Due to the complexity of the system, a sums-of-squares MATLAB toolbox is used to generate a suitable Lyapunov Candidate used for proofs of stability, with claims of local stability made using Barbalat;;s Lemma. This provides us with a local domain of attraction for the altered classical nonlinear adaptive controller. In addition, the algorithm known as LQR Trees is applied to the system in order to create a controller with a larger region of attraction and lower torque requirements, though without an adaptive component. Both control systems are implemented in simulations using MATLAB.

[发布机构] Massachusetts Institute of Technology