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CN112631305A - Anti-collision anti-interference control system for formation of multiple unmanned ships - Google Patents
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CN112631305A - Anti-collision anti-interference control system for formation of multiple unmanned ships - Google Patents

Anti-collision anti-interference control system for formation of multiple unmanned ships Download PDF

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CN112631305A
CN112631305A CN202011580559.8A CN202011580559A CN112631305A CN 112631305 A CN112631305 A CN 112631305A CN 202011580559 A CN202011580559 A CN 202011580559A CN 112631305 A CN112631305 A CN 112631305A
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unmanned ship
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CN112631305B (en
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彭周华
吕光颢
王丹
尹勇
刘陆
王浩亮
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Dalian Maritime University
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Abstract

本发明公开了防碰撞抗干扰多无人船编队控制系统，包括用于对受控无人船模块建立的运动学与动力学模型进行重构的模型重构模块，获取无人船编队中与所述无人船存在信息交互的无人船信息并发送至位置预测控制模块的交互信息网络拓扑模块，获取无人船的航行信息和交互信息计算纵向速度控制输入和参考艏摇角序列并输入至艏摇角预测控制模块的位置预测控制模块，计算艏摇角速度控制输入值并输入至无人船运动学与动力学模型模块的艏摇角预测控制模块，以及计算艏摇角方向和模型不确定和时变海流扰动未知函数的估计值的不确定与扰动估计模块。该系统可以实现在复杂海洋环境下，提高无人船的抗扰动性与控制精确性，并能防止编队中无人船之间的碰撞。

Figure 202011580559

The invention discloses an anti-collision and anti-jamming multi-unmanned ship formation control system, which includes a model reconstruction module for reconstructing the kinematics and dynamics models established by the controlled unmanned ship module, and obtains the correlation between the unmanned ship formation and the unmanned ship. The unmanned ship has the unmanned ship information of information interaction and sends it to the interactive information network topology module of the position prediction control module, obtains the navigation information and interactive information of the unmanned ship, calculates the longitudinal speed control input and the reference yaw angle sequence and inputs it To the position prediction control module of the yaw angle prediction control module, to calculate the yaw angle speed control input value and input it to the yaw angle prediction control module of the unmanned ship kinematics and dynamics model module, and to calculate the yaw angle direction and the model uncertainty. Uncertainty and Disturbance Estimation Module for Determining and Estimated Time-Varying Current Disturbance Unknown Functions. The system can improve the anti-disturbance and control accuracy of unmanned ships in complex marine environments, and can prevent collisions between unmanned ships in formations.

Figure 202011580559

Description

Anti-collision anti-interference control system for formation of multiple unmanned ships
Technical Field
The invention relates to the technical field of multi-unmanned ship formation motion control, in particular to an anti-collision anti-interference control system for multi-unmanned ship formation.
Background
The unmanned ship is an important tool for human beings to know, develop and protect the ocean and is an important embodiment of the national ocean science and technology level. The cooperativity is a mark for measuring the intelligent degree of the unmanned ship and is also an inevitable requirement for the intelligent development of the ship. The cooperative operation of the unmanned ships can obviously improve the operation efficiency and form the complementary advantages and the large-scale effect. In the key technical field of unmanned ship cooperation, the formation control technology is an important component, and the exploration of the unmanned ship formation control technology has important significance.
Some feasible technical solutions are already available for the problem of unmanned ship formation motion control. For example, chinese patent CN111506079A proposes a novel method for controlling formation of a virtual structure of an unmanned ship in consideration of obstacle avoidance, which constructs a reference trajectory by a virtual structure method and parameterizes a basic trajectory, thereby ensuring that the formation can be maintained at any time. Aiming at the condition that an obstacle exists in the environment, the basic track is adjusted by utilizing an artificial potential field method to generate a reference track for avoiding the obstacle, and the anti-collision of the unmanned ship in the moving process is realized. Chinese patent CN107015562A discloses an optimized formation tracking control method based on distributed model prediction control, which is used for establishing an under-actuated unmanned ship motion model and a tracking error model, carrying out state prediction according to neighbor information and the error model, establishing a model prediction algorithm and realizing formation optimized tracking control.
Through observation, the following defects of the current unmanned ship formation motion control method are found:
firstly, most of the existing unmanned ship formation methods only pay attention to control robustness and stability, and actual state constraints, actuator constraints, formation collision avoidance constraints and optimized performance indexes of the unmanned ships, such as energy optimization and control input smoothness, are not systematically and comprehensively considered. If the design of the control method is carried out by neglecting the factors, the optimality and the engineering applicability of the control method are inevitably reduced;
secondly, the existing unmanned ship formation control method based on optimization mostly depends on a fixed and accurate unmanned ship mathematical model to design a controller. The actual unmanned ship dynamic system under the complex marine environment has model uncertainty and disturbance of marine time-varying storm flow, so the control performance is reduced by designing the control method based on the fixed mathematical model without considering the model uncertainty and the disturbance of the marine time-varying storm flow under the actual marine environment.
Disclosure of Invention
The invention provides an anti-collision and anti-interference control system for formation of multiple unmanned ships.
