CN112965375A - Multi-unmanned-boat formation control method based on fixed-time terminal sliding mode - Google Patents
Multi-unmanned-boat formation control method based on fixed-time terminal sliding mode Download PDFInfo
- Publication number
- CN112965375A CN112965375A CN202110144673.4A CN202110144673A CN112965375A CN 112965375 A CN112965375 A CN 112965375A CN 202110144673 A CN202110144673 A CN 202110144673A CN 112965375 A CN112965375 A CN 112965375A
- Authority
- CN
- China
- Prior art keywords
- time
- fixed
- unmanned
- sliding mode
- terminal sliding
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Pending
Links
Images
Classifications
-
- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
- G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
- G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
- G05B13/04—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators
- G05B13/042—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators in which a parameter or coefficient is automatically adjusted to optimise the performance
Landscapes
- Engineering & Computer Science (AREA)
- Health & Medical Sciences (AREA)
- Artificial Intelligence (AREA)
- Computer Vision & Pattern Recognition (AREA)
- Evolutionary Computation (AREA)
- Medical Informatics (AREA)
- Software Systems (AREA)
- Physics & Mathematics (AREA)
- General Physics & Mathematics (AREA)
- Automation & Control Theory (AREA)
- Feedback Control In General (AREA)
- Control Of Position, Course, Altitude, Or Attitude Of Moving Bodies (AREA)
Abstract
The invention provides a multi-unmanned ship formation control method based on a fixed time terminal sliding mode, which comprises the steps of establishing a kinematics and dynamics model of an unmanned ship control system; building an unmanned ship formation control framework based on the established unmanned ship control system kinematics and dynamics model; designing a fixed-time rapid terminal sliding mode surface based on the built unmanned ship formation control frame; designing a controller of a tracking control subsystem based on a designed fixed-time quick terminal sliding mode surface and carrying out stability analysis; and designing a controller of the formation control subsystem based on the designed fixed-time quick terminal sliding mode surface and carrying out stability analysis. The invention mainly utilizes an unmanned ship formation control strategy based on a fixed time fast terminal sliding mode to solve the problem of unmanned ship formation under the conditions of complex unknown disturbance inside and outside and system uncertainty.
Description
Technical Field
The invention relates to the technical field of multi-unmanned-boat collaborative formation control, in particular to a multi-unmanned-boat formation control method based on a fixed time terminal sliding mode.
Background
In recent years, unmanned systems represented by unmanned boats, unmanned planes and unmanned vehicles on water have been widely used and have assumed more and more important tasks, and unmanned boats play an important role in military aspects such as information acquisition, offshore safety, water surface operations, mine sweeping and anti-diving, and civil aspects such as environmental monitoring, personnel search and rescue, chart drawing and the like. Along with the diversification of tasks undertaken by unmanned boats and the complexity and changeability of the environment facing the actual water area, a single unmanned boat is not compelled, a plurality of unmanned boats form a uniform formation system, the reliability of task completion is greatly improved through cooperative control, and the unmanned boat has higher fault tolerance, robustness and adaptability. The common multi-agent formation control methods include the following methods: navigation-following methods, behavior-based methods, virtual structure methods, graph theory, consistency-based methods, and the like. The piloting-following method is simple in structure, well compensates the defects of centralized communication and distributed communication in multi-agent formation, and adopts a completely distributed formation control method, so that the method is widely applied.
