CN113093804B - Unmanned ship formation control method and control system based on inversion sliding mode control - Google Patents

Unmanned ship formation control method and control system based on inversion sliding mode control Download PDF

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CN113093804B
CN113093804B CN202110367311.1A CN202110367311A CN113093804B CN 113093804 B CN113093804 B CN 113093804B CN 202110367311 A CN202110367311 A CN 202110367311A CN 113093804 B CN113093804 B CN 113093804B
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unmanned ship
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王琳玲
吴恭兴
安顺民
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Shanghai Maritime University
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Abstract

The invention provides an unmanned ship formation control method based on inversion sliding mode control, which comprises the following steps: establishing a fixed coordinate system and a following coordinate system of a single unmanned ship in a working plane of the unmanned ship, wherein the fixed coordinate system takes the ground as reference, the following coordinate system takes a ship body of the unmanned ship as reference, and establishing a kinematics model of the single unmanned ship; establishing a mathematical model of the position relation between a piloting unmanned ship and a following unmanned ship; performing formation transformation planning on the piloting unmanned ship based on virtual sub-targets, wherein the virtual sub-targets refer to the position of the next moment in the piloting unmanned ship navigation process; performing formation transformation planning on the following unmanned ship based on a pre-established priority model and a formation adjusting strategy; and performing inversion sliding mode control on the unmanned ship formation, and controlling the speed of the following unmanned ships in the formation transformation process. The method can ensure the stability and robustness of the formation of the unmanned ship, and can effectively transform the formation to deal with the situations of navigation environments such as islands and narrow water areas.

Description

Unmanned ship formation control method and control system based on inversion sliding mode control
Technical Field
The invention relates to the technical field of unmanned boats, in particular to an unmanned boat formation control method and system based on inversion sliding mode control.
Background
In recent years, Unmanned Surface Vehicles (USV) have attracted high attention from researchers in developing and utilizing the sea as a typical offshore Unmanned intelligent platform system. Because the unmanned ship has the advantages of shallow draft, high speed, strong maneuverability and the like, the unmanned ship plays more and more important roles in the fields of military affairs and civil use, such as application in the fields of chart drawing, water area environment monitoring, information reconnaissance, marine scientific research and development, marine rescue, enclosure capture and the like. However, with the complexity of the water environment and the diversification of tasks, the capabilities of a single unmanned boat are often limited and cannot perform the tasks well. Compared with single unmanned boat operation, the unmanned boat cluster has a larger operation range, stronger fault-tolerant capability, lower cost and higher resource utilization rate by keeping a preset formation, and has more important significance for completing the water task. This makes the cooperative control of many unmanned boats gradually become the hot spot of research.
Formation control is one of the most important problems in the field of multi-unmanned-boat cooperative control, and mainly comprises a piloting-following control method, a behavior-based control method, a virtual pilot control method, a neural network method, a graph theory method and the like. Among these methods, the pilot-follow control method is most widely used, and the method means that the following unmanned ship effectively tracks the motion track of the pilot unmanned ship, thereby realizing a stable formation.
For the piloting-following control method, when the unmanned ship formation is used for executing tasks in the sea, the interference of wind, wave and flow exists, the interference has great influence on the high-performance navigation of the unmanned ship, the working efficiency of equipment carried on the unmanned ship is reduced, the track of the unmanned ship is influenced, and the unmanned ship cannot track the expected track with high precision. Therefore, in order to ensure the navigation of the unmanned ship, the unmanned ship controller needs to perform high-precision control on the navigation state of the unmanned ship. The unmanned boat controller directly determines whether the unmanned boat can run in a desired track, and is the core of the unmanned boat formation system.
The control algorithm of the unmanned ship controller has been developed from a classical control algorithm and a modern control algorithm to an intelligent control algorithm which can not depend on an accurate mathematical model nowadays, and generally comprises neural network control, fuzzy control, self-adaptive control, sliding mode control and the like.
The sliding mode control is to design a sliding mode surface according to the expected dynamic characteristics of the system, and the system state is enabled to rapidly move towards the sliding mode surface through a sliding mode controller. And after the system state reaches the sliding mode surface, the system state continues to slide to a system balance point along the sliding mode surface, and the expected control target is finished. The sliding mode control algorithm is simple in physical implementation and insensitive to parameter change and disturbance, so that the method has strong stability and robustness and is suitable for being applied to a nonlinear system. However, the slip-form control accuracy is poor due to non-ideality in the practical application process, the system is difficult to strictly slide along the slip-form surface, and the system passes through the two sides of the slip-form surface back and forth, so that the system generates buffeting. In addition, in reality, formation of unmanned boats often travels to an environment such as an island or a narrow water area, and in this case, formation change of unmanned boats is rarely considered in the conventional research.
Therefore, there is a need for a control method for unmanned boat formation based on sliding mode control, which can ensure stability and robustness of unmanned boat formation, control unmanned boat formation to sail along an expected track, and effectively change formation to cope with sailing environments such as islands and narrow water areas.
Disclosure of Invention
The invention provides an unmanned ship formation control method and system based on inversion sliding mode control, which can ensure the stability and robustness of unmanned ship formation, control the unmanned ship formation to sail along an expected track, and effectively change the formation to cope with the situation of sailing environments such as islands and narrow water areas.