The technical means adopted by the invention are as follows: an anti-collision anti-interference control system for multi-unmanned ship formation comprises a model reconstruction module, an interactive information network topology module, a position prediction control module, a bow roll angle prediction control module and an uncertain and disturbance estimation module;
the model reconstruction module is used for acquiring a kinematics and dynamics model of the controlled unmanned ship established by the controlled unmanned ship module and reconstructing the kinematics and dynamics model to acquire the position information p of the controlled unmanned ship under the terrestrial coordinate systemiSpeed information q in a global coordinate systemiHeading angle information in global coordinate system
Figure BDA0002865146240000021
And the yaw rate r under the hull coordinate systemi；
The interactive information network topology module is used for acquiring the position information p of the controlled unmanned ship in the unmanned ship formation under the terrestrial coordinate system, wherein the position information p is interacted with the information of the controlled unmanned shipiSpeed information q in a global coordinate systemiHeading angle information in global coordinate system
Figure BDA0002865146240000022
And the yaw rate r under the hull coordinate systemiAnd position information p of the controlled unmanned ship under the terrestrial coordinate system, which has information interaction with the controlled unmanned shipiAnd speed information q in a terrestrial coordinate systemiSending the position information to a position prediction control module;
the position prediction control module is used for acquiring the position information p of the controlled unmanned ship in a terrestrial coordinate systemiSpeed information q in a global coordinate systemiEstimation of unknown function of model uncertainty and time-varying ocean current disturbance
Figure BDA0002865146240000023
And the information input by the interactive information network topology module calculates the longitudinal speed control input tauiuAnd reference yaw sequence
Figure BDA0002865146240000024
And inputting the longitudinal speed control into tauiuInputting the reference bow and roll angle sequence into the controlled unmanned ship
Figure BDA0002865146240000025
Inputting the angle to the yaw angle prediction control module;
the heading angle prediction control module is used for acquiring the reference heading angle sequence
Figure BDA0002865146240000026
Controlled unmanned ship's angular yaw rate r under ship body coordinate systemiAnd an estimate of the heading angle direction unknown function
Figure BDA0002865146240000027
Controlling input value tau by calculating yaw rateirAnd controlling the yaw rate by the input value tauirInput to the controlled unmanned vessel;
the uncertainty and disturbance estimation module is usedObtaining the position information p of the controlled unmanned ship in the terrestrial coordinate systemiSpeed information q in a global coordinate systemiHeading angle information in global coordinate system
Figure BDA0002865146240000028
Bow angular velocity r under ship body coordinate systemiLongitudinal speed control input value tauiuAnd yaw rate control input value tauirTo calculate an estimate of the heading angle direction unknown function
Figure BDA0002865146240000029
And an estimate of an unknown function of model uncertainty and time-varying ocean current disturbances
Figure BDA00028651462400000210
And the estimated value of the unknown function of the heading angle direction is calculated
Figure BDA00028651462400000211
Inputting the estimated value of the unknown function of model uncertainty and time-varying ocean current disturbance into the yaw angle prediction control module
Figure BDA00028651462400000212
Input to the position prediction control module.
Further, the kinematics and dynamics model of the controlled unmanned ship is represented as:
Figure BDA0002865146240000031
wherein: x is the number ofi、yi、
Figure BDA0002865146240000032
Position information of the unmanned ship in the X-axis direction, position information of the unmanned ship in the Y-axis direction and heading angle information under a terrestrial coordinate system; u. ofi、viAnd riLongitudinal speed and transverse speed of unmanned ship under ship body coordinate systemA drift velocity and a yaw rate; f. ofiu、fivAnd firLongitudinal unknown functions, transverse unknown functions and heading angle direction unknown functions with uncertainty and time-varying ocean current disturbance; tau isiuAnd τirControl input values for longitudinal velocity and yaw rate; m isiuAnd mirInertia coefficients in the longitudinal direction and the heading direction of the ship body are respectively; t is time.
Further, the process of reconstructing the kinematic and kinetic model includes: the method comprises the following steps of carrying out transformation decoupling on a kinematics and dynamics model (1) of the unmanned ship to form a position ring model (2) and a bow and roll angle ring model (3), and specifically comprising the following steps:
Figure BDA0002865146240000033
Figure BDA0002865146240000034
wherein: p is a radical ofi＝[xi,yi]、qi＝[qix,qiy]For the position information and the speed information of the controlled unmanned ship in the terrestrial coordinate system,
Figure BDA0002865146240000035
speed information of the controlled unmanned ship in X-axis and Y-axis directions under a terrestrial coordinate system;
Figure BDA0002865146240000036
are each pi、qiA derivative; f. ofiq＝[fix,fiy]As an unknown function of model uncertainty and time-varying ocean current disturbance of the unmanned ship in a terrestrial coordinate system, fix、fiyThe specific conversion mode of the unknown function of model uncertainty and time-varying ocean current disturbance in the X-axis and Y-axis directions of the unmanned ship in the terrestrial coordinate system is as follows:
Figure BDA00028651462400000310
further, calculating estimated values of uncertainty of a model of an unknown function of the heading angle direction and time-varying ocean current disturbance
Figure BDA0002865146240000037
And an estimate of an unknown function of model uncertainty and time-varying ocean current disturbances
Figure BDA0002865146240000038
The process comprises the following steps:
Figure BDA0002865146240000039
wherein
Figure BDA0002865146240000041
Are respectively fiq,fir,qi,riEstimated value of kiq,kirRespectively gain factors.
Further, the calculating longitudinal speed control input τiuAnd reference yaw sequence
Figure BDA0002865146240000042
The process is as follows:
d1, rewriting the position ring model (2) as follows:
Figure BDA0002865146240000043
wherein: tau isiq＝[τix,τiy]TFor the control input of the unmanned ship under the terrestrial coordinate system, wherein
Figure BDA0002865146240000044
For the control input of the unmanned ship in the X-axis direction under the terrestrial coordinate system,
Figure BDA0002865146240000045
the control input of the unmanned ship in the Y-axis direction under the terrestrial coordinate system is carried out;
d2, making the unmanned ship contain the estimation value of the unknown function of model uncertainty and time-varying ocean current disturbance in the earth coordinate system
Figure BDA0002865146240000046
Substituting the model (6) and discretizing, wherein the concrete formula is as follows:
Xiq(k+Ts)＝AiXiq(k)+Biτiq(k)+Ci (7)
wherein: xiq(k)＝[pi(k),qi(k)]TRepresenting the unmanned ship state vector at the moment k; ts is sampling interval time; vector quantity
Figure BDA0002865146240000047
(Vector)
Figure BDA0002865146240000048
(Vector)
Figure BDA0002865146240000049
In the formula:
Figure BDA00028651462400000410
02＝[0,0]T；
d3, using equation (7) to predict the state at time k as follows:
Figure BDA00028651462400000411
wherein: xiq(k | k) is the sampling value of the state at time k; xiq(k+lTs|k),l＝1,...,NpFor state prediction at time k vs. time k + lTs, NpIs a prediction time domain; tau isiq(k-1) is a control input applied to the controlled unmanned ship at the moment k-1 under the terrestrial coordinate system; delta tauiq(k+mTs|k)N, Nc is the control increment at time k + mTs, NcRepresenting a control time domain;
d4, equation (8) is expressed using a recursive relationship as follows:
Figure BDA00028651462400000412
wherein
Figure BDA00028651462400000413
Outputting a sequence for the predicted state at time k;
Figure BDA0002865146240000051
controlling the increment sequence for the k time;
Figure BDA0002865146240000052
Figure BDA0002865146240000053
Figure BDA0002865146240000054
Figure BDA0002865146240000055
corresponding order
Figure BDA0002865146240000056
Equation (9) is written as follows:
Figure BDA0002865146240000057
d5, constructing an optimization problem model as follows:
Figure BDA0002865146240000058
equations (11a), (11b), (11c), (11d) are control increment constraint, control input constraint, state constraint and collision avoidance constraint, respectively;
Figure BDA0002865146240000059
and
Figure BDA00028651462400000510
and
Figure BDA00028651462400000511
and
Figure BDA00028651462400000512
and
Figure BDA00028651462400000513
respectively the upper and lower bounds of the control increment, the control input and the speed state under the terrestrial coordinate system; zijIs a collision avoidance coefficient matrix; q1、Q2And Q3Respectively keeping a weight matrix for the energy index, a weight matrix for the formation form and a weight matrix for the formation tracking error;
d6, converting the optimization problem model (11) into the following form:
Figure BDA0002865146240000061
wherein:
Figure BDA0002865146240000062
Figure BDA0002865146240000063
obtaining an optimal control input increment by solving an optimization problem model (12)Sequence of
Figure BDA0002865146240000064
Thereby obtaining an optimal control input sequence
Figure BDA0002865146240000065
D7, calculating the optimum longitudinal speed control input tau by the equation (13)iu：
Figure BDA0002865146240000066
Wherein tau is1i(k) And τ2i(k) Optimally controlling the first two elements of the input sequence;
d8, calculating the reference yaw angle by equation (14):
Figure BDA0002865146240000067
wherein tau is2i(l) And τ1i(l) Respectively 2l and 2l-1 elements in the optimal control input sequence.
