Point-stabilization And Formation Control Forautonomous Underwater Vehicles

Ocean resources have played a very important role in the development of economic society,Autonomous underwater vehicles (AUVs) are very useful tools in exploring, developing andutilizing of ocean resources. Due to the dynamic of AUVs are complicated nonlinear systemsand the inflexible driving charecteristics, the driving trajectory compared to the desired path isoften unsatisfactory. What’s worse, the external disturbances for AUV’s are complex and havelarge power caused by underwater environmental extremes. Therefore, researches onpoint-stabilization problems ofAUVs have important significance in theory and practice.With the increasing requirements of marine research and ocean exploring, it has paid moreattention to the AUVs collaborative work to complete complex tasks. The formation controlproblem is a typical one of cooperation and coordination of multiple AUVs. The formationproblem is a control technology, in which multiple AUVs keep a special formation in theprocess of destination under constraint conditions. Unfortunately, the research about multipleAUVs formation research is at the beginning stage, and there are not general control methodsfor multiple AUVs formation control.The major results and innovations of this dissertation are summarized as follows.1. Based on the characters of AUVs and wave force, the dynamic models for AUV’s withlow speed and the wave force are constructed. By simplifying the Fossen’s six degrees model ofAUVs, the AUV’s four degrees model is obtained, in which the linear terms and nonlinear termsare separated, and mathematical model with time delay under disturbances is built. Then, the mathematical model of AUVs under wave force disturbances is constructed by using the waveforce theory.2. The optimal zero steady-error to point-stabilization for AUV nonlinear systems withtime delay is considered. By using the inserted internal model, the zero steady-error disturbancecompensation and the augmented system are introduced. Then, the optimal point-stabilizationproblem is formulated based on the augmented system. Based on the maximum principle, thetwo-point boundary value problem (TPBV) without disturbance is obtained. By introducing asequence of iteration, the optimal problem for nonlinear systems is transformed into a nonlinearTPBV iteration problem, and the iterative sequences of the solution converging to the optimalcontrol law is proved. In each step of iteration, the feedback linear term of optimal control law isobtained from a Riccati equation, and the nonlinear compensation is the limitation of lineariterative sequences with vector equations. Simulation results demonstrate the effectiveness ofthe optimal zero steady-error control law.3. A linear decomposition control strategy for AUV point-stabilization problems isresearched. By proposing a3-D-Spacing dynamic model, decomposing AUV’s five statevariables into three groups according to the state’s order, the control task will be divided intothree stage control tasks based on group’s sequence, and the control law is proposed for eachcontrol process. The simulation of the point-stabilization for AUV’s3D-spacing dynamic modelshows the effectiveness of proposed decomposition control strategy, which completes the AUV’sfix-point driving with low consumption.4. The optimal feedback stabilization for AUV systems with delayed state and input isstudied. By using a state transformation, the AUV dynamic equation with input delay istransformed into a delay-free system. By designing the feedback control law with a delaymemory and an embedding disturbance compensation, the stability of the AUV control system is ensured. By using optimal theory, the TPBV problem with time-advance and time-delay terms isobtained. By using the successive approximation approach, the optimal problem is transformedinto the decoupling form of optimal feedback term without time delay and optimalcompensation term for time-delay, in which the optimal feedback terms without time delay is thesolution of the Riccati equation, and the optimal compensation for time delay is obtained fromthe limitation of linear iterative sequences with vector equations. Finally, the results ofsimulations show the effectiveness of the proposed algorithm. Because proposed algorithm onlyiterates the vector equation, it has good convergence and lower requirements about time andspace.5. The formation control algorithm for multiple AUVs is proposed based on an outputfeedback control. First, the framework of the formation tracking control is proposed. A similarcombination transform is proposed. And the formation control problem for multiple AUVs istransformed into an optimal tracking control for the multiple AUVs. The nonlinear TPBVproblem from the necessary condition of the maximum principle is introduced. The optimaltracking control law is obtained in infinite-time domain by using the successive approximationapproach to solve the adjoint vector sequence iteratively. The uniqueness and existence of theproposed tracking control law is proved. Simulation examples are employed to test the validityof the proposed formation control law.6. The formation control for multiple AUVs under external disturbances is researched.Due to the external disturbances, the stability of the formation system becomes worse. So, adisturbance compensation is designed by using the internal model principle. The argumentsystem is obtained by embedding the disturbance compensation into the original AUV controlsystems. By using the similar combination transformation, the composite multiple AUVs controlsystem is obtained. Then, the formation control for AUVs under external disturbances is reformed into an optimal feedback control problem for this composite control system, and thefeedback optimal formation control law is proposed. Simulation examples are employed to testthe validity of the proposed formation control law.