In the current unmanned ship formation control system, unknown parameters of the model and complex external disturbance bring huge challenges to the stability of the system. Sliding mode control is an important control method in the field of nonlinear control, and is widely applied due to the fact that the sliding mode control is simple in structure, strong in robustness and anti-interference performance. The traditional sliding mode control adopts a linear sliding mode surface, and a Lyapunov function is utilized to prove that the system can converge to a balance point within a gradual time; later, terminal sliding mode control is proposed, so that a system can converge to a balance point within limited time, but the convergence speed of the traditional terminal sliding mode is slower when the system approaches the balance point; in order to solve the problem of convergence speed, a fast terminal sliding mode surface is proposed later, and the terminal sliding mode has higher convergence speed than a linear sliding mode and a terminal sliding mode in the whole domain of discourse on the premise of ensuring the limited time convergence of the system. In order to process the complex external disturbance of the system, a disturbance observer is usually adopted to observe the disturbance, such as a nonlinear disturbance observer, a sliding mode disturbance observer, a dimension reduction observer, and the like. In order to achieve a better observation effect on the disturbance, the finite time uncertainty observer is applied to the disturbance observation processing of the marine unmanned system, and a better effect is achieved.
In the formation control system, the rapid convergence of the system ensures the response characteristic of the unmanned ship formation system. The concept of an algebraic connectivity graph is put forward and a progressive convergence algorithm is applied to prove the convergence of the first-order multi-agent system, but the convergence time of the system cannot be accurately predicted by progressive convergence, so that the stability of the system cannot be guaranteed. Later, in order to ensure the control precision of the system and simultaneously enable the convergence within a limited time, a limited time control algorithm is adopted to solve the convergence problem of the formation of the intelligent agent. A fixed time control algorithm is proposed for the first time by Polyakov in the future, the influence of the initial state of the system on the convergence time of the system is solved, and the upper bound of the convergence time of the system is accurately calculated.
Through the discussion, the unmanned ship formation control strategy based on the fixed-time fast terminal sliding mode is provided to solve the unmanned ship formation problem under the conditions of internal and external complex unknown disturbance and system uncertainty.
Disclosure of Invention
According to the scheme, the unmanned ship formation control method based on the fixed time terminal sliding mode is provided according to the problem that unmanned ship formation under the conditions of internal and external complex unknown disturbance and system uncertainty exists. The invention mainly utilizes an unmanned ship formation control strategy based on a fixed time fast terminal sliding mode to solve the problem of unmanned ship formation under the conditions of complex unknown disturbance inside and outside and system uncertainty.
The technical means adopted by the invention are as follows:
a multi-unmanned ship formation control method based on fixed time terminal sliding mode comprises the following steps:
s1, establishing a kinematics and dynamics model of the unmanned ship control system;
s2, building an unmanned ship formation control framework based on the established unmanned ship control system kinematics and dynamics model;
s3, designing a fixed-time rapid terminal sliding mode surface based on the constructed unmanned ship formation control frame;
s4, designing a controller of the tracking control subsystem based on the designed fixed time quick terminal sliding mode surface and carrying out stability analysis;
and S5, designing a controller of the formation control subsystem based on the designed fixed-time quick terminal sliding mode surface and carrying out stability analysis.
Further, the step S1 specifically includes:
s11, establishing a kinematics and dynamics model of the unmanned ship, as follows:
wherein, B (η)i,vi)＝-C(vi)vi-D(vi)viThe navigation unmanned ship mathematical model is defined as i ═ 0, the following unmanned ship mathematical model is defined as i ═ 1,2, …, and n; etai＝[xi,yi,ψi]TFor the position and course of the unmanned ship in the geodetic coordinate system, vi＝[ui,vi,ri]TThe speeds of surging, drifting and yawing of the unmanned boat under an attached coordinate system are obtained; tau isi＝[τi1,τi2,τi3]TControl input for a pilot boat and a following boat; deltai＝MiRT(ψi)di(t)，di(t) is external perturbation; b (-) represents the hydrodynamic characteristics of the unmanned boat position under the unknown sea condition; g (η) represents the force and moment of buoyancy and gravity of the unmanned ship, and ideally, g (η) is 0; r (psi)i) For a rotation matrix, Mi＝M i T0 is inertia matrix, C (v)i)＝-C(vi)TIs a Coriolis force matrix, D (v)i) Is a damping matrix;
s12, considering the following expected tracks based on the established unmanned ship kinematics and dynamics model:
wherein, E (η)d,vd)＝-C(vd)vd-D(vd)vd，ηd＝[xd,yd,ψd]TV and vd＝[ud,vd,rd]TRespectively the desired position vector and velocity vector, tau, for the unmanned boatd＝[τd1,τd2,τd3]TIs the desired control input.