Further, the calculating of the yaw rate control input value τirThe process comprises the following steps:
e1, discretizing the model (3) as follows:
Xir(k+Ts)＝AirXir(k)+Birτir(k)+Cir (15)
wherein:
Figure BDA0002865146240000068
representing a bow rocking angle state vector of the unmanned ship at the moment k; ts is sampling interval time; vector quantity
Figure BDA0002865146240000069
(Vector)
Figure BDA00028651462400000610
(Vector)
Figure BDA00028651462400000611
E2, using equation (15), as follows:
Figure BDA00028651462400000612
wherein: xir(k | k) is the sampling value of the state at time k; xir(k+lTs|k),l＝1,...,NpFor the prediction of the yaw state at time k to time k + lTs, NrpPredicting a time domain for the yaw angle; tau isir(k-1) a yaw rate control input applied at a previous sampling moment; delta tauir(k + mTs | k), m 1, Nc is the yaw rate control increment at time k + mTs, NrcRepresenting a yaw angle control time domain;
e3, expressing equation (16) as follows using a recursive relationship:
Figure BDA0002865146240000071
wherein:
Figure BDA0002865146240000072
outputting a sequence for the heading angle prediction state at the moment k;
Figure BDA0002865146240000073
controlling an increment sequence for the yaw rate at the time k;
Figure BDA0002865146240000074
Figure BDA0002865146240000075
Figure BDA0002865146240000076
Figure BDA0002865146240000077
corresponding order
Figure BDA0002865146240000078
Equation (17) is written as follows:
Figure BDA0002865146240000079
e4, constructing an optimization problem model as follows:
Figure BDA0002865146240000081
equations (19a), (19b), (19c) are respectively the yaw angular velocity control increment constraint, the yaw angular velocity control input constraint, and the yaw angular velocity state constraint;
Figure BDA0002865146240000082
and
Figure BDA0002865146240000083
respectively, the upper and lower bounds of the yaw rate control increment.
Figure BDA0002865146240000084
And
Figure BDA0002865146240000085
upper and lower boundaries of the yaw angular speed control input are respectively;
Figure BDA0002865146240000086
and
Figure BDA0002865146240000087
respectively the upper and lower boundaries of the yaw angular velocity state;
Figure BDA0002865146240000088
is a reference yaw sequence;
e5, converting the optimization problem model (11) into the following form:
Figure BDA0002865146240000089
wherein:
Figure BDA00028651462400000810
Figure BDA00028651462400000811
Figure BDA00028651462400000812
solving an optimization problem model (20) to obtain an optimal yaw rate control input increment sequence
Figure BDA00028651462400000813
Obtaining an optimal control input sequence
Figure BDA00028651462400000814
The first element in the sequence is applied to the controlled unmanned vessel.
Compared with the prior art, the anti-collision and anti-interference control system for the formation of the multiple unmanned ships disclosed by the invention has the following beneficial effects: firstly, the unmanned ship model is reconstructed into a position ring model and a bow-rocking angle ring model through a model reconstruction module, and uncertainty and disturbance estimation modules are used for collecting input and output information of the unmanned ship to carry out real-time estimation on model uncertainty and time-varying disturbance unknown functions in the unmanned ship position ring model and the bow-rocking angle ring model in the actual marine environment. Therefore, a fixed and accurate mathematical model of the unmanned ship is not needed, and the model information is estimated and dynamically updated only by controlling the input information and the output state information of the unmanned ship, so that the disturbance resistance and the control accuracy of the unmanned ship can be improved in a complex marine environment.
The position prediction control module and the bow-roll angle prediction control module perform state prediction by utilizing model information obtained through real-time estimation and reconstruction, consider unmanned ship actual state constraint, execution mechanism constraint and formation collision avoidance constraint, use control target, energy optimization and control input smoothness as optimization performance indexes of an optimization problem, design a distributed optimization problem to perform rolling optimization control on formation movement, and improve optimality and engineering applicability of a control method.
Drawings
Fig. 1 is a schematic structural diagram of an anti-collision and anti-interference control system for formation of multiple unmanned ships, which is disclosed by the invention.
Fig. 2 is a schematic diagram of an interworking information network topology in accordance with the present invention.
FIG. 3 is a schematic diagram of collision-free tracking trajectories for formation of unmanned ships.
Fig. 4a, 4b, 4c and 4d are diagrams of unmanned ship formation tracks at different time points respectively.
Fig. 5a and 5b are schematic diagrams of control inputs, respectively.
Fig. 6a and 6b are schematic diagrams of unmanned ship formation tracking errors respectively.
Fig. 7a, fig. 7b and fig. 7c are schematic diagrams of estimation of uncertain and time-varying disturbance unknown functions of the i-th unmanned ship model, respectively.
Fig. 8a, 8b and 8c are schematic diagrams of the speed state of the unmanned ship, respectively.
