CN105955268B - A kind of UUV moving-target sliding mode tracking control methods considering Local obstacle avoidance - Google Patents
A kind of UUV moving-target sliding mode tracking control methods considering Local obstacle avoidance Download PDFInfo
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Abstract
Description
技术领域technical field
本发明涉及的是一种水下无人航行器的目标跟踪方法,具体地说是一种水下无人航行器的动目标跟踪方法。The invention relates to a target tracking method for an underwater unmanned vehicle, in particular to a moving target tracking method for an underwater unmanned vehicle.
背景技术Background technique
随着UUV使命任务和应用领域的增加,对UUV目标跟踪的能力要求也有大大提高,要求其不仅能识别静止的目标(例如援救定位尽快到达失事点、矿产开采、管道定位检修),还可以跟踪机动目标,通过预测目标状态变化做出适应性调整以免丢失跟踪对象。With the increase of UUV mission tasks and application fields, the ability requirements for UUV target tracking have also been greatly improved. It is required not only to identify stationary targets (such as rescue positioning to reach the crash point as soon as possible, mineral mining, pipeline positioning and maintenance), but also to track Maneuvering targets, making adaptive adjustments by predicting target state changes to avoid losing tracked objects.
目前,动目标跟踪问题研究主要集中在航空航天等领域,主要指的是基于卡尔曼、粒子滤波等目标状态估计;比例导引法、尾追法、固定提前角法、平行接近法等动目标导引方法;人工势场、模糊避碰法等自主避障方法。针对UUV水下环境的研究还不够成熟,对于动态环境中执行既定目标轨迹跟踪过程中可能出现的碍航物考虑较少,即使有实时的运动规划,也很少结合UUV动力学模型及操纵性能通过运动控制加以实现。因此,将上述因素引入UUV目标跟踪控制中,真实反映其动态跟踪避障能力,对于安全可靠执行各种作业任务具有重要意义。At present, the research on moving target tracking is mainly concentrated in aerospace and other fields, mainly referring to target state estimation based on Kalman and particle filter; Induction method; artificial potential field, fuzzy collision avoidance method and other autonomous obstacle avoidance methods. The research on the UUV underwater environment is not yet mature enough, and there are few considerations for the obstacles that may occur during the execution of the established target trajectory tracking in the dynamic environment. Even if there is real-time motion planning, it is rarely combined with the UUV dynamic model and maneuverability This is achieved through motion control. Therefore, introducing the above factors into the UUV target tracking control to truly reflect its dynamic tracking and obstacle avoidance capabilities is of great significance for the safe and reliable execution of various tasks.
发明内容Contents of the invention
本发明的目的在于提供一种能够实现UUV对运动目标跟踪、同时规避其航路上障碍物的导引策略,稳定快速、鲁棒性强的考虑局部避碰的UUV动目标滑模跟踪控制方法。The purpose of the present invention is to provide a UUV moving target sliding mode tracking control method that can realize UUV tracking of moving targets while avoiding obstacles on its route, is stable, fast, and robust and considers local collision avoidance.
本发明的目的是这样实现的:The purpose of the present invention is achieved like this:
步骤一:UUV通过导航姿态传感器、位置测量系统、前视声呐,实时探测UUV、运动目标以及障碍物位置信息;Step 1: UUV detects UUV, moving target and obstacle position information in real time through navigation attitude sensor, position measurement system and forward-looking sonar;
步骤二:建立运动目标和障碍物运动学模型,基于不敏卡尔曼滤波获取运动目标k时刻状态估计;Step 2: Establish the kinematics model of the moving target and the obstacle, and obtain the state estimation of the moving target at time k based on the insensitive Kalman filter;
步骤三:建立UUV和运动目标以及障碍物的相对运动模型,用于计算k时刻跟踪距离和视线角;Step 3: Establish the relative motion model of the UUV, the moving target, and the obstacle for calculating the tracking distance and line-of-sight angle at time k;
步骤四:基于目标跟踪半径D1和障碍物规避安全半径D2的大小,根据UUV与运动目标及障碍物的相对位置,在跟踪策略和避碰策略之间自主切换,改变UUV控制视线,规划UUVk时刻指令速度和航向;Step 4: Based on the size of the target tracking radius D 1 and the obstacle avoidance safety radius D 2 , according to the relative position of the UUV, the moving target and the obstacle, switch between the tracking strategy and the collision avoidance strategy autonomously, change the UUV control line of sight, and plan UUVk command speed and heading at all times;
步骤五:根据步骤四中得到的指令速度和航向与UUV航速及转艏角速度测量反馈,得到跟踪控制偏差,基于水平面非奇异终端滑模控制器解算得到k时刻UUV推进器推力和方向舵转艏力矩;Step 5: According to the command speed and heading obtained in step 4, and the UUV speed and bow angular velocity measurement feedback, the tracking control deviation is obtained, and the thrust of the UUV propeller and the rudder turning bow at time k are obtained based on the non-singular terminal sliding mode controller on the horizontal plane. torque;
步骤六:循环执行步骤一至步骤五,实现运动目标下一刻的跟踪控制,直到任务结束。Step 6: Perform steps 1 to 5 cyclically to realize the tracking control of the moving target at the next moment until the end of the task.