In order to achieve the above objects and other related objects, the present invention provides a method for controlling unmanned ship formation based on inversion sliding mode control, the unmanned ship formation comprises a pilot unmanned ship and at least two following unmanned ships, and the method comprises:
establishing a fixed coordinate system and a following coordinate system of a single unmanned ship in a working plane of the unmanned ship, wherein the fixed coordinate system takes the ground as reference, the following coordinate system takes an unmanned ship hull as reference, and a kinematics model of the single unmanned ship is established through the fixed coordinate system and the following coordinate system, and the piloting unmanned ship and the following unmanned ship both adopt the kinematics model;
establishing a mathematical model of the position relation between the piloting unmanned ship and the following unmanned ship on the basis of the kinematic model;
on the basis of the kinematic model and the mathematical model, performing formation transformation planning on the piloted unmanned ship based on virtual sub-targets, wherein the virtual sub-targets refer to the position of the piloted unmanned ship at the next moment in the navigation process;
on the basis of the kinematic model and the mathematical model, performing formation transformation planning on the following unmanned ship based on a pre-established priority model and a formation adjustment strategy;
and performing inversion sliding mode control on the unmanned ship formation, and controlling the speed of the following unmanned ship in the formation transformation process.
Preferably, the kinematic model is:
Figure BDA0003007704510000031
wherein eta is [ x y psi ═ n]TIs the inertial position of an unmanned boat in the fixed coordinate system [ x y]TAnd the heading angle psi is set at a predetermined value,
Figure BDA0003007704510000032
denotes an inertial velocity, V ═ u V r]TRepresenting the surge, sway and yaw rate of the unmanned ship in an onboard coordinate system, a rotation matrix J (psi) converts the onboard coordinate system of the unmanned ship into the fixed coordinate system, and is defined as:
Figure BDA0003007704510000033
preferably, the mathematical model is used to describe expected poses of the following unmanned vehicle in the fixed coordinate system and pose errors from actual poses, and the expected poses of the i-th following unmanned vehicle in the fixed coordinate system at time t are:
Figure BDA0003007704510000034
Figure BDA0003007704510000035
Figure BDA0003007704510000036
wherein the content of the first and second substances,
Figure BDA0003007704510000037
representing the i-th said following unmanned boat in said fixed positionExpected pose under coordinate system, (x)L,yL,θL)TRepresenting the pose of the piloted unmanned ship under the fixed coordinate system,
Figure BDA0003007704510000038
representing the distance between the piloting unmanned vehicle and the ith following unmanned vehicle in the desired formation,
Figure BDA0003007704510000039
representing an azimuth of the piloting drone relative to the ith said following drone in a desired formation;
the pose error (x) of the i-th following unmanned ship in the fixed coordinate systemie,yie,θie)TComprises the following steps:
Figure BDA00030077045100000310
wherein (x)i,yi,θi)TRepresenting the actual pose of the ith said following drones.
Preferably, the formation transformation planning for the piloted unmanned ship based on the virtual sub-targets includes:
determining an ideal angle at which the piloted unmanned vehicle needs to be adjusted to travel from the current position towards the virtual sub-targets according to the following formula:
Figure BDA00030077045100000311
wherein (x)L(t),yL(t)) represents the position of the piloted unmanned ship in the fixed coordinate system at time t,
Figure BDA0003007704510000041
and the position of the virtual sub-targets under the fixed coordinate system is represented, the current moment is t, and the moment when the piloting unmanned ship navigates to the virtual sub-targets is t + 1.
Preferably, the formation adjustment policy includes:
when d iss＜d0In time, no formation change is needed;
when d iss＞d0When it is necessary to perform formation transformation, d is reduceds；
Wherein d is0Represents the minimum width of the water channel at a certain moment after the current moment in the formation sailing process of the unmanned ship, dsAnd the formation width of the unmanned boat formation at the current moment is represented.
Preferably, the formation adjustment policy further includes:
when d iss＞d0＞2NrsWhen it is necessary to make formation adjustment, d is reducedsAnd ensure dsIs always greater than 2Nrs；
When d iss＜d0≤2NrsWhen the formation needs to be adjusted, d is reducedsCollision among the following unmanned boats is avoided;
wherein, 2NrsAnd (3) representing a critical collision value, namely the width of the unmanned ship formation when N following unmanned ships are sailed side by side and are at the minimum distance.
Preferably, the priority model is:
Figure BDA0003007704510000042
Figure BDA0003007704510000043
wherein the content of the first and second substances,
Figure BDA0003007704510000044
indicating the distance priority of the ith following drones,
Figure BDA0003007704510000045
indicating the angular priority of the ith following drones,/iLRepresenting i of the followingThe distance between the drones and the piloted drones,
Figure BDA0003007704510000046
representing an azimuth angle of the piloting drone relative to an i-th of the following drones;
and, the distance priority is given priority,
Figure BDA0003007704510000047
the larger the value of (b), the higher the priority, the equal the distance priority the angle priority,
Figure BDA0003007704510000048
the higher the numerical value is, the higher the priority is, and the formation of each following unmanned ship is sequentially changed according to the high-low order of the priority.