Detailed Description
Fig. 1 shows an anti-collision and anti-interference control system for formation of multiple unmanned ships, which comprises a model reconstruction module, an interactive information network topology module, a position prediction control module, a heading angle prediction control module and an uncertainty and disturbance estimation module;
the model reconstruction module is used for acquiring the controlled unmanned ship built by the controlled unmanned ship moduleThe kinematics and dynamics model of the unmanned ship is reconstructed to obtain the position information p of the controlled unmanned ship under the terrestrial coordinate systemiSpeed information q in a global coordinate systemiHeading angle information in global coordinate system
Figure BDA0002865146240000091
And the yaw rate r under the hull coordinate systemi；
Specifically, in the presence of model uncertainty and time-varying ocean current disturbance, the kinematics and dynamics model of the i-th under-actuated unmanned ship in the controlled unmanned ship formation is represented as follows:
Figure BDA0002865146240000092
wherein: x is the number ofiPosition information of the unmanned ship in the X-axis direction under a terrestrial coordinate system; y isiPosition information of the unmanned ship in the Y-axis direction under a terrestrial coordinate system;
Figure BDA0002865146240000093
the bow rocking angle information of the unmanned ship under the terrestrial coordinate system is obtained; u. ofiThe longitudinal speed of the unmanned ship under a ship body coordinate system is obtained; vi is the speed of the unmanned ship drifting under a ship body coordinate system; r isiThe ship is the ship's yaw velocity under the ship body coordinate system; f. ofiu、fivAnd firRespectively a longitudinal unknown function, a transverse unknown function and a heading angle direction unknown function which comprise model uncertainty and time-varying ocean current disturbance under a ship body coordinate system; tau isiuA longitudinal speed control input value; tau isirControlling an input value for the yaw rate; m isiuAnd mirInertia coefficients in the longitudinal direction and the heading direction of the ship body are respectively; t is time;
Figure BDA0002865146240000094
are respectively xi、yi、
Figure BDA0002865146240000101
ui、vi、riThe derivative of (c).
The process of reconstructing the controlled unmanned ship kinematics and dynamics model comprises the following steps:
the method comprises the following steps of carrying out transformation decoupling on a kinematics and dynamics model (1) of the unmanned ship to form a position ring model (2) and a bow and roll angle ring model (3), and specifically comprising the following steps:
Figure BDA0002865146240000102
Figure BDA0002865146240000103
wherein: p is a radical ofi＝[xi,yi]Position information of the unmanned ship under a terrestrial coordinate system; q. q.si＝[qix,qiy]For the speed information of the unmanned ship in the terrestrial coordinate system,
Figure BDA0002865146240000104
the speed information of the unmanned ship in the X-axis direction under the terrestrial coordinate system,
Figure BDA0002865146240000105
the speed information of the unmanned ship in the Y-axis direction under the terrestrial coordinate system is obtained;
Figure BDA0002865146240000106
are each pi、qiA derivative; f. ofiq＝[fix,fiy]As an unknown function of model uncertainty and time-varying ocean current disturbance of the unmanned ship in a terrestrial coordinate system, fixFor the unknown function of model uncertainty and time-varying ocean current disturbance in the X-axis direction of the unmanned ship in the terrestrial coordinate system, fiyThe method is an unknown function of model uncertainty and time-varying ocean current disturbance of an unmanned ship in the Y-axis direction under a terrestrial coordinate system, and the specific conversion mode is as follows:
Figure BDA0002865146240000107
the interactive information network topology module is used for acquiring the position information p of the controlled unmanned ship in the unmanned ship formation under the terrestrial coordinate system, wherein the position information p is interacted with the information of the controlled unmanned shipiSpeed information q in a global coordinate systemiHeading angle information in global coordinate system
Figure BDA0002865146240000108
And the yaw rate r under the hull coordinate systemiAnd position information p of the controlled unmanned ship under the terrestrial coordinate system, which has information interaction with the controlled unmanned shipiAnd speed information q in a terrestrial coordinate systemiSending the position information to a position prediction control module;
specifically, as shown in fig. 2, the topology map for the interworking information network topology module
Figure BDA0002865146240000109
Is shown in which
Figure BDA00028651462400001010
A node set formed by N unmanned ships in the formation; namely, it is
Figure BDA00028651462400001011
ε represents the set of edges between the ith and jth unmanned vessels in the formation, an
Figure BDA00028651462400001012
If (i, j) is epsilon, the fact that the information interaction relationship exists between the ith unmanned ship and the jth unmanned ship is represented, and a communication variable aij1, otherwise the communication variable aij＝0。diFor the reference track access authority variable, if the i-th unmanned ship can access the reference track information, d i1, otherwise di＝0。
The position prediction controlA system module for acquiring the position information p of the controlled unmanned ship under the terrestrial coordinate systemiSpeed information q in a global coordinate systemiEstimation of unknown function of model uncertainty and time-varying ocean current disturbance
Figure BDA0002865146240000111
And the information input by the interactive information network topology module calculates the longitudinal speed control input tauiuAnd reference yaw sequence
Figure BDA0002865146240000112
And inputting the longitudinal speed control into tauiuInputting the reference bow and roll angle sequence into the controlled unmanned ship
Figure BDA0002865146240000113
Inputting the angle to the yaw angle prediction control module;
the position prediction control module receives the neighbor ship information with communication relation in formation through the interactive information network topology module, and the neighbor ship information is obtained by a position ring model (2) in the model reconstruction module and a model uncertainty and disturbance estimation module
Figure BDA0002865146240000114
And (5) carrying out prediction and optimization problem construction.