本发明还可以包括:The present invention may also include:
1、跟踪策略和避碰策略之间自主切换的导引方式具体表示为:在全局跟踪过程中,如果出现ρoiv,k≤D2+(Rio+Rv),就激活避碰导引律式将视线切换到障碍物规避方面,一旦确认UUV运动到安全区域就执行目标跟踪导引律式立即恢复跟踪过程,1. The guidance method of autonomous switching between the tracking strategy and the collision avoidance strategy is specifically expressed as: during the global tracking process, if ρ oiv,k ≤ D 2 +(R io +R v ), the collision avoidance guidance is activated Rhythm Switch the line of sight to obstacle avoidance, and execute the target tracking and guidance formula once the UUV is confirmed to move to a safe area Immediately resume the tracking process,
其中:ρoiv,k为k时刻UUV与第i个障碍物之间的距离,UUV简化为半径Rv,Rio为第i个障碍物的半径,uvRef,k为k时刻UUV导引速度、rvRef,k为k时刻UUV导引转艏角速度、为最大航速、为最小航速、ψv,k为k时刻UUV的航向角、为UUV最大转艏角速度、n0为跟踪速度增益、n1为跟踪转艏控制增益、n2为避碰速度增益、n3为避碰转艏控制增益、ρvg,k为k时刻UUV与目标之间的距离、φvg,k为k时刻UUV与目标的视线角即视线矢量与惯性坐标系Eξ轴之间的夹角、φoiv,k为k时刻UUV与第i个障碍物之间的视线角、D1为目标跟踪半径、D2为障碍物规避安全半径、为饱和函数且取视线控制和饱和角速度的最小值、Φ(α)将转角转换到区间[-π,π]。Where: ρ oiv,k is the distance between UUV and the i-th obstacle at time k, UUV is simplified to radius R v , R io is the radius of the i-th obstacle, u vRef,k is the UUV guidance speed at time k , r vRef,k is the UUV guidance turning angle velocity at time k, for the maximum speed, is the minimum speed, ψv ,k is the course angle of the UUV at time k, is the UUV maximum bow angle velocity, n 0 is the tracking speed gain, n 1 is the tracking bow control gain, n 2 is the collision avoidance speed gain, n 3 is the collision avoidance bow control gain, ρvg,k is the UUV and The distance between the targets, φ vg,k is the sight angle between the UUV and the target at time k, that is, the angle between the line of sight vector and the Eξ axis of the inertial coordinate system, φ oiv,k is the distance between the UUV and the i-th obstacle at time k The line of sight angle, D 1 is the target tracking radius, D 2 is the obstacle avoidance safety radius, is a saturation function and takes the minimum value of line of sight control and saturation angular velocity, Φ(α) converts the rotation angle to the interval [-π,π].
2、步骤五中所述UUV推进器推力和方向舵转艏力矩具体表示为:2. The thrust of the UUV propeller and the turning moment of the rudder described in step five are specifically expressed as:
其中:k时刻UUV推进器推力τu,k、k时刻方向舵转艏力矩τr,k、k时刻UUV实际航速uv,k、k时刻UUV导引速度uvRef,k、k时刻UUV实际转艏角速度rv,k、k时刻UUV导引转艏角速度rvRef,k、k时刻UUV横向运动速度vv,k;非奇异终端航速控制滑模面s1和转艏控制滑模面s2,滑模面可调参数β1>0、β2>0,p1、q1、p2、q2为正奇数且航速跟踪控制偏差ue,k=uvRef,k-uv,k、艏向角速度控制偏差re,k=rref,k-rv,k; d11=Xu+X|u|u|u|,d22=Yv+Y|v|v|v|,d33=Zw+Z|w|w|w|为动力学模型参数;“^”表示系统模型参数的估计值,且i=1,2,3,5,6,表示模型参数的摄动量,c1sat(s1/φ1)、c2sat(s2/φ2)为滑模控制器的不连续切换项,c1、φ1、c2、φ2为改变抖振及摄动能力的可调参数。Among them: UUV thruster thrust τ u, k at time k, rudder turning bow moment τ r, k at time k, UUV actual speed u v, k at time k, UUV guidance speed u vRef, k at time k, actual UUV rotation speed at time k Bow angular velocity r v,k , UUV guidance turning bow angular velocity r vRef,k , UUV lateral motion velocity v v,k at time k ; non-singular terminal speed control sliding mode surface s 1 and turning bow control sliding mode surface s 2 , sliding mode surface adjustable parameters β 1 >0, β 2 >0, p 1 , q 1 , p 2 , q 2 are positive odd numbers and Speed tracking control deviation u e,k =u vRef,k -u v,k , heading angular velocity control deviation r e,k =r ref,k -r v,k ; d 11 =X u +X |u|u |u|, d 22 =Y v +Y |v|v |v|, d 33 =Z w +Z |w|w |w| is a dynamic model parameter; "^" indicates the estimated value of the system model parameters, and i = 1, 2, 3, 5, 6, indicating the perturbation of the model parameters, c 1 sat(s 1 /φ 1 ), c 2 sat(s 2 /φ 2 ) are the discontinuous switching items of the sliding mode controller , c 1 , φ 1 , c 2 , φ 2 are adjustable parameters for changing chattering and perturbation capabilities.