Preferably, a closed-loop control mode is adopted to perform inversion sliding mode control on each following unmanned ship, and the control process comprises the following steps:
comparing the actual pose with the expected pose of the following unmanned ship to obtain a pose error;
the motion controller generates a speed-deceleration control quantity according to the pose error and the ideal speed of the following unmanned ship, and then adjusts the ideal speed based on the speed-deceleration control quantity to obtain a control speed, wherein the ideal speed is obtained according to the expected pose;
and controlling the following unmanned ship to sail at the control speed.
Preferably, the speed-deceleration control amount is calculated by:
Figure BDA0003007704510000051
Figure BDA0003007704510000052
wherein, [ v ]if wif]TRepresenting said speed-a deceleration control amount of the vehicle,
Figure BDA0003007704510000053
representing said ideal speed, (x)ie,yie,θie) Representing pose error, parameter kil＞0,ki2＞0,α1＞1,0＜α2＜1，siIs a sliding mode variable delta selected in the sliding mode variable structure control designiIs a positive decimal.
In conclusion, the invention provides an unmanned ship formation control method based on inversion sliding mode control, which not only has the stability and robustness of sliding mode control, but also integrates an inversion method to effectively process the problem of non-matching uncertainty; further, closed-loop control is adopted on the basis of an inversion method, so that the actual pose of the unmanned ship formation is continuously close to the expected pose, and the buffeting problem of sliding mode control is solved; furthermore, a formation transformation mode based on virtual sub-targets solves the problem that formation transformation is needed when unmanned boat formation sails to narrow water areas.
Drawings
Fig. 1 is a schematic flow chart of an unmanned ship formation control method based on inversion sliding mode control according to an embodiment of the present invention;
FIG. 2 is a schematic diagram of a fixed coordinate system and a satellite coordinate system according to an embodiment of the present invention;
fig. 3 is a schematic view of a kinematics model of an unmanned surface vehicle according to an embodiment of the present invention;
fig. 4 is a schematic diagram of relative relationships between unmanned boats in a general route formation according to an embodiment of the present invention;
fig. 5 is a schematic view of a navigation plan of piloted unmanned boats in a triangular formation according to an embodiment of the present invention;
fig. 6 is a schematic diagram of a dual-island obstacle distribution and a representation of an internal collision threshold of a formation according to an embodiment of the present invention;
FIG. 7 is a schematic view of a navigation plan for following drones in a triangular formation according to an embodiment of the present invention;
fig. 8 is a schematic view of a navigation plan of each following unmanned ship in a triangular formation under a priority model according to an embodiment of the present invention;
fig. 9 is a schematic diagram of an unmanned ship formation control model based on closed-loop control according to an embodiment of the present invention.
Detailed Description
The present invention provides an unmanned ship formation control method and control system based on inversion sliding mode control, which is described in further detail below with reference to fig. 1-9 and the detailed description. The advantages and features of the present invention will become more apparent from the following description. It is to be noted that the drawings are in a very simplified form and are all used in a non-precise scale for the purpose of facilitating and distinctly aiding in the description of the embodiments of the present invention. To make the objects, features and advantages of the present invention comprehensible, reference is made to the accompanying drawings. It should be understood that the structures, ratios, sizes, and the like shown in the drawings and described in the specification are only used for matching with the disclosure of the specification, so as to be understood and read by those skilled in the art, and are not used to limit the implementation conditions of the present invention, so that the present invention has no technical significance, and any structural modification, ratio relationship change or size adjustment should still fall within the scope of the present invention without affecting the efficacy and the achievable purpose of the present invention.
Fig. 1 is a schematic flow chart of an unmanned ship formation control method based on inversion sliding mode control according to an embodiment of the present invention, and referring to fig. 1, the control method includes the following steps:
s100, establishing a fixed coordinate system and a following coordinate system of a single unmanned ship in a working plane of the unmanned ship, wherein the fixed coordinate system takes the ground as reference, the following coordinate system takes a hull of the unmanned ship as reference, establishing a kinematics model of the single unmanned ship through the fixed coordinate system and the following coordinate system, and the piloting unmanned ship and the following unmanned ship both adopt the kinematics model;
s200, establishing a mathematical model of the position relation between the piloting unmanned ship and the following unmanned ship on the basis of the kinematic model;
s300, performing formation transformation planning on the piloted unmanned ship based on a virtual sub-target on the basis of the kinematic model and the mathematical model, wherein the virtual sub-target refers to the position of the next moment in the piloted unmanned ship in the sailing process;
s400, performing formation transformation planning on the following unmanned ship based on a pre-established priority model and a formation adjustment strategy on the basis of the kinematic model and the mathematical model;
s500, performing inversion sliding mode control on the unmanned ship formation, and controlling the speed of the following unmanned ship in the formation transformation process.
For step S100, referring to fig. 2, first a fixed coordinate system o of the unmanned boat is establishedn-xnynznAnd an associated coordinate system ob-xbybzbThe fixed coordinate system takes the ground as a reference, and the satellite coordinate system takes the hull of the unmanned ship as a reference.