In particular, the calculating longitudinal speed control input τiuAnd reference yaw sequence
Figure BDA0002865146240000115
The process is as follows:
d1, rewriting the position ring model (2) as follows:
Figure BDA0002865146240000116
wherein: tau isiq＝[τix,τiy]TFor the control input of the unmanned ship under the terrestrial coordinate system, wherein
Figure BDA0002865146240000117
For the control input of the unmanned ship in the X-axis direction under the terrestrial coordinate system,
Figure BDA0002865146240000118
the control input of the unmanned ship in the Y-axis direction under the terrestrial coordinate system is carried out;
d2, making the unmanned ship contain the estimation value of the unknown function of model uncertainty and time-varying ocean current disturbance in the earth coordinate system
Figure BDA0002865146240000119
Substituting the model (6) and discretizing, wherein the concrete formula is as follows:
Xiq(k+Ts)＝AiXiq(k)+Biτiq(k)+Ci (7)
wherein: xiq(k)＝[pi(k),qi(k)]TRepresenting the unmanned ship state vector at the moment k; ts is sampling interval time; vector quantity
Figure BDA00028651462400001110
(Vector)
Figure BDA00028651462400001111
(Vector)
Figure BDA00028651462400001112
In the formula:
Figure BDA00028651462400001113
02＝[0,0]T；
d3, using equation (7) to predict the state at time k as follows:
Figure BDA00028651462400001114
wherein: xiqWhen (k | k) is kState sampling values are carved; xiq(k+lTs|k),l＝1,...,NpFor state prediction at time k vs. time k + lTs, NpIs a prediction time domain; tau isiq(k-1) is a control input applied to the controlled unmanned ship at the moment k-1 under the terrestrial coordinate system; delta tauiq(k + mTs | k), m 1, Nc is the control increment at time k + mTs, NcRepresenting a control time domain;
d4, equation (8) is expressed using a recursive relationship as follows:
Figure BDA0002865146240000121
wherein
Figure BDA0002865146240000122
Outputting a sequence for the predicted state at time k;
Figure BDA0002865146240000123
controlling the increment sequence for the k time;
Figure BDA0002865146240000124
Figure BDA0002865146240000125
Figure BDA0002865146240000126
Figure BDA0002865146240000127
corresponding order
Figure BDA0002865146240000128
Equation (9) is written as follows:
Figure BDA0002865146240000129
d5, constructing an optimization problem model as follows:
Figure BDA00028651462400001210
equations (11a), (11b), (11c), (11d) are control increment constraint, control input constraint, state constraint and collision avoidance constraint, respectively;
Figure BDA0002865146240000131
and
Figure BDA0002865146240000132
respectively an upper bound and a lower bound of the control increment under the terrestrial coordinate system;
Figure BDA0002865146240000133
and
Figure BDA0002865146240000134
respectively an upper bound and a lower bound of control input under a terrestrial coordinate system;
Figure BDA0002865146240000135
and
Figure BDA0002865146240000136
the upper and lower bounds of the speed state under the terrestrial coordinate system are respectively; zijIn order to obtain a matrix of collision avoidance coefficients,
Figure BDA0002865146240000137
and r isijCollision avoidance safety distance is set between the unmanned ship and the ships in the formation; q1、Q2And Q3Respectively keeping a weight matrix for the energy index, a weight matrix for the formation form and a weight matrix for the formation tracking error;
Figure BDA0002865146240000138
wherein
Figure BDA0002865146240000139
Xj＝[pj,qj]For the position state information and the speed state information of the neighboring unmanned ship j at the time k received by the ith unmanned ship,
Figure BDA00028651462400001310
Dijforming a formation deviation vector in a formation mode;
d6, converting the optimization problem model (11) into the following form:
Figure BDA00028651462400001311
wherein:
Figure BDA00028651462400001312
Figure BDA00028651462400001313
obtaining an optimal control input increment sequence by solving an optimization problem model (12)
Figure BDA00028651462400001314
Thereby obtaining an optimal control input sequence
Figure BDA00028651462400001315
D7, calculating the optimum longitudinal speed control input tau by the equation (13)iu：
Figure BDA00028651462400001316
Wherein tau is1i(k) And τ2i(k) Optimal control of the first two elements of the input sequence；
D8, calculating the reference yaw angle by equation (14):
Figure BDA00028651462400001317
wherein tau is2i(l) And τ1i(l) Respectively 2l and 2l-1 elements in the optimal control input sequence.
The heading angle prediction control module is used for acquiring the reference heading angle sequence
Figure BDA00028651462400001318
Controlled unmanned ship's angular yaw rate r under ship body coordinate systemiAnd an estimate of the heading angle direction unknown function
Figure BDA00028651462400001319
Controlling input value tau by calculating yaw rateirAnd controlling the yaw rate by the input value tauirInput to the controlled unmanned vessel;
in particular, said calculating a yaw rate control input value τirThe process comprises the following steps:
e1, discretizing the model (3) as follows:
Xir(k+Ts)＝AirXir(k)+Birτir(k)+Cir (15)
wherein:
Figure BDA0002865146240000141
representing a bow rocking angle state vector of the unmanned ship at the moment k; ts is sampling interval time; vector quantity
Figure BDA0002865146240000142
(Vector)
Figure BDA0002865146240000143
(Vector)
Figure BDA0002865146240000144
E2, using equation (15), as follows:
Figure BDA0002865146240000145
wherein: xir(k | k) is the sampling value of the state at time k; xir(k+lTs|k),l＝1,...,NpFor the prediction of the yaw state at time k to time k + lTs, NrpPredicting a time domain for the yaw angle; tau isir(k-1) a yaw rate control input applied at a previous sampling moment; delta tauir(k + mTs | k), m 1, Nc is the yaw rate control increment at time k + mTs, NrcRepresenting a yaw angle control time domain;
e3, expressing equation (16) as follows using a recursive relationship:
Figure BDA0002865146240000146
wherein:
Figure BDA0002865146240000147
outputting a sequence for the heading angle prediction state at the moment k;
Figure BDA0002865146240000148
controlling an increment sequence for the yaw rate at the time k;
Figure BDA0002865146240000149
Figure BDA00028651462400001410
Figure BDA0002865146240000151
Figure BDA0002865146240000152
corresponding order
Figure BDA0002865146240000153
Equation (17) is written as follows:
Figure BDA0002865146240000154
e4, constructing an optimization problem model as follows:
Figure BDA0002865146240000155
equations (19a), (19b), (19c) are respectively the yaw angular velocity control increment constraint, the yaw angular velocity control input constraint, and the yaw angular velocity state constraint;
Figure BDA0002865146240000156
and
Figure BDA0002865146240000157
the upper and lower bounds of the yaw rate control increment.
Figure BDA0002865146240000158
And
Figure BDA0002865146240000159
upper and lower bounds for yaw rate control input;
Figure BDA00028651462400001510
and
Figure BDA00028651462400001511
the upper and lower boundaries of the bow angular velocity state;
Figure BDA00028651462400001512
calculated from formula (14) in D8 for reference to the heading angle sequence;
e5, converting the optimization problem model (11) into the following form:
Figure BDA00028651462400001513
wherein:
Figure BDA00028651462400001514
Figure BDA00028651462400001515
Figure BDA00028651462400001516
obtaining an optimal yaw rate control input increment sequence by solving an optimization problem model (20)
Figure BDA00028651462400001517
Thereby obtaining an optimal control input sequence
Figure BDA0002865146240000161
Applying a first element in a sequence to the controlled unmanned vessel.