Further, the step S2 specifically includes:
s21, dividing the formation system into a tracking control subsystem and a formation control subsystem;
s22, the complex external interference suffered by the formation control subsystem is assumed to have an upper bound, namely, the complex external interference is satisfied
Introducing an auxiliary variable chii,χdThe following are:
wherein the content of the first and second substances,
a first derivative representing the external perturbation; ziRepresenting an external disturbance upper bound value; chi shapei＝[χi,1,χi,2,χi,3]T，χd＝[χd,1,χd,2,χd,3]T，Ri，RdRepresenting an auxiliary rotation matrix, Ri＝R(ψi)，Rd＝R(ψd)；
S23, combining equations (1) - (3), the following coordinate transformation is obtained:
wherein, F (eta)i,χi) Representing a reduced matrix; f (eta)i,χi)＝S(χi3)χi+RiMi -1B(ηi,Ri Tχi)；S(χi3) Representing an antisymmetric matrix; b (eta)i,Ri Tχi) Representing an internal disturbance of the unmanned ship system;
wherein, H (eta)d,χd) Represents; h (eta)d,χd)＝S(χd3)χd+RdMd -1E(ηd,Rd Tχd)；S(χd3) Represents; e (eta)d,Rd Tχd) Representing an internal disturbance of the desired trajectory.
Further, the step S3 specifically includes:
s31, designing a fixed-time rapid terminal sliding mode surface on the basis of the limited-time terminal sliding mode surface, as follows:
wherein the content of the first and second substances,
represents the first derivative of x; l1，l2，κ1Representing a sliding mode surface parameter; z represents a positive integer;
l1＞0,l2＞0；p1,q1are all positive odd numbers, and p1＞q1；
S32, when ζ is 0, integral conversion processing is performed on the time t required for the unmanned ship control system to converge to the equilibrium position from the initial state x (0), and the following is obtained:
s33, obtaining based on formula (7), that is, when N is 1, the fast terminal sliding mode convergence time is related to the system initial state and is finite time convergence; when N > 1, the convergence time is independent of the initial state of the system, and the upper convergence limit of the system convergence time is as follows:
further, the step S4 specifically includes:
s41, obtaining the following tracking error dynamics between the piloted unmanned ship and the desired track based on equations (4) and (5):
wherein eta is0,d＝η0-ηd,χ0,d＝χ0-χdRespectively representing a position error vector and a velocity error vector after coordinate transformation, IeThe auxiliary matrix is represented by a matrix of pixels,
τdindicating a desired control input;
s42, taking N as 3, designing eta0,d,χ0,dThe fixed-time fast terminal slip-form face of (a), as follows:
s43, calculating the time derivative of the fixed-time fast terminal sliding mode surface as follows:
s44, designing a tracking control strategy based on a fixed-time fast terminal sliding mode by combining the theorem 1 as follows:
wherein λ is0,λ1,λ2Indicating a controller parameter, λ, of the tracking control subsystem0,λ1,λ2＞0，l1，l2Represents a sliding mode surface parameter, ζ represents a fixed time control parameter, and m, n represents a simplified parameter.
