Robust Spline Path Following for Redundant Mechanical Systems
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Path following controllers make the output of a control system approach and traverse a pre-specified path with no a priori time-parametrization. The first part of the thesis implements a path following controller for a simple class of paths, based on transverse feedback linearization (TFL), which guarantees invariance of the path to be followed. The coordinate and feedback transformation employed allows one to easily design control laws to generate arbitrary desired motions on the path for the closed-loop system. The approach is applied to an uncertain and simplified model of a fully actuated robot manipulator for which none of the dynamic parameters are measured. The controller is made robust to modelling uncertainties using Lyapunov redesign. The experimental results show a substantial improvement when using the robust controller for path following versus standard state feedback. In the second part of the thesis, the class of paths and systems considered are extended. We present a method for path following control design applicable to framed curves generated by spline interpolating waypoints in the workspace of kinematically redundant mechanical systems. The class of admissible paths include self-intersecting curves. Kinematic redundancies of the system are resolved by designing controllers that solve a suitably defined constrained quadratic optimization problem that can be easily tuned by the designer to achieve various desired poses. The class of redundant systems considered include mobile manipulators for a large class of wheeled ground vehicles. The result is a path following controller that simultaneously controls the manipulator and mobile base, without any trajectory planning performed on the mobile base. The approach is experimentally verified using the robust controller developed in the first part of the thesis on a 4-degree-of-freedom (4DOF) redundant manipulator and a mobile manipulator system with a differential drive base.