Then, the speed conversion relationship of the unmanned ship in the fixed coordinate system and the satellite coordinate system is:
Figure BDA0003007704510000071
Figure BDA0003007704510000072
ψ＝r
the kinematics equation for an unmanned boat can be established as follows:
Figure BDA0003007704510000073
referring to fig. 2, USV denotes an unmanned boat, in which η ═ x y ψ]TIs the inertial position of an unmanned boat in the fixed coordinate system [ x y]TAnd the heading angle psi is set at a predetermined value,
Figure BDA0003007704510000074
denotes an inertial velocity, V ═ u V r]TDescribing the surge, sway and yaw rate of the unmanned ship in an onboard coordinate system, a rotation matrix J (psi) converts the onboard coordinate system of the unmanned ship into the fixed coordinate system, defined as:
Figure BDA0003007704510000075
regarding the unmanned ship as a rigid body, the motion of the unmanned ship can be expressed as follows under the satellite coordinates by applying the momentum theorem and the momentum moment theorem:
Figure BDA0003007704510000076
Figure BDA0003007704510000077
Figure BDA0003007704510000078
wherein X is the unmanned boat along X under the fixed coordinate systemnMomentum of direction, Y represents the unmanned ship along Y under the fixed coordinate systemnMomentum in direction, m represents the mass of the unmanned boat; i isZZIndicating that unmanned boat is around ob-zbThe moment of inertia of the shaft, N, represents the moment of inertia; x is the number ofOGAnd yOGRespectively representing the center of gravity of the unmanned boat in the fixed coordinate system xnAxis and ynThe position under the shaft.
Thereby creating a kinematic model of the individual unmanned boat.
For step S200, in the formation of unmanned ships, the kinematic models of each unmanned ship are the same, and a connection between unmanned ships is established on the same kinematic models, that is, a mathematical model of the formation of unmanned ships mainly includes a distance relationship and an angle relationship between a piloting unmanned ship and a following unmanned ship. Taking the triangular formation as an example, that is, a single piloting unmanned ship and two following unmanned ships, it should be understood by those skilled in the art that the control method is not limited to the triangular formation, and the piloting unmanned ship and any plurality of following unmanned ships are applicable, and the triangular formation is taken as an example only for convenience of description, and the following steps are also taken as an example of the triangular formation, and the reason will not be described again.
Referring to FIGS. 3 and 4, the USVLUnmanned surface vehicle, USV, for pilotingiAnd USVjRespectively representing the ith and jth following unmanned vessels, USVidAnd USVjdThen they are their desired pose. By captain of formation
Figure BDA0003007704510000081
And formation azimuth
Figure BDA0003007704510000082
The expected pose of the following unmanned ship under a fixed coordinate system o-xyz, which is the same as the fixed coordinate system on-xnynznThe following fixed coordinate systems are all o-xyz in the same coordinate system, which is not described in detail, and the expected pose may be expressed as:
Figure BDA0003007704510000083
Figure BDA0003007704510000084
Figure BDA0003007704510000085
wherein the content of the first and second substances,
Figure BDA0003007704510000086
is the i-th said expected pose of the following drones, [ x [ ]L yL θL]TIs pilotlessAnd (5) the pose of the boat under a fixed coordinate system.
The ith actual pose of the following unmanned ship in the fixed coordinate system is [ x ]i yi θi]TAnd then the pose error when tracking along the unmanned ship is as follows:
Figure BDA0003007704510000087
in the formula [ xie yie θie]TI.e. the pose error. This translates the formation control problem into making the above-equation error model as small or zero as possible.
As shown in fig. 4, the ith following unmanned vehicle USViAnd the piloting unmanned ship USVLThe relationship of (c) can be expressed as:
di＝[dxi dyi dψi]T
wherein d isxiIndicating the following unmanned vehicle USViIn the piloting unmanned vehicle USVLThe longitudinal relative position in the satellite coordinate system; dyiIndicating the following unmanned vehicle USViIn the piloting unmanned vehicle USVLThe relative lateral position in the satellite coordinate system; dψiThe relative heading angle is changed along with the path, xi (theta) is used for representing the path, and theta is a parameter. The following unmanned ship USViHeading angle psiiAnd said piloted unmanned vehicle USVLHeading angle psiLThe relationship of (1) is:
dψi＝ψi-ψL
the heading angle is used for expressing the direction pointed by the bow, and a mathematical model of the position relation between the following unmanned ship and the piloting unmanned ship is established by the parameters and the parameter relation.
For step S300, the embodiment provides a method for performing motion route planning on the formation of unmanned ships, where the motion route planning is based on virtual sub-targets, the virtual sub-targets are positions for piloting unmanned ships at the next time, a series of virtual sub-targets are established to guide the formation to change formation shapes, and a triangular formation sails to barriers of double islands is taken as an example for the following description, and of course, it should be understood by those skilled in the art that the formation control model is not only applicable to models of double islands. When the formation sails to the island, the piloting unmanned boat establishes virtual sub-targets by taking the inner and outer side boundaries of the island close to the target point as supports according to the detected island distribution information and the position of the target point.
Taking the case that a triangular formation sails through double islands, referring to fig. 5, the piloting unmanned ship USVLThe advancing direction is located between two islands, the two islands need to be avoided, and the area between the adjacent islands is enough for piloting the unmanned ship USVLAnd passing through. The piloting unmanned vehicle USVLFirst, the points and their distances on the boundary of different islands, i.e. a in fig. 5, are detectediAnd Bj. Then, on-line formation transformation planning is carried out according to the detection result, and A in the graph is usediBjIs at the midpoint of
Figure BDA0003007704510000091
The position of (A) is the next moment of the piloting unmanned ship USVLThe position of the virtual sub-target of (2) can be calculated as follows:
1、Aiand BjA distance d between0(t) can be expressed as:
Figure BDA0003007704510000092
wherein d isAiAnd dBjFrom a point on the boundary of the island to be avoided at time t to the piloted unmanned ship USVLIs referred to as a boundary near another island, α1Representing the angle between two distances (i.e. O)LAiAnd OLBjThe angle therebetween).