Further, the lemma 1 in the step S44 is specifically as follows:
for a scalar system:
wherein, γ1,γ2Respectively representing a system parameter, gamma1,γ2> 0, p, q are two positive odd numbers, and p < q is satisfied, the scalar system (13) is stationary time stable, and the convergence time upper bound is satisfied:
further, the step S5 specifically includes:
s51, regarding system unmodeled dynamics and complex external disturbance in ship model of unmanned ship formation control subsystem as lumped uncertainty fiu(. to), designing an unmanned boat formation controller;
s52, dynamically rewriting the formation control error to be:
in the above formula, the first and second carbon atoms are,
Birepresenting internal disturbances following the unmanned ship, Bi＝B(ηi,νi)，B0(. represents an internal disturbance of the piloted unmanned ship, B0(·)＝B(η0,ν0)；
S53, let omegai,1To disturb fiuThe finite time uncertainty observer is designed as follows:
wherein, ω isi,j:＝[ωi,j,1,ωi,j,2,ωi,j,3]T,(j＝0,1,2)，ξi,k:＝[ξi,k,1,ξi,k,2,ξi,k,3]T(k is 0,1) is the disturbance observer state; lambda [ alpha ]i,j＞0,(j＝3,4,5)，Zi＝diag(zi1,zi2,zi3) Design parameters for the observer;
s54, designing an observation error variable for the finite time uncertainty observer, which is as follows:
s55, obtaining the following result by differentiating the observation error variable:
s56, according to lemma 2, the observation error system (18) is stable for a finite time, and when the disturbance is effectively observed, we can obtain:
s57, designing a fixed-time quick terminal sliding mode as follows:
s58, calculating the time derivative of the fixed-time fast terminal sliding mode surface as follows:
s59, designing a fixed-time fast terminal sliding-mode formation controller strategy based on a finite-time uncertain observer as follows:
wherein λ isi,jAnd j is greater than 0 (0, 1 and 2), m and n are positive odd numbers, and m is less than n.
Further, the theorem 2 in the step S56 specifically includes:
the following system is aimed at:
wherein l5,l6＞0，m1＞1，0＜m2Less than 1; the balance point of the system is stable in fixed time, and the upper bound of the convergence time can be obtained by calculation independent of the initial state:
compared with the prior art, the invention has the following advantages:
1. according to the multi-unmanned-boat formation control method based on the fixed-time terminal sliding mode, the whole unmanned-boat formation control system is divided into the tracking control subsystem and the formation control subsystem on the basis of the piloting-following formation control framework, so that the flexibility of the formation control system is improved.
2. The invention provides a fixed time terminal sliding mode-based multi-unmanned-boat formation control method, and provides a novel fixed time rapid terminal sliding mode tracking control strategy, so that the convergence rate of a tracking control subsystem is greatly improved.
3. The multi-unmanned-boat formation control method based on the fixed-time terminal sliding mode guarantees rapidity and stability of a formation control system.
Based on the reason, the method can be widely popularized in the fields of multi-unmanned-boat collaborative formation control and the like.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings needed to be used in the description of the embodiments or the prior art will be briefly introduced below, and it is obvious that the drawings in the following description are some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to these drawings without creative efforts.
FIG. 1 is a flow chart of the method of the present invention.
Fig. 2 is a schematic diagram of a geodetic coordinate system and an attached coordinate system of the unmanned surface vehicle according to the embodiment of the present invention.
Fig. 3 is a diagram of unmanned ship formation trajectories according to an embodiment of the present invention.
Fig. 4 is a view of unmanned surface vehicle position tracking provided by an embodiment of the invention.
Fig. 5 is a velocity tracking diagram of an unmanned boat provided in an embodiment of the present invention.
Fig. 6 is a schematic control input diagram of a piloted unmanned ship according to an embodiment of the present invention.
Fig. 7 is a schematic diagram of control input of the following unmanned surface vehicle 1 according to the embodiment of the present invention.
Fig. 8 is a schematic diagram of control input of the following unmanned surface vehicle 2 according to the embodiment of the present invention.
Fig. 9 is an observation result of the finite time uncertainty observer 1 according to the embodiment of the present invention.
Fig. 10 is an observation result of the finite time uncertainty observer 2 according to the embodiment of the present invention.