本发明导引策略的控制目标为:考虑UUV饱和约束条件下,二维动态环境中的目标跟踪和局部避障问题。①对于位置跟踪,如果则存在D1>0,使得对于有②对于障碍物避碰问题,如果ρoiv(t0)>D2,则存在D2>0,使对于有ρoiv(t)>(Rio+Rv)成立。The control target of the guidance strategy of the present invention is: considering the UUV saturation constraints, the problem of target tracking and local obstacle avoidance in a two-dimensional dynamic environment. ① For position tracking, if Then there exists D 1 >0 such that for Have ②For the obstacle avoidance problem, if ρ oiv (t 0 )>D 2 , then there exists D 2 >0, so that for ρ oiv (t)>(R io +R v ) holds.
其中,q=[x y ψ]T表示惯性坐标系中位置和航向角,U=[u r]T表示航速和转艏角速度组成的运动学控制向量,用qv,k=[xv,k yv,k ψv,k]T、Uv,k=[uv,k rv,k]T表示k时刻的UUV状态,qg,k=[xg,k yg,k ψg,k]T、Ug,k=[ug,k rg,k]T表示k时刻的目标状态,qio,k=[xio,k yio,kψio,k]T、Uio,k=[uio,k rio,k]T表示k时刻第i个障碍物状态。将UUV简化为半径Rv,中心位置为(xv,k,yv,k)的圆,类似得到半径为Rg的目标和半径为Rio的障碍物的简化表示形式。ρvg,k为k时刻UUV与目标之间的距离,φvg,k为k时刻UUV与目标的视线角(视线矢量与惯性坐标系Eξ轴之间的夹角);ρoiv,k为k时刻UUV与第i个障碍物之间的距离,φoiv,k为k时刻UUV与第i个障碍物之间的视线角;D1为目标跟踪半径,D2为障碍物规避安全半径。Among them, q=[xy ψ] T represents the position and heading angle in the inertial coordinate system, U=[ur] T represents the kinematics control vector composed of the speed of the ship and the angular velocity of the bow, and q v,k =[x v,k y v,k ψ v,k ] T , U v,k =[u v,k r v,k ] T represents the UUV state at time k, q g,k =[x g,k y g,k ψ g, k ] T , U g,k =[u g,k r g,k ] T represents the target state at time k, q io,k =[x io, ky io,k ψ io,k ] T , U io ,k =[u io,k r io,k ] T represents the state of the i-th obstacle at time k. Simplify the UUV into a circle with radius R v and center position (x v, k , y v, k ) , which is similar to the simplified representation of the target with radius R g and the obstacle with radius R io . ρ vg,k is the distance between the UUV and the target at time k, φ vg,k is the line-of-sight angle between the UUV and the target at time k (the angle between the line-of-sight vector and the Eξ axis of the inertial coordinate system); ρ oiv,k is k The distance between the UUV and the i-th obstacle at time, φ oiv,k is the line-of-sight angle between the UUV and the i-th obstacle at time k; D 1 is the target tracking radius, and D 2 is the obstacle avoidance safety radius.
对于UUV速度和航向上的饱和约束,设最大航速为最大转向变化率为另外为保证UUV潜伏在水下,其速度不能减速到零(会浮出水面),设最小航速为则有:制定的导引策略具体如下:For the saturation constraint on UUV speed and course, set the maximum speed as Maximum steering change rate In addition, in order to ensure that the UUV is lurking underwater, its speed cannot be decelerated to zero (it will surface), and the minimum speed is set as Then there are: The guidance strategy formulated is as follows:
(1)目标跟踪导引律为:(1) The target tracking and guidance law is:
其中,n0为正常数速度增益,为保证跟踪的平滑性,使UUV在落后目标较远时以与距离成正比的速度跟踪;n1为转艏控制增益,Φ(α)将转角限制在区间[-π,π);为饱和函数,取视线控制和饱和角速度的最小值。Among them, n 0 is the constant speed gain, in order to ensure the smoothness of tracking, the UUV will track at a speed proportional to the distance when it is far behind the target; n 1 is the control gain of turning the bow, and Φ(α) limits the turning angle to interval[-π,π); is the saturation function, taking the minimum value of line-of-sight control and saturation angular velocity.