2、
Figure BDA0003007704510000093
Represents fromThe piloting unmanned vehicle USVLPoint O of center of gravityLTo point
Figure BDA0003007704510000094
Distance (c):
Figure BDA0003007704510000095
wherein alpha is2Is that
Figure BDA0003007704510000096
And AiBjThe angle therebetween can be obtained by the following equation:
α2＝arccos((dAi-dBjcosα1)/d0(t))
α3is shown in the figure
Figure BDA0003007704510000097
And OLAiThe angle therebetween:
Figure BDA0003007704510000098
3. the position of the virtual sub-target in the fixed coordinate system can be expressed as:
Figure BDA0003007704510000101
wherein the content of the first and second substances,
Figure BDA0003007704510000102
is point A on the boundary of two islandsiAnd BjThe connecting line between the islands forms an included angle with the horizontal line determined by the centers of gravity of the two islands. Then, the piloted unmanned vehicle USVLStarting towards the virtual sub-goal at time t, and arriving at the virtual sub-goal at time t +1, (x)L(t),yL(t)) represents the piloted unmanned vehicle USVLCoordinates at time tPosition, said piloted unmanned vehicle USVLAn ideal angle to be adjusted to proceed towards the virtual sub-target
Figure BDA0003007704510000103
Comprises the following steps:
Figure BDA0003007704510000104
whereby the piloted unmanned vehicle USV can be establishedLA navigation plan to navigate to the virtual sub-targets.
For step S400, taking the example that a triangle formation passes between two islands, the formation adjustment is needed to follow the unmanned boat, and the formation is changed to avoid the obstacles of the two islands, which provides a priority model for the formation adjustment of the unmanned boat.
Comparing the following unmanned vehicle USV in real time in the triangular formationiAnd USVjAnd the piloting unmanned ship USVLA distance l betweeniLAnd relative angle
Figure BDA0003007704510000105
Follow priority of unmanned boat by piRepresentation, including distance priority
Figure BDA0003007704510000106
And angle priority
Figure BDA0003007704510000107
Establishing a priority model as follows:
Figure BDA0003007704510000108
Figure BDA0003007704510000109
for the above priority model, the current is compared firstDistance l between each following unmanned ship and piloting unmanned ship in stateiLThe priority is high when the distance is small. When the distances are equal, judging the included angle between the following boat and the pilot boat
Figure BDA00030077045100001010
The method comprises the steps that an included angle of a connecting line between a following unmanned ship and a piloting unmanned ship, which is located on the left side of the sailing direction of the unmanned ship, is positive, the priority of the following unmanned ship with the positive included angle is high, and if the number of the following unmanned ships with the positive included angle is more than one, the unmanned ship with the minimum included angle is selected as the priority unmanned ship.
Of course, consideration needs to be given to whether a collision with an obstacle occurs and whether a collision between following drones occurs during the adjustment before the formation adjustment is performed.
If the unmanned ship does not collide with the barrier, the formation length of the unmanned ship and the piloted unmanned ship are kept in formation along with the unmanned ship, and the relative azimuth angle of the unmanned ship and the piloted unmanned ship is only required to be changed according to the positions of the virtual sub targets. If collision exists, collision is avoided through priority coordination, the following unmanned ship with high priority can be adjusted to reach the avoidance position preferentially, and the following unmanned ship with low priority can be adjusted by referring to the adjustment path of the following unmanned ship with high priority. For example, the following unmanned ship with high priority keeps the formation length of the piloted unmanned ship unchanged, only the relative azimuth angle between the following unmanned ship with high priority and the piloted unmanned ship is changed to obtain a formation change path point, and the following unmanned ship with low priority simultaneously changes the formation length and the relative azimuth angle between the following unmanned ship with low priority and the piloted unmanned ship.
For triangle formation passing through double islands, the judgment method is shown in fig. 6, d0Representing the maximum width that can pass between two islands, 4rsRepresenting critical collision value, two of said following unmanned vehicles USViAnd USVjParallel to the piloting unmanned ship USVLAnd the distance is at the minimum value of not colliding with each other, and the width of the triangular fleet is the critical collision value 4rs，dsIndicating the formation width at a current time. It will be appreciated that in other formation formations, the criticality is given when there are N following drones traveling side-by-side through the islandsCollision number of 2NrsIn the following description, only two following boats are used for parallel travel (i.e., the critical collision value is set), but the present invention is not limited thereto.
When d iss＜d0In time, the triangle formation can smoothly pass through the two islands without formation change.
When d iss＞d0In this case, although the formation conversion is required to reduce the formation width, the problem of internal collision needs to be considered, and therefore, d needs to be compared0And 4rsThe size relationship of (1):
1)d0＞4rsat this time, formation conversion is performed, and the pass width which can be adjusted is larger than the critical collision value 4rsSo that there is no need to consider two of said following unmanned USVsiAnd USVjAnd collision therebetween.
