Robust control and motion planning for nonlinear underactuated systems using H-infinity techniques

This thesis presents new techniques for planning and robustly controlling the motion of nonlinear underactuated vehicles when disturbances are present and only imperfect state measurements are available for feedback. The basic motion planning algorithm uses cubic splines or Pythagorean hodograph curves to connect the initial and final configurations and to generate a feasible trajectory for the system. The feasible trajectory and its control inputs are improved through an iterative H∞-filter. Techniques are demonstrated for generalizing the motion planning algorithm to address the obstacle avoidance, multiple vehicle, and minimum distance planning problems. To track a desired trajectory, first a state feedback control law is developed for the linearized system using an H ∞-optimal design. The state feedback controller produces a locally exponentially stable closed-loop system and guarantees a precomputable level of disturbance attenuation for the system. Subsequently, an imperfect state measurement feedback controller is developed by combining a state estimate with the state feedback control law. The state estimator exploits a unique structure in the nonlinear equations of motion to decompose the system into two interlaced subsystems, which leads to a direct solution. The estimator is actually an H∞-filter, and under it the controller achieves a modified form of disturbance attenuation. Simulations included in the thesis illustrate the motion planning, the state feedback control, and the imperfect state measurement control algorithms derived, for selected models of nonlinear underactuated vehicles.