自主式水下航行器的最优编队控制研究
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摘要
本文主要研究多自主式水下航行器（Autonomous underwater vehicles，AUVs）编队中的轨迹跟踪控制问题与能量最省控制问题。AUV的动态特性是一类比较复杂的非线性系统，状态向量相互之间的耦合性很高，控制难度较大。本文首先综述了国内外AUV控制研究领域的最新成果，对AUV航行中所涉及的多个因素进行数学建模，然后在模型基础上对AUV提出了多种控制要求，并给出了各种要求下系统控制律的求解过程。文章从不同尺度考虑了不同机动类型的AUV在不同编队模式下对应的时滞系统的最优控制问题，对多AUV编队与时滞系统的相关研究做出了贡献。本文主要的研究内容和创新点现概括如下：
1.化简了六自由度AUV运动学和动力学系统的数学模型，建立了海浪力干扰模型，并考虑了时滞对数学模型的影响。通过对Fossen提出的六自由度AUV模型的简化，给出了合理假设条件下四自由度的AUV非线性数学模型，降低了控制复杂度；依据海浪力学理论，得出了海浪力作为外界扰动系统的一般状态空间描述形式；根据AUV实验数据和水声通信理论，给出了AUV航行过程中时滞的估计，及其在AUV运动系统中的数学表现形式。
2.研究了一类小尺度下AUV非线性时滞系统的有限时间点到达问题。视AUV运动方程为AUV姿态控制方程与轨迹控制方程组成的级联系统，利用先控制姿态后跟踪轨迹的方法，实现非线性控制问题的线性化。接下来考虑时滞对AUV系统的影响，对线性化模型进行修正使其更贴近实际系统。最后对轨迹控制过程提出有限时间到达的问题，并给出AUV最优控制律的设计方案。用Matlab仿真实例验证了设计方法的有效性。
3.考虑了一类二维水平面上带有队形约束条件的多AUV编队最优控制问题。提出了地坐标系下描述队形约束条件的控制性能指标，设计以速度为输入量的控制律代替驱动力控制，将AUV动态模型转换为非线性低耦合系统。针对控制要求设计控制器实现最优跟踪控制，并给出了数值仿真实例与轨迹效果图，验证了控制方法的可行性。
4.提出了“观察者”编队模式，建立了一类大尺度下编队跟踪控制模型。对AUV系统进行了离散化处理，提出了一类含有等状态与控制时滞的离散系统的最优跟踪问题。在求解最优控制律时，将扰动下含有状态与输入时滞的离散系统进行模型转化，使之变成一个无时滞的系统。对该系统求解所得结果为一前馈反馈控制律。仿真结果表明所设计的控制律的有效性。
5.讨论了大尺度网络环境下AUV的远程能量最省控制问题。首先考虑了大尺度条件下水声通信产生的网络诱导时滞对AUV二阶动力模型的影响，建立了含有时滞的控制模型，并提出最小能量控制的最优性能指标。在控制律设计过程中，首先将系统转换为无时滞状态向量描述的形式，然后通过设计新状态描述的无时滞系统的最优控制律，使AUV系统能够在完成预定要求的同时控制能量输出最省。最后我通过仿真实例证明这套方法的有效性。
6.研究了含有多时滞影响的多AUV能量最省编队控制问题。描述了“指挥者”编队模式，建立了含有多状态时滞与多控制时滞的AUV集中编队控制系统数学模型，提出了编队能量最省问题。将该问题归纳到一类一般性多时滞时变系统控制问题中，给出该类问题最优控制律的求解方法，得到了最优控制律的解析解形式。通过进行仿真，验证了该算法的有效性。
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.
1.化简了六自由度AUV运动学和动力学系统的数学模型，建立了海浪力干扰模型，并考虑了时滞对数学模型的影响。通过对Fossen提出的六自由度AUV模型的简化，给出了合理假设条件下四自由度的AUV非线性数学模型，降低了控制复杂度；依据海浪力学理论，得出了海浪力作为外界扰动系统的一般状态空间描述形式；根据AUV实验数据和水声通信理论，给出了AUV航行过程中时滞的估计，及其在AUV运动系统中的数学表现形式。
2.研究了一类小尺度下AUV非线性时滞系统的有限时间点到达问题。视AUV运动方程为AUV姿态控制方程与轨迹控制方程组成的级联系统，利用先控制姿态后跟踪轨迹的方法，实现非线性控制问题的线性化。接下来考虑时滞对AUV系统的影响，对线性化模型进行修正使其更贴近实际系统。最后对轨迹控制过程提出有限时间到达的问题，并给出AUV最优控制律的设计方案。用Matlab仿真实例验证了设计方法的有效性。
3.考虑了一类二维水平面上带有队形约束条件的多AUV编队最优控制问题。提出了地坐标系下描述队形约束条件的控制性能指标，设计以速度为输入量的控制律代替驱动力控制，将AUV动态模型转换为非线性低耦合系统。针对控制要求设计控制器实现最优跟踪控制，并给出了数值仿真实例与轨迹效果图，验证了控制方法的可行性。
4.提出了“观察者”编队模式，建立了一类大尺度下编队跟踪控制模型。对AUV系统进行了离散化处理，提出了一类含有等状态与控制时滞的离散系统的最优跟踪问题。在求解最优控制律时，将扰动下含有状态与输入时滞的离散系统进行模型转化，使之变成一个无时滞的系统。对该系统求解所得结果为一前馈反馈控制律。仿真结果表明所设计的控制律的有效性。
5.讨论了大尺度网络环境下AUV的远程能量最省控制问题。首先考虑了大尺度条件下水声通信产生的网络诱导时滞对AUV二阶动力模型的影响，建立了含有时滞的控制模型，并提出最小能量控制的最优性能指标。在控制律设计过程中，首先将系统转换为无时滞状态向量描述的形式，然后通过设计新状态描述的无时滞系统的最优控制律，使AUV系统能够在完成预定要求的同时控制能量输出最省。最后我通过仿真实例证明这套方法的有效性。
6.研究了含有多时滞影响的多AUV能量最省编队控制问题。描述了“指挥者”编队模式，建立了含有多状态时滞与多控制时滞的AUV集中编队控制系统数学模型，提出了编队能量最省问题。将该问题归纳到一类一般性多时滞时变系统控制问题中，给出该类问题最优控制律的求解方法，得到了最优控制律的解析解形式。通过进行仿真，验证了该算法的有效性。
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.
引文
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