Referring to FIG. 7, assume the following unmanned surface vehicle USV in triangular formationiAnd USVjAnd the piloting unmanned ship USVLThe distances of the following unmanned ship are equal, the angle priority is considered, the distance is kept unchanged, and the following unmanned ship USViIs of high priority. Dynamically adjusting the following unmanned vehicle USViAnd USVjAnd the piloting unmanned ship USVLRelative angle of (A) to (B) make the USViAnd USVjRespectively reach the point USV of the dotted unmanned boat in figure 7idAnd USVjdThe specific process is as follows:
oiis a USViThe actual position point of (a) is,
Figure BDA0003007704510000111
is a USViAt the next moment in time the virtual location point,
Figure BDA0003007704510000112
USV after representation transformationiVirtual boat USVidTo the piloted unmanned vehicle USVLThe perpendicular distance in the direction of movement,
Figure BDA0003007704510000113
is USV after transformationiAnd the piloting unmanned ship USVLThe desired formation distance between the two,
Figure BDA0003007704510000114
representing the desired azimuth after transformation.
Figure BDA0003007704510000115
Figure BDA0003007704510000116
Piloting the unmanned vehicle USVLThe moving direction is the x direction, and the coordinate system (x) of the moving direction is followed by the bodyL,yL) Lower virtual warship USVidIn the position of
Figure BDA0003007704510000117
For desired angle
Figure BDA0003007704510000118
Representation, i.e. the following unmanned surface vehicle USViThe desired position to which adjustment is required.
Figure BDA0003007704510000121
Figure BDA0003007704510000122
Obtaining the following unmanned ship USV from the expected position and the current position which need to be adjustediThe path of the adjustment.
2)d0≤4rsWhen the collision between the following unmanned boats needs to be considered.
Referring to FIG. 8, the following unmanned surface vehicle USViIs higher than the following unmanned vehicle USVj. The following unmanned ship USViContinuing to adjust according to the path in 1), wherein the following is notMan-boat USVjWithout reference to the following unmanned vehicle USViThe adjustment path of the following unmanned surface vehicle USV can not only ensure that the unmanned surface vehicle passes between two islands but also cannot generate internal collision because of the front-back position differencejThe adjustment method is as follows:
ojis a USVjThe actual position point of (a) is,
Figure BDA0003007704510000123
is a USVjAt the next moment in time the virtual location point,
Figure BDA0003007704510000124
USV after representation transformationjVirtual boat USVjdTo the piloted unmanned vehicle USVLThe perpendicular distance in the direction of movement,
Figure BDA0003007704510000125
is USV after transformationjAnd the piloting unmanned ship USVLThe desired formation distance between the two,
Figure BDA0003007704510000126
representing a desired azimuth angle after transformation, after adjustment the following unmanned vehicle USViWith said following unmanned vehicle USVjPerpendicular to the piloted unmanned vehicle USVLThe distance in the moving direction is less than 4rsAnd is less than d0For example, it can be assumed that 2rs。
Figure BDA0003007704510000127
Figure BDA0003007704510000128
Piloting the unmanned vehicle USVLThe moving direction is the x direction, and the coordinate system (x) of the moving direction is followed by the bodyL,yL) Lower virtual warship USVjdIn the position of
Figure BDA0003007704510000129
For desired angle
Figure BDA00030077045100001210
Representation, i.e. the following unmanned surface vehicle USVjThe desired position to which adjustment is required.
Figure BDA00030077045100001211
Figure BDA00030077045100001212
Obtaining the following unmanned ship USV from the expected position and the current position which need to be adjustedjThe path of the adjustment.
For step S500, performing inverse sliding mode control on the formation of the unmanned vehicles, where the inverse sliding mode control is performed by changing the speed of the following unmanned vehicles so that the actual pose of the following unmanned vehicles is continuously close to the expected pose, and the infinite approximation mode is actually a closed-loop control mode, and the control method is as follows:
1) the formation control problem provided by the present invention generally includes formation generation and maintenance. When the motion trail of the piloting unmanned ship is artificially given, the following unmanned ship can follow the initial actual pose and carry out the vector of the expected formation
Figure BDA0003007704510000131
Obtaining the error amount of the formation vector by comparing
Figure BDA0003007704510000132
Then, guidance is carried out according to the error amount of the formation vector to obtain the expected pose when the formation is kept, and referring to fig. 9, a motion controller is arranged to enable the following boat to track the expected pose at any moment, namely, the problem of trajectory tracking is solved. The motion controller inputs an ideal speed set according to the expected pose, and the motion controller outputs an ideal speed set according to the pose errorAnd adjusting the ideal speed to obtain a control speed, and outputting the control speed to the following unmanned ship, wherein the movement speed of the unmanned ship formation is the control speed.
In summary, consider that each unmanned boat has the same kinematic model. First, the expected pose is considered
Figure BDA0003007704510000133
And ideal speed
Figure BDA0003007704510000134
By finding a reasonable control speed
Figure BDA0003007704510000135
Let the system correct for initial error e1Is bounded, i.e.:
Figure BDA0003007704510000136
as shown in fig. 9, the control speed of the unmanned surface vehicle is obtained by inputting the pose error in a closed-loop control manner, so that the unmanned surface vehicle can track the expected pose of the unmanned surface vehicle at any time. The motion controller is used as the core of the closed-loop control rate, and the reasonable motion controller can constantly ensure that the errors between the expected pose and the actual pose of the robot are zero.