(2)避碰导引律为:(2) The guidance law for collision avoidance is:
其中,0<n2≤1转速控制增益,n3设计为正常数的转艏控制增益。Among them, 0<n 2 ≤1 speed control gain, n 3 is designed as a normal constant bow control gain.
(3)视线切换策略:在全局跟踪过程中,如若出现ρoiv,k≤D2+(Rio+Rv)的时刻,就激活避碰导引律,将视线切换到障碍物规避方面,一旦确认UUV运动到安全区域就执行目标跟踪导引律,立马恢复跟踪过程。(3) Line of sight switching strategy: During the global tracking process, if ρ oiv,k ≤ D 2 +(R io +R v ) occurs, the collision avoidance guidance law is activated to switch the line of sight to obstacle avoidance, Once it is confirmed that the UUV has moved to a safe area, the target tracking and guidance law will be executed, and the tracking process will be resumed immediately.
本发明设计了如下的非奇异终端滑模速度控制器和转艏控制器:The present invention designs the following non-singular terminal sliding mode speed controller and bow controller:
UUV推进器推力控制律为:The thrust control law of the UUV thruster is:
UUV方向舵转艏力矩控制律为:The UUV rudder steering moment control law is:
其中,d11=Xu+X|u|u|u|,d22=Yv+Y|v|v|v|,d33=Zw+Z|w|w|w|为动力学模型参数;“^”表示系统模型参数的估计值,且 i=1,2,3,5,6,表示模型参数的摄动量,c1sat(s1/φ1)、c2sat(s2/φ2)为滑模控制器的不连续切换项,通过调整参数c1,φ1,c2,φ2可增强控制器鲁棒性并改善滑模抖振现象。in, d 11 =X u +X |u|u |u|, d 22 =Y v +Y |v|v |v|, d 33 =Z w +Z |w|w |w| is a dynamic model parameter; "^" indicates the estimated value of the system model parameters, and i = 1, 2, 3, 5, 6, indicating the perturbation of the model parameters, c 1 sat(s 1 /φ 1 ), c 2 sat(s 2 /φ 2 ) are the discontinuous switching items of the sliding mode controller , by adjusting the parameters c 1 , φ 1 , c 2 , φ 2 can enhance the robustness of the controller and improve the chattering phenomenon of the sliding mode.
UUV的航速跟踪误差为ue,k=uvRef,k-uv,k,转艏角速度跟踪误差为re,k=rref,k-rv,k,设计的非奇异Terminal滑模面分别为:The speed tracking error of UUV is u e,k =u vRef,k -u v,k , and the tracking error of turning bow angle velocity is r e,k =r ref,k -r v,k , the designed non-singular Terminal sliding surface They are:
其中,β1>0,β2>0,p1,q1,p2,q2为正奇数且 Among them, β 1 >0, β 2 >0, p 1 , q 1 , p 2 , q 2 are positive odd numbers and
本发明提供了一种能够实现UUV对运动目标跟踪同时规避其航路上障碍物的导引策略,并且结合UUV动力学模型和运动控制能力给出具体实现方法。本发明的有益效果在于:The present invention provides a guidance strategy capable of realizing UUV tracking a moving target while avoiding obstacles on its route, and provides a specific implementation method in combination with the UUV dynamic model and motion control capability. The beneficial effects of the present invention are:
(1)以UUV与目标及障碍物之间的距离作为动态规划准则,简化了动态环境目标跟踪和局部避障问题的分析,考虑了UUV的运动控制约束制定的简单有效切换策略,实现了UUV安全性和跟踪精度要求下的实时平稳运动规划。(1) Using the distance between the UUV and the target and obstacles as the dynamic programming criterion, the analysis of the dynamic environment target tracking and local obstacle avoidance problems is simplified, and the simple and effective switching strategy formulated by considering the motion control constraints of the UUV realizes the UUV Real-time smooth motion planning with safety and tracking accuracy requirements.
(2)设计了非奇异终端滑模控制器,能够消除控制过程中可能出现的系统奇异点,有限时间内实现对指令的稳定控制,并且十分适用于水下非线性,存在环境干扰和模型参数摄动的复杂工况。实现了考虑UUV动力学模型的有效跟踪过程,稳定快速、鲁棒性强。(2) A non-singular terminal sliding mode controller is designed, which can eliminate the possible singularity of the system during the control process, realize stable control of the command within a limited time, and is very suitable for underwater nonlinearity, where there are environmental disturbances and model parameters Perturbed complex working conditions. An effective tracking process considering the UUV dynamics model is realized, which is stable, fast and robust.