The uncertainty and disturbance estimation module is used for acquiring the position information p of the controlled unmanned ship in a terrestrial coordinate systemiSpeed information q in a global coordinate systemiHeading angle information in global coordinate system
Figure BDA0002865146240000162
Bow angular velocity r under ship body coordinate systemiLongitudinal speed control input value tauiuAnd the bow angleSpeed control input value tauirTo calculate an estimate of the heading angle direction unknown function
Figure BDA0002865146240000163
And an estimate of an unknown function of model uncertainty and time-varying ocean current disturbances
Figure BDA0002865146240000164
And the estimated value of the unknown function of the heading angle direction is calculated
Figure BDA0002865146240000165
Inputting the estimated value of the unknown function of model uncertainty and time-varying ocean current disturbance into the yaw angle prediction control module
Figure BDA0002865146240000166
Input to the position prediction control module.
Specifically, further, the estimation value of the unknown function of the heading angle direction is calculated
Figure BDA0002865146240000167
And an estimate of an unknown function of model uncertainty and time-varying ocean current disturbances
Figure BDA0002865146240000168
The process comprises the following steps:
Figure BDA0002865146240000169
wherein
Figure BDA00028651462400001610
Are respectively fiq,fir,qi,riEstimated value of kiq,kirRespectively gain factors.
Example 1
The following description of the invention is made by taking the trajectory tracking simulation of a specific unmanned ship formation as an exampleAnd (5) explaining the steps. The topological schematic diagram of the interactive information network is shown in FIG. 2, and the No. 1 ship can access the reference track information generated by the virtual leader, namely d 11 is ═ 1; no. 2 ship and No. 3 ship can receive the information of No. 1 ship, namely a21＝1，d2＝0，a31＝1，d 30; no. 4 ship can receive the information of No. 2 ship, namely a42＝1，d 40; no. 5 ship can receive the information of No. 3 ship, namely a52＝1，d 50. Tracking a reference trajectory generated by the virtual leader:
Figure BDA00028651462400001611
in this example the unmanned vehicles are all under-actuated unmanned vehicles, i.e. only the longitudinal speed control input τiuAnd yaw rate control input τir. Because of the thrust and torque limitations of an actual unmanned ship, there are constraints on the longitudinal speed control input and the yaw rate control input, i.e., τiumax＝3，τiumax＝0，τirmax＝-τ irmin1 is ═ 1; due to the limitations of the actual unmanned ship's actuator, there are constraints on the longitudinal velocity and the yaw rate, i.e. uimax＝0.8，uimin＝0rimax＝-rimin＝0.6；
The initial states of unmanned ships in the formation are respectively as follows: x1q(0)＝[-8,-8,0,0]T，X1r(0)＝[0,0]T，X2q(0)＝[-25,0,0,0]T，X2r(0)＝[0,0]T，X3q(0)＝[1,-24,0,0]T，X3r(0)＝[4π/7,0]T，X4q(0)＝[-16,-25,0,0]T，X4r(0)＝[π/5,0]T，X4q(0)＝[-26,-13,0,0]T，X5r(0)＝[π/4,0]T. Formation mode: d10＝[0,0,0,0]T，D21＝[0,-8,0,0]T，D31＝[-8,0,0,0]T，D42＝[0,-8,0,0]T，D53＝[-8,,0,0,0]T。
Sample interval time Ts is 0.1s, time domain N is predictedpControl time domain N5 c4. Time domain N of prediction of fore-roll angle time domain rp4, the heading angle controls the time domain Nrc＝3。
The simulation results are shown in fig. 3-8. Fig. 3 is a schematic diagram of collision-free tracking tracks of unmanned ship formation, and it can be seen that five unmanned ships gradually enter a formation mode in the formation and track reference straight-line tracks in a fixed formation shape. Fig. 4 a-4 b are schematic diagrams of unmanned ship formation tracks at different time points, fig. 4 a-4 d are schematic diagrams of unmanned ship formation track diagrams and positions of unmanned ships at 46 th, 54 th, 64 th and 90 th seconds respectively, and it can be seen from the diagrams that five unmanned ships can realize collision avoidance during formation aggregation to formation shape keeping.
Fig. 5a and 5b are schematic diagrams of control inputs of five unmanned ships in formation, which are a schematic diagram of longitudinal speed control input and a schematic diagram of yaw rate control input, respectively. It can be seen from the figure that the longitudinal speed control input satisfies the set constraint upper and lower limits. The control input quantity of the heading angular speed direction meets the set constraint upper and lower limits.
Fig. 6a and 6b are schematic diagrams of tracking errors of formation of unmanned ships, which respectively show schematic diagrams of tracking errors in the X direction and the Y direction, and it can be seen from the schematic diagrams that the position error between each unmanned ship and each target position in formation for about 100 seconds is reduced to about 0, which indicates that the formation of unmanned ships can realize track tracking in formation.
Fig. 7 a-7 c are schematic diagrams of model uncertainty and time-varying disturbance unknown function estimation of the i-th unmanned ship, wherein a dotted line is a model uncertainty and time-varying disturbance estimation value, a solid line is a model uncertainty and time-varying disturbance actual value, and the coincidence degree between the solid line and the dotted line is high, which shows that the method provided by the invention can accurately estimate the model uncertainty and the time-varying disturbance in real time.
Fig. 8 a-8 c are schematic speed state diagrams of five unmanned ships in formation, and it can be seen that the longitudinal speed, the drift speed and the yaw rate of the unmanned ships are all within set ranges.
The above description is only for the preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any person skilled in the art should be considered to be within the technical scope of the present invention, and the technical solutions and the inventive concepts thereof according to the present invention should be equivalent or changed within the scope of the present invention.

