Underactuated control for an autonomous underwater vehicle with four thrusters

摘要

The control of Autonomous Underwater Vehicles (AIJVs) is a very challenging task because the model of AUV system has nonlinearities and time-variance,and there are uncertain external disturbances and difficulties in hydrodynamic modeling.The problem of AUV control continues to pose considerable challenges to system designers,especially when the vehicles are underactuated (defined as systems with more degrees-of-freedom(DOFs) than the number of inputs) and exhibit large parameter uncertainties.Hence the dynamical equations of the AUV exhibit so-called second-order nonholonomic constraints,i.e., non-integrable conditions are imposed on the acceleration in one or more DOFs becauseudthe AUV lacks capability to command instantaneous accelerations in these directions of the configuration space.Such a nonholonomic system cannot be stabilized by the usual smooth,time-invariant,state feedback control algorithms.From a conceptual standpoint,the problem is quite rich and the tools used to solve it must necessarily be borrowed from solid nonlinear control theory.However,the interest in this type of problem goes well beyond the theoretical aspects because it is well rooted in practical applications that constitute the core of new and exciting underwater mission scenarios.The problem of steering an underactuated AUV to a point with a desired orientation has only recently received special attention in the literature and references therein.This task raises some challenging questions in system control theory because,in addition to being underactuated,the vehicle exhibits complex hydrodynamic effects that must necessarily be taken into account during the controller design phase.Therefore, researchers attempted to design a steering system for the AUV that would rely on its kinematic equations only.In this research, an X4-AUV is modelled as a slender, axisymmetric rigid body whose mass equals the mass of the fluid which it displaces;thus,the vehicle is neutrally buoyant.X4-AUV equipped with four thrusters has 6-DOFs in motion, falls in an underactuated system and also has nonholonomic features.Modelling of ATJV maneuverability first involved the mathematical computation of the rigid body's kinematics,in which roll-pitch-yaw angles in 6-DOFs kinematics are used.We also derive the dynamics model of an X4-AUV with four thrusters using a Lagrange approach, where the modelling includes the consideration of the effect of added mass and inertia.We present a point-to-point control strategy for stabilizing control of an X4-AUV which is not linearly controllable.The goal in point-to-point control is to bring a system from any initial state of the system to a desired state of the system.The construction of stabilizing control for this system is often further complicated by the presence of a drift term in the differential equation describing it dynamically.udTwo different controllers are developed to stabilize the system.The first stabilization strategy is based on the Lyapunov stability theory.The design of the controller is separated into two parts: one is the rotational dynamics-related part and the other is the translationaluddynamics-related one.A controller for the translational subsystem stabilizes one position out of x-, y-, and z-coordinates, whereas.a controller for the rotational subsystems generates the desired roll, pitch and yaw angles. Thus,the rotational controller stabilizes all the attitudes of the X4-ALJV at a desired (x-, y- or z-) position of the vehicle.The stability of the corresponding closed-loop system is proved by imposing a suitable Lyapunov function and then using LaSalles's invariance principle.The second stabilization strategy is based on a discontinuous control law,involving the a-process for exponential stabilization of nonholonomic system.This technique is applied to the system by two different approaches.The first approach does not necessitate 11 any conversion of the system model into a chained form, and thus not rely on any special transformation techniques.The system is written in a control-affine form by applying a partial linearization technique and a dynamic controller based on Astolfi's discontinuous control is derived to stabilize all the states of the system to the desired equilibrium point exponentially.Motivated by the fact that the discontinuous dynamic-model without using a chained form transformation assures only a local stability (or controllability) of the dynamics based control system, instead of guaranteeing a global stability of the system, the conversion of system model into a second-order chained form is implemented in the second approach.The second-order chained form consisting of a dynamical model is obtained by separating the original dynamical model into three subsystems so as to use the standard canonical form with two inputs and three states second-order chained form.Here,two subsystems are subject to a second-order nonlinear model with two inputs and three states,and the other subsystem is subject to a linear second-order model with two inputs and two states. Then,the Astolfi's discontinuous control approach is applied for such second-order chained forms.The present method can only realize partially underactuated control, which controls five states out of six states by using four inputs.The derived results are specialized to an X4-AUV but,in principle,analogous results can be obtained for vehicles with similar dynamics. Some computer simulations are presented to demonstrate the effectiveness of our approach.