附图说明Description of drawings
图1为本发明的总体框图;Fig. 1 is the overall block diagram of the present invention;
图2为平面中UUV目标跟踪和被动避障双目标控制问题示意图;Fig. 2 is a schematic diagram of UUV target tracking and passive obstacle avoidance dual target control problem in the plane;
图3为UUV目标跟踪导引示意图;Fig. 3 is a schematic diagram of UUV target tracking guidance;
图4为UUV障碍物避碰导引示意图;Figure 4 is a schematic diagram of UUV obstacle collision avoidance guidance;
图5为UUV跟踪运动目标仿真案例轨迹;Figure 5 is the trajectory of the UUV tracking moving target simulation case;
图6a至图6d为UUV跟踪运动目标仿真案例的控制参数图;Figures 6a to 6d are the control parameter diagrams of the UUV tracking moving target simulation case;
图7为UUV跟踪运动目标同时规避动态障碍物仿真案例轨迹;Figure 7 is the trajectory of a UUV tracking a moving target while avoiding a dynamic obstacle simulation case;
图8a至图8d为UUV跟踪运动目标同时规避动态障碍物仿真案例的控制参数图;Figures 8a to 8d are control parameter diagrams of a simulation case of UUV tracking a moving target while avoiding dynamic obstacles;
图9是本发明的流程图。Fig. 9 is a flowchart of the present invention.
具体实施方式Detailed ways
下面结合附图对本发明做进一步说明:The present invention will be further described below in conjunction with accompanying drawing:
UUV在执行回收对接等任务时,需要尾随跟踪特定目标,对于水下复杂环境,在跟踪目标运动航路上不可避免会出现随机障碍物(船只、浮游生物、水下垃圾等),针对此情况本发明给出一种简单有效的UUV动态环境跟踪控制方法。When UUV performs tasks such as recovery and docking, it needs to follow and track specific targets. For complex underwater environments, random obstacles (ships, plankton, underwater garbage, etc.) will inevitably appear on the track of target movement routes. The invention provides a simple and effective UUV dynamic environment tracking control method.
图1为本发明的总体工作框图,主要分为UUV模型及探测系统、目标状态估计、动态规划模块和非奇异终端滑模控制器四个部分,目标和障碍物位置由UUV声呐探测系统获取,UUV实时状态信息由其组合导航系统测定,结合图9描述本发明的具体步骤。Fig. 1 is an overall working block diagram of the present invention, which is mainly divided into four parts: UUV model and detection system, target state estimation, dynamic programming module and non-singular terminal sliding mode controller. The positions of targets and obstacles are obtained by the UUV sonar detection system, The UUV real-time status information is determined by its integrated navigation system, and the specific steps of the present invention are described in conjunction with FIG. 9 .
步骤一:UUV通过导航姿态传感器、位置测量系统、前视声呐等,实时探测UUV、运动目标以及障碍物位置信息(本发明的仿真图由直接给出目标及障碍物运动轨迹得到);Step 1: UUV detects UUV, moving target and obstacle position information in real time through navigation attitude sensor, position measurement system, forward-looking sonar, etc.
步骤二:根据目标和障碍物运动规律,建立其运动学模型,基于轨迹点位置由不敏卡尔曼(UKF)滤波算法获取其k时刻状态估计;Step 2: Establish the kinematics model according to the movement law of the target and the obstacle, and obtain the state estimation at time k by the Unsensitive Kalman (UKF) filter algorithm based on the position of the track point;
设目标动态模型为Xk=FXk-1+GWk,状态向量F为系统转移矩阵,G为系统噪声变换矩阵,系统状态噪声Wk=[wx,k,wy,k]T为零均值高斯噪声,协方差为Qk。观测模型为Zk=h(Xk)+Vk,其中h为观测函数,Vk为服从高斯分布的测量噪声序列,协方差为Rk,且存在Let the target dynamic model be X k =FX k-1 +GW k , the state vector F is the system transition matrix, G is the system noise transformation matrix, the system state noise W k =[w x,k ,w y,k ] T is zero-mean Gaussian noise, and the covariance is Q k . The observation model is Z k =h(X k )+V k , where h is the observation function, V k is the measurement noise sequence obeying the Gaussian distribution, the covariance is R k , and there is
cov[Wk]=Qk,cov[Vk]=Rk cov[W k ]=Q k , cov[V k ]=R k
UKF算法的简化流程为:The simplified process of the UKF algorithm is:
1.给定系统初值(初始状态均值估计值初始状态方差估计值P0)1. Given the initial value of the system (the estimated value of the initial state mean value Initial state variance estimate P 0 )
2.计算Sigma采样点χi及其权值λi,以最小的样本集来近似系统状态的分布函数2. Calculate the Sigma sampling point χ i and its weight λ i , and approximate the distribution function of the system state with the smallest sample set
其中n为状态向量的维度,κ为尺度参数,本设计中取2。Among them, n is the dimension of the state vector, and κ is the scale parameter, which is 2 in this design.
