Research Of Optimal Formation Control For Multiple Autonomous Underwater Vehicles

This paper considers a class of trajactory tracking control and minimum-energy controlproblem for multiple autonomous underwater vehicles (AUVs) formation. The kinematics modelof AUV is a complex non-linear system which has strong coupling between state variables. It’s avery difficult problem to design an optimal control law for AUV kinematics system. In the paper,many research results are surveyed from the field about AUV control. Considering time-delay’seffects, the kinematics model of AUV is developed. Some novel control problems are proposedbase on the AUV system model with time-delays. At the same time, some approaches areproposed to solve them. The optimal control problem for AUV kinematics system is consideredfrom different scales, driving force types and formation patterns. And that is the paper’scontribution to the research of AUVs formation with time-delays. The organization of this paper isas follows.1. The kinematics model of AUV is transformed into a simple one from the six degrees offreedom model proposed by Fossen. The novel model has four degrees of freedom, and fourindependent input variables. The wave force is modeling by two ways. One is treated as adisturbance from external system. The other is treated as a part of input vector. Beyond that, thetime-delays’ effect is described in the kinematic model of AUV according to the experiment dataand underwater acoustic communication.2. A class of point-arrive problem was proposed in this section. The AUV kinematic model isa nonlinear system with time-delays which is considered in a small scale. First, the kinematic model of AUV is treated into a cascade system composed of attitude control part and trajectorycontrol part. Then, the approach is proposed like that, controlling the attitude of AUV stable to thereference one at first. After that, controlling the trajectory to follow the reference one underpoint-arrive demand. Next an optimal controller is designed to solve the control problem.Simulation results demonstrate that the approach is simple and effective.3. An optimal control problem of multiple AUVs with formation constraint is considered inthis section. First, a reference feasible trajectory for the position and orientation based on velocitycontrol is planned so that it is consistent with vehicle dynamics. Then an optimal performanceindex is proposed to pay attention to both tracking quality and formation constraint. In thefollowing the optimal controller is designed to solve the problem. Using the controller wedemonstrate the physical realization of control system. Simulation results validate that theproposed formation methodology is presented and discussed.4. An ‘Observer’ formation mode is proposed and modeling in a large scale. The systemmodel is a linear discrete one with input and state delays under disturbance. Consider an optimaltracking control problem for the system. By introducing a variable transformation, the system istransformed into a non-delayed one. The dynamic output feedback control law has been presentedbased on the design idea of the feedforward and feedback optimal control law. Simulation resultsdemonstrate the effectiveness of the contrl law.5. The minimum-energy remote control problem of AUV formation is discussed in a largescale. First, the effects of network delays are considered in the kinematic model of remote controlsystem, and a linear model is constructed with input and state delays. Then, a performance indexis proposed to describe the minimum-energy demand. Next, an optimal control law is designed tosolve the problem. At last, simulation results are shown the performance of the optimal controllaw. 6. Consider a minimum-energy centralization control problem for multiple AUVs formationwith communication delays. A ‘commander’ formation mode is described to realize the centralizecontrol. The mathematic model of AUVs system is given as a time-varying system with multiplestate and input delays. According to the model, a minimum-energy performance index is proposed.The optimal control law and performance index are given in the form of analytic solutions.Simulation results demonstrate the effectiveness of this approach.