自主式水下航行器的点镇定及编队控制研究
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摘要
海洋资源对于经济的发展和社会的进步来说至关重要，自主式水下航行器（Autonomous underwater vehicles，AUVs）是海洋探测、开发以及完成各类水下作业的重要工具。AUV的动态特性是一个比较复杂的非线性系统，其驱动行驶很不灵活，行驶的轨迹与期望路径相比往往不尽人意，且水下环境恶劣系统扰动源多，扰动力大，使得研究如何实现AUV的点镇定具有重要意义。随着海洋科学考察和海洋开发需求的增加，AUV应用领域的日趋扩大，人们开始关注利用多个AUV的协同作业，共同完成复杂任务的研究。多AUV编队问题是多AUV协调合作中的一个典型性的问题，所谓的编队控制是指多个机器人在到达目的地的过程中，要求在适应环境约束的条件下保持某种队形的控制技术。目前多AUV编队控制技术的研究处于起步阶段，还没有形成有关多AUV编队控制的一般研究方法。
本文主要的研究内容和创新点现概括如下：
1.建立低速运行情况下AUV运动的数学模型以及海浪力模型。通过对Fossen六自由度模型的简化，得到了线性部分与非线性部分分离的四自由度的AUV的数学模型和受外部扰动以及时滞作用下的AUV控制系统的数学模型。再依据海浪力学理论，给出能够描述在AUV运行中所受到的海浪力的数学模型。
2.研究AUV非线性时滞系统的最优无静差点镇定问题。首先通过嵌入内模，构造了无静差扰动补偿器，并由其与原系统共同构成一个增广系统，然后研究由原系统与无静差补偿器构成的增广系统的最优点镇定问题。由极大值原理，得到了无扰动作用下的增广系统的两点边值问题。通过构造一个迭代序列将非系统的最优点镇定问题转化为求解非线性两点边值序列问题，证明了该迭代方程序列的解一致收敛于原系统的最优控制律。在每次迭代过程中，最优控制律的线性反馈部分是通过求解一个Riccati方程精确得到的，非线性补偿项则是线性伴随向量方程迭代序列的极限值。仿真实例验证了不同扰动情况下，所设计的无静差控制律的有效性。
3.对于AUV非线性系统的点镇定问题提出一种线性分解控制策略。首先建立了AUV的三维空间运动模型，其次将该AUV系统的5个状态变量按顺序分解为3组，并按分组顺序将控制过程分为3个阶段完成控制任务，最后给出了每个阶段的系统控制律。通过对AUV三维空间的点镇定问题进行仿真，验证了该线性分解控制策略的有效性，且其能够在小能耗的情况下完成AUV的定点行驶。
4.研究带有控制和状态时滞的AUV最优反馈镇定问题。利用状态变换，把带有控制时滞的AUV动态系统转化成没有控制时滞的系统，并设计了带有时滞记忆的最优反馈控制律，同时通过嵌入扰动补偿器，保证了AUV控制系统的稳定性。根据最优控制理论，得到既含有时滞项又含有超前项的两点边值问题。利用逐次逼近方法将问题转化为求解无时滞最优反馈项和最优时滞补偿项的解耦形式，无时滞最优反馈项由求解一个Riccati方程直接得到，最优时滞补偿项由迭代求解伴随向量序列近似求得。最后给出算法，并以仿真算例验证了该算法在不同时滞下的有效性，算法仅对向量方程进行迭代，收敛性好，时空需求低。
5.基于输出反馈控制提出了一种多AUV的编队控制算法。首先，建立了一个编队跟踪控制模型。通过提出一个相似组合变换，将多AUV的编队控制问题转化成了整体系统的最优跟踪控制问题。针对由极大值原理导出的非线性两点边值问题，采用逐次逼近方法分别构造了已知初始条件和终端条件的两个微分方程迭代序列，对于无限时域的情形，给出并证明了最优跟踪控制律的存在性和唯一性。仿真算例验证了编队控制律的有效性和高效性。
6.研究受外部扰动影响下多AUV的编队控制问题。外部扰动的的存在使编队稳定性变差，因此利用内模原理设计了扰动补偿器中，得到嵌入扰动补偿器的原AUV控制系统的增广系统。经过相似组合变换，得到一个组合后的多AUV控制系统，把原受持续扰动影响的AUV的编队控制问题转化为该组合系统的最优反馈控制问题，并依据该系统设计了最优反馈控制律，即原系统的最优编队控制律。理论分析和仿真算例验证了该编队控制策略的有效性和高效性。
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.
