Adaptive Control for Guidance of Underwater Vehicles

JORDAN, MARIO; BUSTAMANTE, JORGE

Intelligent Underwater Vehicles

In-Tech

Lugar: Vienna, Austria, EU; Año: 2009; p. 251 - 278

Underwater vehicles are sophisticated mechanisms with complex nonlinear dynamics and large lumped perturbations. They can be remotely operated or eventually they can autonomously navigate to targets along specified scheduled trajectories with geometric and kinematic restrictions for obstacle avoidance or time-optimal operations. Due to the inherent nonlinear equations of motions, subaquatic vehicles require of complex controllers that involve automatic speed controls, dynamic positioning and tracking, as well as autopilot for automatic steering of depth and altitude. It is experimentally corroborated that adaptive techniques may provide superior trajectory tracking performance compared with the fixed model-based controllers. Many different adaptive and robust adaptive approaches for underwater vehicles have been discussed in the literature in the past 15 years to handle uncertainties related to the dynamics, hydrodynamic and external disturbances. However, the employment of novel, high-performance nonlinear control design methodologies like backstepping and speed-gradient designs do not appear in the literature except as incipient applications. While backstepping designs presuppose classes of system with triangular structures like some canonical representations in state space, speed-gradient techniques, on the contrary, are more inclined to passivity and goal-oriented control problems. Both methodologies can cope with uncertainties, perturbations and transient effects the same. From previous theoretic results it seems that novel adaptive techniques can give rise to an improvement of the global performance in path tracking of underwater vehicles, mainly, when precise manoeuvrability is necessary in a changeable and uncertain environment, without demanding any knowledge of physical parameters neither of the dynamics nor hydrodynamics. The goal of the chapter is to describe the design of high-performance approaches based on speed-gradient methodology to solve the servo-tracking and regulation problems adaptively for any desirable smooth path in the six modes of motion of a full-actuated underwater vehicle like ROVs. The approach can be straightforwardly extended to under-actuated vehicles like AUVs as well. The chapter is organized as follows. First a description of the vehicle dynamics and hydrodynamics under environmental perturbations in 6 degrees of freedom is given. Additionally, thruster dynamics is embedded in the complete dominant dynamics as a fast dynamics (parasitics). Then, the tracking and regulation problems are introduced in a general form as minimization of energy cost functionals involving positioning and kinematic errors. Afterwards, a design of a fixed controller is presented. The same methodology is extended to the adaptive case considering a complete vehicle dynamics on one side, and a simplified dominant dynamics without parasitics on the other side. It is shown that the solution of the first case requires of state observation for the thruster dynamics, for which a disturbance/state observer is developed. Next, the effects of exogenous and endogenous perturbations in the transient and steady-state control behavior are analyzed and posed as a problem of total stability. Global convergence of positioning and kinematic error trajectories is proved as well. Next, the problem of setup of design parameters is aimed and from here useful guidelines to achieve high performance in transitory and permanent behavior are given. It is shown that this procedure can be automated in order to reach optimal tuned design parameters in a commissioning phase during adaptive control. Hereafter, the problem of path tracking with maximal advance speed along a specified reference trajectory in 6 degrees of freedom avoiding thruster saturation, is tackled as an optimization problem with restrictions. Finally, the analysis of selected case studies of navigation in simple and complex missions pretends to illustrate the achievable control performance with the presented approaches.