3.预测/时间更新,对Sigma采样点进行非线性变换和加权处理,得到状态向量均值、状态向量方差和输出向量的一步预测值Pk|k-1、 3. Prediction/time update, perform nonlinear transformation and weighting processing on the Sigma sampling points, and obtain the one-step prediction value of the state vector mean, state vector variance and output vector P k|k-1 、
使用变换后的状态变量进行滤波估计,以减小估计误差,同时由于该算法采用了非线性的动态方程或量测方程,避免了线性化误差。The transformed state variable is used for filter estimation to reduce the estimation error, and at the same time, the linearization error is avoided because the algorithm uses nonlinear dynamic equation or measurement equation.
4.校正/测量更新4. Calibration/measurement update
其中,Yk为k时刻观测值,Pk分别为k时刻输出向量和状态向量方差,为其两者协方差,Mk为UKF校正增益,即为k时刻状态的滤波估计值。Among them, Y k is the observed value at time k, P k is the variance of output vector and state vector at time k respectively, is the covariance of the two, M k is the UKF correction gain, That is, the filtered estimated value of the state at time k.
步骤三:根据步骤二中滤波后的状态信息,基于UUV和运动目标以及障碍物的相对运动模型,计算k时刻的跟踪距离和视线角,如图2所示的平面中UUV目标跟踪和被动避障双目标控制问题;Step 3: According to the state information filtered in step 2, based on the relative motion model of UUV, moving target and obstacle, calculate the tracking distance and line-of-sight angle at time k, as shown in Figure 2, UUV target tracking and passive avoidance in the plane Obstacle dual-objective control problem;
在制定导引策略时,认为UUV横向速度是个微小的耦合量,对运动轨迹影响较小,设计时将运动学模型简化为如式(5)的形式,并且假定目标和障碍物满足相同的运动规律:When formulating the guidance strategy, it is considered that the UUV lateral velocity is a small coupling quantity, which has little influence on the trajectory. When designing, the kinematics model is simplified to the form of formula (5), and it is assumed that the target and the obstacle satisfy the same motion law:
其中q=[x y ψ]T表示惯性坐标系中位置和航向角,U=[u r]T表示航速和转艏角速度组成的运动学控制向量。k时刻,对于UUV以向量qv,k=[xv,k yv,k ψv,k]T、Uv,k=[uv,krv,k]T来表示,目标以qg,k=[xg,k yg,k ψg,k]T、Ug,k=[ug,k rg,k]T来表示,第i个障碍物以qio,k=[xio,k yio,k ψio,k]T、Uio,k=[uio,k rio,k]T来表示;在示意图中UUV简化为半径Rv,中心位置为(xv,k,yv,k)的圆,类似得到半径为Rg的目标和半径为Rio的障碍物的简化表示形式。Where q=[xy ψ] T represents the position and heading angle in the inertial coordinate system, U=[ur] T represents the kinematics control vector composed of the speed and the angular velocity of the bow. At time k, UUV is represented by vector q v,k =[x v, ky v,k ψ v,k ] T , U v,k =[u v,k r v,k ] T , and the target is represented by q g,k =[x g,k y g,k ψ g,k ] T , U g,k =[u g,k r g,k ] T , and the i-th obstacle is represented by q io,k = [x io, ky io,k ψ io,k ] T , U io,k =[u io,k r io,k ] T to represent; in the schematic diagram UUV is simplified to radius R v , and the center position is (x v,k ,y v,k ), similar to the simplified representation of the target with radius R g and the obstacle with radius R io .
带入UUV和目标的相对运动模型:Bring in the relative motion model of UUV and target:
其中,ρvg,k为k时刻UUV与目标之间的距离,φvg,k为k时刻UUV与目标的视线角(视线矢量与惯性坐标系Eξ轴之间的夹角)。Among them, ρ vg,k is the distance between the UUV and the target at time k, and φ vg,k is the line-of-sight angle between the UUV and the target at time k (the angle between the line-of-sight vector and the Eξ axis of the inertial coordinate system).
式(6)取微分形式,联立式(5)推导得到UUV与目标的跟踪误差形式:Formula (6) takes the differential form, and the simultaneous formula (5) is derived to obtain the form of tracking error between UUV and target:
同理,UUV和第i个障碍物的相对运动模型为:Similarly, the relative motion model of the UUV and the i-th obstacle is:
其中,ρoiv,k为k时刻UUV与第i个障碍物之间的距离,φoiv,k为k时刻UUV与第i个障碍物之间的视线角。Among them, ρ oiv,k is the distance between the UUV and the i-th obstacle at time k, and φ oiv,k is the line-of-sight angle between the UUV and the i-th obstacle at time k.