本文主要的研究内容和创新点现概括如下：
1.建立低速运行情况下AUV运动的数学模型以及海浪力模型。通过对Fossen六自由度模型的简化，得到了线性部分与非线性部分分离的四自由度的AUV的数学模型和受外部扰动以及时滞作用下的AUV控制系统的数学模型。再依据海浪力学理论，给出能够描述在AUV运行中所受到的海浪力的数学模型。
2.研究AUV非线性时滞系统的最优无静差点镇定问题。首先通过嵌入内模，构造了无静差扰动补偿器，并由其与原系统共同构成一个增广系统，然后研究由原系统与无静差补偿器构成的增广系统的最优点镇定问题。由极大值原理，得到了无扰动作用下的增广系统的两点边值问题。通过构造一个迭代序列将非系统的最优点镇定问题转化为求解非线性两点边值序列问题，证明了该迭代方程序列的解一致收敛于原系统的最优控制律。在每次迭代过程中，最优控制律的线性反馈部分是通过求解一个Riccati方程精确得到的，非线性补偿项则是线性伴随向量方程迭代序列的极限值。仿真实例验证了不同扰动情况下，所设计的无静差控制律的有效性。
3.对于AUV非线性系统的点镇定问题提出一种线性分解控制策略。首先建立了AUV的三维空间运动模型，其次将该AUV系统的5个状态变量按顺序分解为3组，并按分组顺序将控制过程分为3个阶段完成控制任务，最后给出了每个阶段的系统控制律。通过对AUV三维空间的点镇定问题进行仿真，验证了该线性分解控制策略的有效性，且其能够在小能耗的情况下完成AUV的定点行驶。
4.研究带有控制和状态时滞的AUV最优反馈镇定问题。利用状态变换，把带有控制时滞的AUV动态系统转化成没有控制时滞的系统，并设计了带有时滞记忆的最优反馈控制律，同时通过嵌入扰动补偿器，保证了AUV控制系统的稳定性。根据最优控制理论，得到既含有时滞项又含有超前项的两点边值问题。利用逐次逼近方法将问题转化为求解无时滞最优反馈项和最优时滞补偿项的解耦形式，无时滞最优反馈项由求解一个Riccati方程直接得到，最优时滞补偿项由迭代求解伴随向量序列近似求得。最后给出算法，并以仿真算例验证了该算法在不同时滞下的有效性，算法仅对向量方程进行迭代，收敛性好，时空需求低。
5.基于输出反馈控制提出了一种多AUV的编队控制算法。首先，建立了一个编队跟踪控制模型。通过提出一个相似组合变换，将多AUV的编队控制问题转化成了整体系统的最优跟踪控制问题。针对由极大值原理导出的非线性两点边值问题，采用逐次逼近方法分别构造了已知初始条件和终端条件的两个微分方程迭代序列，对于无限时域的情形，给出并证明了最优跟踪控制律的存在性和唯一性。仿真算例验证了编队控制律的有效性和高效性。
6.研究受外部扰动影响下多AUV的编队控制问题。外部扰动的的存在使编队稳定性变差，因此利用内模原理设计了扰动补偿器中，得到嵌入扰动补偿器的原AUV控制系统的增广系统。经过相似组合变换，得到一个组合后的多AUV控制系统，把原受持续扰动影响的AUV的编队控制问题转化为该组合系统的最优反馈控制问题，并依据该系统设计了最优反馈控制律，即原系统的最优编队控制律。理论分析和仿真算例验证了该编队控制策略的有效性和高效性。
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.
引文
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