Claims (6)

1. The utility model provides an anti-interference control system of anticollision of many unmanned ship formation which characterized in that: the system comprises a model reconstruction module, an interactive information network topology module, a position prediction control module, a yaw angle prediction control module and an uncertain and disturbance estimation module;
the model reconstruction module is used for acquiring a kinematics and dynamics model of the controlled unmanned ship established by the controlled unmanned ship module and reconstructing the kinematics and dynamics model to acquire the position information p of the controlled unmanned ship under the terrestrial coordinate systemiSpeed information q in a global coordinate systemiHeading angle information in global coordinate system
Figure FDA0002865146230000011
And the yaw rate r under the hull coordinate systemi；
The interactive information network topology module is used for acquiring the position information p of the controlled unmanned ship in the unmanned ship formation under the terrestrial coordinate system, wherein the position information p is interacted with the information of the controlled unmanned shipiSpeed information q in a global coordinate systemiHeading angle information in global coordinate system
Figure FDA0002865146230000012
And the yaw rate r under the hull coordinate systemiAnd position information p of the controlled unmanned ship under the terrestrial coordinate system, which has information interaction with the controlled unmanned shipiAnd speed information q in a terrestrial coordinate systemiSending the position information to a position prediction control module;
the position prediction control module is used for acquiring the sitting position of the controlled unmanned ship on the earthPosition information p under the markiSpeed information q in a global coordinate systemiEstimation of unknown function of model uncertainty and time-varying ocean current disturbance
Figure FDA0002865146230000013
And the information input by the interactive information network topology module calculates the longitudinal speed control input tauiuAnd reference yaw sequence
Figure FDA0002865146230000014
And inputting the longitudinal speed control into tauiuInputting the reference bow and roll angle sequence into the controlled unmanned ship
Figure FDA0002865146230000015
Inputting the angle to the yaw angle prediction control module;
the heading angle prediction control module is used for acquiring the reference heading angle sequence
Figure FDA0002865146230000016
Controlled unmanned ship's angular yaw rate r under ship body coordinate systemiAnd an estimate of the heading angle direction unknown function
Figure FDA0002865146230000017
Controlling input value tau by calculating yaw rateirAnd controlling the yaw rate by the input value tauirInput to the controlled unmanned vessel;
the uncertainty and disturbance estimation module is used for acquiring the position information p of the controlled unmanned ship in a terrestrial coordinate systemiSpeed information q in a global coordinate systemiHeading angle information in global coordinate system
Figure FDA0002865146230000018
Bow angular velocity r under ship body coordinate systemiLongitudinal speed control input value tauiuAnd yaw rate control input value tauirTo calculate an estimate of the heading angle direction unknown function
Figure FDA0002865146230000019
And an estimate of an unknown function of model uncertainty and time-varying ocean current disturbances
Figure FDA00028651462300000110
And the estimated value of the unknown function of the heading angle direction is calculated
Figure FDA00028651462300000111
Inputting the estimated value of the unknown function of model uncertainty and time-varying ocean current disturbance into the yaw angle prediction control module
Figure FDA00028651462300000112
Input to the position prediction control module.
2. The anti-collision and anti-interference control system for formation of multiple unmanned ships according to claim 1, characterized in that: the kinematics and dynamics model of the controlled unmanned ship is expressed as:
Figure FDA0002865146230000021
wherein: x is the number ofiPosition information of the unmanned ship in the X-axis direction under a terrestrial coordinate system; y isiPosition information of the unmanned ship in the Y-axis direction under a terrestrial coordinate system;
Figure FDA0002865146230000022
the bow rocking angle information of the unmanned ship under the terrestrial coordinate system is obtained; u. ofiThe longitudinal speed of the unmanned ship under a ship body coordinate system is obtained; v. ofiThe speed of the unmanned ship drifting under a ship body coordinate system is obtained; r isiThe ship is the ship's yaw velocity under the ship body coordinate system; f. ofiu、fivAnd firRespectively a longitudinal unknown function, a transverse unknown function and a heading angle direction unknown function which comprise model uncertainty and time-varying ocean current disturbance under a ship body coordinate system; tau isiuA longitudinal speed control input value; tau isirControlling an input value for the yaw rate; m isiuAnd mirInertia coefficients in the longitudinal direction and the heading direction of the ship body are respectively; t is time;
Figure FDA0002865146230000023
are respectively xi、yi、
Figure FDA0002865146230000024
ui、vi、riThe derivative of (c).
3. The anti-collision and anti-interference control system for formation of multiple unmanned ships according to claim 2, characterized in that: the process of reconstructing the controlled unmanned ship kinematics and dynamics model comprises the following steps:
the method comprises the following steps of carrying out transformation decoupling on a kinematics and dynamics model (1) of the unmanned ship to form a position ring model (2) and a bow and roll angle ring model (3), and specifically comprising the following steps:
Figure FDA0002865146230000025
Figure FDA0002865146230000026
wherein: p is a radical ofi＝[xi,yi]Position information of the unmanned ship under a terrestrial coordinate system; q. q.si＝[qix,qiy]For the speed information of the unmanned ship in the terrestrial coordinate system,
Figure FDA0002865146230000027
speed information of unmanned ship in X-axis direction under terrestrial coordinate system，
Figure FDA0002865146230000028
The speed information of the unmanned ship in the Y-axis direction under the terrestrial coordinate system is obtained;
Figure FDA0002865146230000029
are each pi、qiA derivative; f. ofiq＝[fix,fiy]An unknown function of model uncertainty and time-varying ocean current disturbance of the unmanned ship in a terrestrial coordinate system, fix is an unknown function of model uncertainty and time-varying ocean current disturbance of the unmanned ship in an X-axis direction in the terrestrial coordinate system, fiyThe method is an unknown function of model uncertainty and time-varying ocean current disturbance of an unmanned ship in the Y-axis direction under a terrestrial coordinate system, and the specific conversion mode is as follows:
Figure FDA0002865146230000031
4. the anti-collision and anti-interference control system for formation of multiple unmanned ships according to claim 3, characterized in that:
calculating an estimated value of the heading angle direction unknown function
Figure FDA0002865146230000032
And an estimate of an unknown function of model uncertainty and time-varying ocean current disturbances
Figure FDA0002865146230000033
The process comprises the following steps:
Figure FDA0002865146230000034
wherein
Figure FDA0002865146230000035
Are respectively fiq,fir,qi,riEstimated value of kiq,kirRespectively gain factors.