步骤四:基于步骤三中计算得到的k时刻UUV与目标及障碍物的相对位置,结合目标跟踪半径D1和障碍物规避安全半径D2的要求,制定全局跟踪和局部避碰自主切换策略,改变UUV控制视线,规划其k时刻的指令速度uvRef,k和指令航向rvRef,k;Step 4: Based on the relative position of the UUV, the target and the obstacle at time k calculated in step 3, combined with the requirements of the target tracking radius D 1 and the obstacle avoidance safety radius D 2 , formulate an autonomous switching strategy for global tracking and local collision avoidance, Change the UUV control line of sight, plan its command speed u vRef,k and command heading r vRef,k at time k ;
(1)目标跟踪导引律:设计在最大转艏角速度的限制下,控制UUV航向尽快向跟踪视线方向转动,并且当UUV在目标接近圆内时以目标速度保持监视,当目标机动逃到跟踪圈以外时UUV采用最大航速追踪,如图3所示。尽量选用恒定线速度的方式有利于减少控制量,以转艏控制来增加航速控制的灵活性,具体可表示为:(1) Target tracking and guidance law: Under the limitation of the maximum turning angle speed, the UUV is designed to control the course of the UUV to turn to the direction of the tracking line of sight as soon as possible, and when the UUV is within the target approach circle, it will keep monitoring at the target speed, and when the target maneuvers to escape to the tracking When the UUV is outside the circle, it uses the maximum speed to track, as shown in Figure 3. It is beneficial to reduce the amount of control to choose the method of constant linear speed as much as possible, and increase the flexibility of speed control by turning the bow control, which can be specifically expressed as:
其中,UUV有最大航速最大转向变化率的饱和约束,并为保证UUV潜伏在水下,设最小航速为即n0为正常数速度增益,为保证跟踪的平滑性,使UUV在落后目标较远时以与距离成正比的速度跟踪;为饱和函数,取视线控制和饱和角速度的最小值,函数表示为:Among them, UUV has a maximum speed Maximum steering change rate The saturation constraint of , and to ensure that the UUV is lurking underwater, the minimum speed is set as which is n 0 is a constant speed gain. In order to ensure the smoothness of tracking, the UUV will track at a speed proportional to the distance when it is far behind the target; is the saturation function, taking the minimum value of line-of-sight control and saturation angular velocity, the function is expressed as:
n1为转艏控制增益,Φ(α)将转角限制在区间[-π,π),定义为:n 1 is the steering bow control gain, Φ(α) limits the steering angle to the interval [-π,π), defined as:
(2)避碰导引律:当目标进入半径为D2的障碍物危险圆以内时,设计在最大转艏角速度的限制下,控制UUV以最大线速度尽快转向远离障碍物的视线方向,如图4所示的避障导引策略,函数表示为:( 2 ) Collision avoidance guidance law: when the target enters the obstacle circle with a radius of D2, the design controls the UUV to turn away from the obstacle’s line of sight direction as soon as possible at the maximum linear velocity under the limit of the maximum turning angle velocity, as shown in The obstacle avoidance guidance strategy shown in Figure 4, the function is expressed as:
其中,0<n2≤1转速控制增益,n3设计为正常数的转艏控制增益。Among them, 0<n 2 ≤1 speed control gain, n 3 is designed as a normal constant bow control gain.
(3)视线切换策略:基于以上两种情况的导引,可以证明存在(n0,n1,D1)使得UUV对目标的跟踪误差一致收敛于D1,存在(n2,n3,D2)使得在初始时刻的条件下,系统能够保证成功避开障碍物。得到动态环境中目标跟踪同时被动避障的策略是:在全局跟踪过程中,如若出现ρoiv,k≤D2+(Rio+Rv)的时刻,就激活避碰导引律,将视线切换到障碍物规避,一旦确认UUV运动到安全区域就立马恢复跟踪过程。(3) Line of sight switching strategy: Based on the guidance of the above two situations, it can be proved that there is (n 0 ,n 1 ,D 1 ) so that the tracking error of the UUV to the target converges to D 1 consistently, and there is (n 2 ,n 3 , D 2 ) such that at the initial moment Under certain conditions, the system can guarantee successful obstacle avoidance. The strategy to obtain target tracking and passive obstacle avoidance in a dynamic environment is: in the global tracking process, if ρ oiv,k ≤ D 2 +(R io +R v ) occurs at the moment, the collision avoidance and guidance law is activated, and the line of sight Switch to obstacle avoidance, and immediately resume the tracking process once the UUV is confirmed to move to a safe area.