2) With the inversion method, the disadvantage of the inversion method is that accurate modeling information of the controlled object is required. If the inversion control method and the sliding mode control are combined, the control method has robustness to the interference of the model. According to the sliding mode variable structure method, firstly, a sliding mode switching function (namely a sliding mode surface s) is correctly designed. Solving a switching function of the sliding mode by using an inversion method, wherein the process is as follows:
suppose xieWhen the value is 0, designing a Lyapunov function:
Figure BDA0003007704510000137
Figure BDA0003007704510000138
the first-order partial derivative of the Lyapunov function is obtained:
Figure BDA0003007704510000139
meanwhile, combining the formula:
Figure BDA00030077045100001310
the pose error differential equation of the unmanned ship can be obtained:
Figure BDA0003007704510000141
thus, there are:
Figure BDA0003007704510000142
three cases of the above formula were analyzed:
when in use
Figure BDA0003007704510000143
When the temperature of the water is higher than the set temperature,
Figure BDA0003007704510000144
then the
Figure BDA0003007704510000145
Then
Figure BDA0003007704510000146
When in use
Figure BDA0003007704510000147
When the utility model is used, the water is discharged,
Figure BDA0003007704510000148
then
Figure BDA0003007704510000149
Then
Figure BDA00030077045100001410
When in use
Figure BDA00030077045100001411
When the temperature of the water is higher than the set temperature,
Figure BDA00030077045100001412
then
Figure BDA00030077045100001413
Then
Figure BDA00030077045100001414
It can be seen that no matter how the material is
Figure BDA00030077045100001415
The value of which is taken out,
Figure BDA00030077045100001416
this is always true. Thus, according to the Lyapunov stability definition, if xieConvergence to 0, thetaieConverge to
Figure BDA00030077045100001417
Then y isieConverging to 0. Therefore, the sliding mode switching function of the motion controller of the unmanned ship can be designed as follows:
Figure BDA00030077045100001418
then, only a corresponding control function needs to be solved, the following error motion point of the unmanned ship tends to the sliding mode surface within limited time, namely s is ordered1→0，s2→ 0, unmanned boat can grow according to desired angle and distanceForming a formation and maintaining the formation.
In addition, in order to weaken the buffeting phenomenon generated in the formation control system of the sliding mode variable structure, a double power approach rate method is used for solving the buffeting problem generated in the motion controller.
Taking a double power approach rate:
Figure BDA00030077045100001419
in the formula, the parameter kil＞0,ki2＞0,α1＞1,0＜α2＜1，siThe sliding mode variable selected in the sliding mode variable structure control design is an error variable of an expected pose and an actual pose in the advancing process of the unmanned ship in the multi-unmanned ship formation track tracking.
To reduce buffeting, the sign function is replaced with a continuous function:
Figure BDA00030077045100001420
wherein deltaiIs a positive decimal, and in combination with the three formulas, the following can be obtained:
Figure BDA0003007704510000151
by changing the above equation, the speed-deceleration control amount [ v ] of the unmanned ship in the control method according to the embodiment of the present invention can be obtainedif wif]TAs shown in the following formula:
Figure BDA0003007704510000152
wherein, the first and the second end of the pipe are connected with each other,
Figure BDA0003007704510000153
by speed-deceleration control quantity, i.e. [ v ]if wif]TAdjusting desired speed
Figure BDA0003007704510000154
To obtain a control speed
Figure BDA0003007704510000155
A computational model of the motion controller is thus established.
The control method provided by the invention has the advantages that the stability and robustness of sliding mode control are achieved, and an inversion method is integrated to effectively process the problem of non-matching uncertainty; furthermore, closed-loop control is adopted on the basis of an inversion method, so that the actual pose of the unmanned ship formation is continuously close to the expected pose, and the buffeting problem of sliding mode control is solved; furthermore, a formation transformation mode based on the virtual sub-targets solves the problem that formation transformation is needed when an unmanned ship formation sails to a narrow water area.
While the present invention has been described in detail with reference to the preferred embodiments, it should be understood that the above description should not be taken as limiting the invention. Various modifications and alterations to this invention will become apparent to those skilled in the art upon reading the foregoing description. Accordingly, the scope of the invention should be determined from the following claims.

