Nonlinear optimization-based motion planning and robust control of mechanical systems with nonholonomic constraints

This research consists of developing numerical approaches for nonholonomic motion planning using nonlinear optimization and robust control for nonholonomic systems using sliding mode. For motion planning, two nonlinear optimization-based schemes are developed for the motion planning of nonholonomic systems. First, an iterative algorithm is proposed to solve for a feasible path satisfying nonholonomic constraints and necessary optimality conditions. Multi-point shooting is used to convert the motion planning problem into the problem of finding the solution of nonlinear equations. Modified Newton's method with line search is then used to ensure the global convergence of the numerical algorithm. Second, by parametrizing the control input, one can transform an infinite-dimensional optimal control problem to a finite-dimensional one and use Quasi-Newton method to solve for a feasible trajectory which satisfies nonholonomic constraints and state/input constraints. For robust control, a sliding mode control scheme is used to improve the performance of nonholonomic systems in terms of robustness and tracking errors. Based on Lyapunov theory, a robust control law is derived to stabilize the nonholonomic systems in reduced configuration space. The proposed scheme for motion planing and robust control is applied to an one-leg hopping robot, a two-wheeled mobile robot, and a free-floating robot. The results of numerical simulation clearly demonstrate the effectiveness of the proposed methods. A three-link planar floating robot was designed and built to verify the proposed motion planning and control scheme. From the experimental results, the proposed optimal motion planning scheme controls the robot from initial state to final state along the planned path within {dollar}pm{dollar}0.1 rad final position error and the slide mode control can increase the robustness to parametric uncertainties and reduce trajectory tracking errors.