5. The anti-collision and anti-interference control system for formation of multiple unmanned ships according to claim 4, characterized in that:
said calculating longitudinal speed control input τiuAnd reference yaw sequence
Figure FDA0002865146230000036
The process is as follows:
d1, rewriting the position ring model (2) as follows:
Figure FDA0002865146230000037
wherein: tau isiq＝[τix,τiy]TFor the control input of the unmanned ship under the terrestrial coordinate system, wherein
Figure FDA0002865146230000038
For the control input of the unmanned ship in the X-axis direction under the terrestrial coordinate system,
Figure FDA0002865146230000039
the control input of the unmanned ship in the Y-axis direction under the terrestrial coordinate system is carried out;
d2, making the unmanned ship contain the estimation value of the unknown function of model uncertainty and time-varying ocean current disturbance in the earth coordinate system
Figure FDA00028651462300000310
Substituting the model (6) and discretizing, wherein the concrete formula is as follows:
Xiq(k+Ts)＝AiXiq(k)+Biτiq(k)+Ci (7)
wherein: xiq(k)＝[pi(k),qi(k)]TRepresenting the unmanned ship state vector at the moment k; ts is sampling interval time; vector quantity
Figure FDA00028651462300000311
(Vector)
Figure FDA00028651462300000312
(Vector)
Figure FDA00028651462300000313
In the formula:
Figure FDA00028651462300000314
02＝[0,0]T；
d3, using equation (7) to predict the state at time k as follows:
Figure FDA0002865146230000041
wherein: xiq(k | k) is the sampling value of the state at time k; xiq(k+lTs|k),l＝1,...,NpFor state prediction at time k vs. time k + lTs, NpIs a prediction time domain; tau isiq(k-1) is a control input applied to the controlled unmanned ship at the moment k-1 under the terrestrial coordinate system; delta tauiq(k + mTs | k), m 1, Nc is the control increment at time k + mTs, NcRepresenting a control time domain;
d4, equation (8) is expressed using a recursive relationship as follows:
Figure FDA0002865146230000042
wherein
Figure FDA0002865146230000043
Outputting a sequence for the predicted state at time k;
Figure FDA0002865146230000044
a sequence of control increments for time k;
Figure FDA0002865146230000045
Figure FDA0002865146230000046
Figure FDA0002865146230000047
Figure FDA0002865146230000051
corresponding order
Figure FDA0002865146230000052
Equation (9) is written as follows:
Figure FDA0002865146230000053
d5, constructing an optimization problem model as follows:
Figure FDA0002865146230000054
equations (11a), (11b), (11c), (11d) are control increment constraint, control input constraint, state constraint and collision avoidance constraint, respectively;
Figure FDA0002865146230000055
and
Figure FDA0002865146230000056
respectively an upper bound and a lower bound of the control increment under the terrestrial coordinate system;
Figure FDA0002865146230000057
and
Figure FDA0002865146230000058
respectively an upper bound and a lower bound of control input under a terrestrial coordinate system;
Figure FDA0002865146230000059
and
Figure FDA00028651462300000510
the upper and lower bounds of the speed state under the terrestrial coordinate system are respectively; zijIn order to obtain a matrix of collision avoidance coefficients,
Figure FDA00028651462300000511
and r isijCollision avoidance safety distance is set between the unmanned ship and the ships in the formation; q1、Q2And Q3Respectively keeping a weight matrix for the energy index, a weight matrix for the formation form and a weight matrix for the formation tracking error;
Figure FDA00028651462300000512
wherein
Figure FDA00028651462300000513
Xj＝[pj,qj]For the position state information and the speed state information of the neighboring unmanned ship j at the time k received by the ith unmanned ship,
Figure FDA00028651462300000514
Dijforming a formation deviation vector in a formation mode;
d6, converting the optimization problem model (11) into the following form:
Figure FDA00028651462300000515
wherein:
Figure FDA00028651462300000516
Figure FDA0002865146230000061
obtaining an optimal control input increment sequence by solving an optimization problem model (12)
Figure FDA0002865146230000062
Thereby obtaining an optimal control input sequence
Figure FDA0002865146230000063
D7, calculating the optimum longitudinal speed control input tau by the equation (13)iu：
Figure FDA0002865146230000064
Wherein tau is1i(k) And τ2i(k) Optimally controlling the first two elements of the input sequence;
d8, calculating the reference yaw angle by equation (14):
Figure FDA0002865146230000065
wherein tau is2i(l) And τ1i(l) Respectively 2l and 2 in the optimal control input sequencel-1 element.
6. The anti-collision and anti-interference control system for formation of multiple unmanned ships according to claim 5, characterized in that:
calculating the yaw rate control input value tauirThe process comprises the following steps:
e1, discretizing the model (3) as follows:
Xir(k+Ts)＝AirXir(k)+Birτir(k)+Cir (15)
wherein:
Figure FDA0002865146230000066
representing a bow rocking angle state vector of the unmanned ship at the moment k; ts is sampling interval time; vector quantity
Figure FDA0002865146230000067
(Vector)
Figure FDA0002865146230000068
(Vector)
Figure FDA0002865146230000069
E2, using equation (15), as follows:
Figure FDA00028651462300000610
wherein: xir(k | k) is the sampling value of the state at time k; xir(k+lTs|k),l＝1,...,NpFor the prediction of the yaw state at time k to time k + lTs, NrpPredicting a time domain for the yaw angle; tau isir(k-1) a yaw rate control input applied at a previous sampling moment; delta tauir(k + mTs | k), m 1, Nc is the yaw rate control increment at time k + mTs, NrcRepresenting a yaw angle control time domain;
e3, expressing equation (16) as follows using a recursive relationship:
Figure FDA0002865146230000071
wherein:
Figure FDA0002865146230000072
outputting a sequence for the heading angle prediction state at the moment k;
Figure FDA0002865146230000073
controlling an increment sequence for the yaw rate at the time k;
Figure FDA0002865146230000074
Figure FDA0002865146230000075
Figure FDA0002865146230000076
Figure FDA0002865146230000077
corresponding order
Figure FDA0002865146230000078
Equation (17) is written as follows:
Figure FDA0002865146230000079
e4, constructing an optimization problem model as follows:
Figure FDA00028651462300000710
equations (19a), (19b), (19c) are respectively the yaw angular velocity control increment constraint, the yaw angular velocity control input constraint, and the yaw angular velocity state constraint;
Figure FDA0002865146230000081
and
Figure FDA0002865146230000082
respectively, the upper and lower bounds of the yaw rate control increment.
Figure FDA0002865146230000083
And
Figure FDA0002865146230000084
upper and lower boundaries of the yaw angular speed control input are respectively;
Figure FDA0002865146230000085
and
Figure FDA0002865146230000086
respectively the upper and lower boundaries of the yaw angular velocity state;
Figure FDA0002865146230000087
is a reference yaw sequence;
e5, converting the optimization problem model (11) into the following form:
Figure FDA0002865146230000088
wherein:
Figure FDA0002865146230000089
Figure FDA00028651462300000810
Figure FDA00028651462300000811
obtaining an optimal yaw rate control input increment sequence by solving an optimization problem model (20)
Figure FDA00028651462300000812
Thereby obtaining an optimal control input sequence
Figure FDA00028651462300000813
Applying a first element in a sequence to the controlled unmanned vessel.
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