Claims (4)

1. An unmanned ship formation control method based on inversion sliding mode control is characterized in that the unmanned ship formation comprises a pilot unmanned ship and at least two following unmanned ships, and the control method comprises the following steps:
establishing a fixed coordinate system and a following coordinate system of a single unmanned ship in a working plane of the unmanned ship, wherein the fixed coordinate system takes the ground as reference, the following coordinate system takes an unmanned ship body as reference, and a kinematics model of the single unmanned ship is established through the fixed coordinate system and the following coordinate system, and the kinematics model is adopted by both the piloting unmanned ship and the following unmanned ship;
establishing a mathematical model of the position relation between the piloting unmanned ship and the following unmanned ship on the basis of the kinematic model;
on the basis of the kinematic model and the mathematical model, performing formation transformation planning on the piloting unmanned ship based on virtual sub-targets, wherein the virtual sub-targets refer to the position of the piloting unmanned ship at the next moment in the navigation process;
on the basis of the kinematic model and the mathematical model, performing formation transformation planning on the following unmanned ship based on a pre-established priority model and a formation adjustment strategy;
performing inversion sliding mode control on the unmanned ship formation, and controlling the speed of the following unmanned ship in the formation transformation process;
the formation adjustment strategy comprises the following steps:
when d iss＜d0In time, no formation change is needed;
when d iss＞d0When it is necessary to perform formation transformation, d is reduceds；
Wherein d is0Represents the minimum width of the water channel at a certain moment after the current moment in the formation sailing process of the unmanned ship, dsRepresenting the formation width of the unmanned boat formation at the current moment;
the formation adjustment strategy further comprises:
when d iss＞d0＞2NrsWhen it is necessary to make formation adjustment, d is reducedsAnd ensure dsIs always greater than 2Nrs；
When d iss＜d0≤2NrsWhen the formation needs to be adjusted, d is reducedsCollision among the following unmanned boats is avoided;
wherein, 2NrsRepresenting a critical collision value, namely the width of the unmanned ship formation when N following unmanned ships are sailed in parallel and are at the minimum distance;
the priority model is as follows:
Figure FDA0003650606520000021
Figure FDA0003650606520000022
wherein the content of the first and second substances,
Figure FDA0003650606520000023
indicating the distance priority of the ith following drones,
Figure FDA0003650606520000024
indicating the angular priority of the ith following drones,/iLRepresenting a distance between an i-th said following drones and said pilot drones,
Figure FDA0003650606520000025
representing an azimuth angle of the piloting drone relative to an i-th of the following drones;
and, the distance priority is given priority,
Figure FDA0003650606520000026
the greater the value of (a), the higher the priority, the equal distance priority taking into account the angle priority,
Figure FDA0003650606520000027
the higher the numerical value is, the higher the priority is, and the following unmanned boats sequentially perform formation transformation according to the high-low order of the priority;
carrying out inversion sliding mode control on each following unmanned ship by adopting a closed-loop control mode, wherein the control process comprises the following steps:
comparing the actual pose with the expected pose of the following unmanned ship to obtain a pose error;
the motion controller generates a speed-deceleration control quantity according to the pose error and the ideal speed of the following unmanned ship, and then adjusts the ideal speed based on the speed-deceleration control quantity to obtain a control speed, wherein the ideal speed is obtained according to the expected pose;
controlling the following unmanned ship to sail at the control speed;
the speed-deceleration control amount is calculated by:
Figure FDA0003650606520000028
Figure FDA0003650606520000029
wherein, [ v ]if wif]TIndicates the speed-deceleration control amount and,
Figure FDA00036506065200000210
represents the ideal speed, (x)ie,yie,θie) Representing pose error, parameter kil＞0,ki2＞0,α1＞1,0＜α2＜1，siIs a sliding mode variable delta selected in the sliding mode variable structure control designiIs a positive decimal.
2. The unmanned boat formation control method based on inversion sliding mode control according to claim 1, wherein the kinematics model is:
Figure FDA00036506065200000211
wherein eta = [ x y ψ ]]TIs the inertial position of an unmanned boat in the fixed coordinate system [ x y]TAnd the heading angle psi is set at a predetermined value,
Figure FDA0003650606520000031
denotes the inertial velocity, V ═ u V r]TUnmanned boatIn the surge, sway and yaw rate in the satellite coordinate system, a rotation matrix J (ψ) converts the satellite coordinate system of the unmanned boat into the fixed coordinate system, defined as:
Figure FDA0003650606520000032
3. the inversion sliding mode control-based unmanned ship formation control method according to claim 1, wherein the mathematical model is used for describing expected poses of the following unmanned ships in the fixed coordinate system and pose errors from actual poses, and the expected poses of the i-th following unmanned ships in the fixed coordinate system at time t are:
Figure FDA0003650606520000033
Figure FDA0003650606520000034
Figure FDA0003650606520000035
wherein the content of the first and second substances,
Figure FDA0003650606520000036
representing the expected pose of the i-th said following drones in said fixed coordinate system, (x)L,yL,θL)TRepresenting the pose of the piloted unmanned ship under the fixed coordinate system,
Figure FDA0003650606520000037
representing the distance between the piloting unmanned vehicle and the ith following unmanned vehicle in the desired formation,
Figure FDA0003650606520000038
representing an azimuth of the piloting drone relative to the ith said following drone in a desired formation;
the pose error (x) of the i-th following unmanned ship in the fixed coordinate systemie,yie,θie)TComprises the following steps:
Figure FDA0003650606520000039
wherein (x)i,yi,θi)TRepresenting the actual pose of the ith said following drones.
4. The inversion sliding mode control-based unmanned ship formation control method according to claim 1, wherein the formation transformation planning of the piloted unmanned ship based on the virtual sub-targets comprises:
determining an ideal angle at which the piloted unmanned vehicle needs to be adjusted to travel from the current position towards the virtual sub-targets according to the following formula:
Figure FDA00036506065200000310
wherein (x)L(t),yL(t)) represents the position of the piloted unmanned ship in the fixed coordinate system at time t,
Figure FDA00036506065200000311
and the position of the virtual sub-targets under the fixed coordinate system is represented, the current moment is t, and the moment when the piloting unmanned ship navigates to the virtual sub-targets is t + 1.
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