步骤五:制定跟踪策略后还需要结合动力机构加以控制,因此根据步骤四中的导引指令与UUV航速及转艏角速度测量反馈,得到跟踪控制偏差,设计对于参数摄动及环境干扰具有很强鲁棒性的非奇异终端滑模控制器,解算得到k时刻UUV推进器推力τu,k和方向舵转艏力矩τr,k;Step 5: After formulating the tracking strategy, it needs to be controlled in combination with the power mechanism. Therefore, according to the guidance command in step 4 and the UUV speed and bow angular velocity measurement feedback, the tracking control deviation is obtained. The design has a strong effect on parameter perturbation and environmental interference. Robust non-singular terminal sliding mode controller, the UUV thruster thrust τ u,k and rudder turning bow moment τ r,k at time k are obtained through calculation;
对于水平面UUV动力学模型具有如下简化形式:For the horizontal plane UUV dynamics model has the following simplified form:
将步骤四中得到的导引律uvRef,k和rvRef,k作为k时刻运动控制期望指令,与UUV实际航速航向相比较,得到跟踪控制偏差ue,k=uvRef,k-uv,k,re,k=rref,k-rv,k,基于非奇异终端滑模原理分别设计速度和转艏控制滑模面:Take the guidance law u vRef,k and r vRef,k obtained in step 4 as the expected motion control command at time k, and compare it with the actual speed and heading of the UUV to obtain the tracking control deviation u e,k =u vRef,k -u v ,k ,r e,k =r ref,k -r v,k , based on the principle of non-singular terminal sliding mode, design the velocity and bow control sliding mode surfaces respectively:
其中,可调参数β1>0,β2>0,p1,q1,p2,q2为正奇数且 Among them, the adjustable parameters β 1 >0, β 2 >0, p 1 , q 1 , p 2 , q 2 are positive odd numbers and
推导得到水平面UUV推力和转艏力矩控制律:The control law of UUV thrust and turning moment on the horizontal plane is derived as follows:
其中,d11=Xu+X|u|u|u|,d22=Yv+Y|v|v|v|,d33=Zw+Z|w|w|w|为动力学模型参数;“^”表示系统模型参数的估计值,且 i=1,2,3,5,6,表示模型参数的摄动量,c1sat(s1/φ1)、c2sat(s2/φ2)为滑模控制器的不连续切换项。in, d 11 =X u +X |u|u |u|, d 22 =Y v +Y |v|v |v|, d 33 =Z w +Z |w|w |w| is a dynamic model parameter; "^" indicates the estimated value of the system model parameters, and i = 1, 2, 3, 5, 6, indicating the perturbation of the model parameters, c 1 sat(s 1 /φ 1 ), c 2 sat(s 2 /φ 2 ) are the discontinuous switching items of the sliding mode controller .
构造Lyapunov函数均正定,分别求导可以证明 Construct Lyapunov function Both are positive definite, respectively deriving can prove that
负定,由此可知UUV跟踪控制偏差能在有限时间向零状态稳定,即实际航速和实际转艏角速度能在有限时间内跟踪导引指令。Negative determination, it can be seen that the UUV tracking control deviation can be stabilized to zero state in a limited time, that is, the actual speed and actual bow angle speed can track the guidance command in a limited time.
步骤六:k+1时刻,跳转至步骤一,执行步骤一~步骤五,得到实时跟踪控制τu,k+1和τr,k+1;随着采样进行,循环上述过程直到收到任务结束指令。Step 6: At time k+1, jump to step 1 and execute steps 1 to 5 to obtain real-time tracking control τ u,k+1 and τ r,k+1 ; as the sampling proceeds, loop the above process until receiving Task end command.
给出本发明的两个实例仿真,轨迹及运动控制参数图分别见附图。图5、图6a至图6d为机动目标跟踪过程,整个过程相对平稳;图7、图8a至图8d展示的是跟踪环境未知,出现运动障碍物在航线上干扰的情况,对突变的运动指令仍然能快速稳定控制。Two example simulations of the present invention are given, and the trajectory and motion control parameter diagrams are shown in the accompanying drawings. Fig. 5, Fig. 6a to Fig. 6d show the maneuvering target tracking process, and the whole process is relatively stable; Fig. 7, Fig. 8a to Fig. 8d show that the tracking environment is unknown, and moving obstacles interfere with the route. Still fast and stable control.
设随机运动障碍物轨迹方程为Let the trajectory equation of the random moving obstacle be
UUV半径Rv=3m,运动障碍物半径Ro=5m,目标接近圆半径D1=10m,障碍物风险区半径D2=25m,数据采集间隔To=0.5s。可以看出滑模控制器精度极高,对控制指令响应快误差小,UUV实际航迹基本能够与规划轨迹重合。在图7案例中,本仿真方法一方面能够保证对动目标的跟踪精度,另一方面ρov(t)≤D2+(Ro+Rv)=33m时激活避障控制直至ρov(t)>D2+(Ro+Rv),短时避障期间ρov(min)=26.8024m>Ro+Rv=8m始终保证了UUV的航行安全性。UUV radius R v =3m, moving obstacle radius R o =5m, target approach circle radius D 1 =10m, obstacle risk zone radius D 2 =25m, data collection interval T o =0.5s. It can be seen that the precision of the sliding mode controller is extremely high, the response to the control command is fast and the error is small, and the actual track of the UUV can basically coincide with the planned track. In the case of Figure 7, on the one hand, this simulation method can guarantee the tracking accuracy of the moving target, on the other hand, when ρ ov (t)≤D 2 +(R o +R v )=33m, the obstacle avoidance control is activated until ρ ov ( t)>D 2 +(R o +R v ), ρ ov (min)=26.8024m>R o +R v =8m during the short-term obstacle avoidance period ensures the navigation safety of UUV all the time.
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