A Global Tracking Control Scheme for Autonomous Vehicles and its Numerical Implementation Using a Variational Integrator

This paper treats the practical and challenging control problem of tracking a prescribed continuous trajectory for an autonomous vehicle in the presence of gravity, buoyancy, fluid dynamic and other forces and moments that are uncertain. These uncertain forces and moments are bounded and may be difficult to model accurately, but they act persistently or over long periods of time. The trajectory is specified in terms of desired attitude and translational motion for a rigid body model of the vehicle. This desired trajectory could be obtained from modelbased motion planning schemes. While applications of this control scheme include autonomous aerial and underwater vehicles, we focus on an autonomous underwater vehicle (AUV) application beacuse of its richer, more nonlinearly coupled, dynamics. We use a global characterization of the desired trajectory and trajectory tracking errors in the nonlinear state space. Almost global convergence to the desired trajectory in the nonlinear state space is demonstrated both analytically and through numerical simulations. For numerical simulations of this control scheme, we obtain and use a variational integrator that discretizes the dynamics of the vehicle. This discretization is carried out using discrete variational mechanics, which maintains the Lagrangian structure of the (continuous) dynamics. The discrete dynamics so obtained is implemented as a numerical algorithm to numerically simulate a few AUV maneuvers with varying complexities.