Detailed Description
In order to make the technical solutions of the present invention better understood, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
It should be noted that the terms "first," "second," and the like in the description and claims of the present invention and in the drawings described above are used for distinguishing between similar elements and not necessarily for describing a particular sequential or chronological order. It is to be understood that the data so used is interchangeable under appropriate circumstances such that the embodiments of the invention described herein are capable of operation in sequences other than those illustrated or described herein. Furthermore, the terms "comprises," "comprising," and "having," and any variations thereof, are intended to cover a non-exclusive inclusion, such that a process, method, system, article, or apparatus that comprises a list of steps or elements is not necessarily limited to those steps or elements expressly listed, but may include other steps or elements not expressly listed or inherent to such process, method, article, or apparatus.
As shown in fig. 1, the invention provides a multi-unmanned-boat formation control method based on a fixed-time terminal sliding mode, which comprises the following steps:
s1, establishing a kinematics and dynamics model of the unmanned ship control system;
in a specific implementation, as a preferred embodiment of the present invention, the step S1 specifically includes:
s11, as shown in fig. 2, the unmanned ship kinematics and dynamics model is established as follows:
wherein, B (η)i,vi)＝-C(vi)vi-D(vi)viThe navigation unmanned ship mathematical model is defined as i ═ 0, the following unmanned ship mathematical model is defined as i ═ 1,2, …, and n; etai＝[xi,yi,ψi]TFor the position and course of the unmanned ship in the geodetic coordinate system, vi＝[ui,vi,ri]TThe speeds of surging, drifting and yawing of the unmanned boat under an attached coordinate system are obtained; tau isi＝[τi1,τi2,τi3]TControl input for a pilot boat and a following boat; deltai＝MiRT(ψi)di(t)，di(t) is external perturbation; b (-) represents the hydrodynamic characteristics of the unmanned boat position under the unknown sea condition; g (η) represents the force and moment of buoyancy and gravity of the unmanned ship, and ideally, g (η) is 0; r (psi)i) For a rotation matrix, Mi＝M i T0 is inertia matrix, C (v)i)＝-C(vi)TIs a Coriolis force matrix, D (v)i) Is a damping matrix;
s12, considering the following expected tracks based on the established unmanned ship kinematics and dynamics model:
wherein, E (η)d,vd)＝-C(vd)vd-D(vd)vd，ηd＝[xd,yd,ψd]TV and vd＝[ud,vd,rd]TRespectively the desired position vector and velocity vector, tau, for the unmanned boatd＝[τd1,τd2,τd3]TIs the desired control input.
S2, building an unmanned ship formation control framework based on the established unmanned ship control system kinematics and dynamics model;
in a specific implementation, as a preferred embodiment of the present invention, the step S2 specifically includes:
s21, in order to ensure the integrity of the design of the formation system, the formation system is divided into a tracking control subsystem and a formation control subsystem; and the controllers are respectively designed, thereby ensuring the effectiveness of the formation system.
S22, the complex external interference suffered by the formation control subsystem is assumed to have an upper bound, namely, the complex external interference is satisfied
Introducing an auxiliary variable chii,χdThe following are:
wherein the content of the first and second substances,
a first derivative representing the external perturbation; ziRepresenting an external disturbance upper bound value; chi shapei＝[χi,1,χi,2,χi,3]T，χd＝[χd,1,χd,2,χd,3]T，Ri，RdRepresenting an auxiliary rotation matrix, Ri＝R(ψi)，Rd＝R(ψd)；
S23, combining equations (1) - (3), the following coordinate transformation is obtained:
wherein, F (eta)i,χi) Representing a reduced matrix;
S(χi3) Representing an inverse symmetryA matrix; b (eta)i,Ri Tχi) Representing an internal disturbance of the unmanned ship system;
wherein, H (eta)d,χd) Represents; h (eta)d,χd)＝S(χd3)χd+RdMd -1E(ηd,Rd Tχd)；S(χd3) Represents; e (eta)d,Rd Tχd) Representing an internal disturbance of the desired trajectory.
S3, in order to enable the designed unmanned ship formation control system to be in fixed time convergence in the whole theoretical domain and have faster convergence speed when being far away from or close to a balance point, a fixed time fast terminal sliding mode surface is designed based on the built unmanned ship formation control frame;
in a specific implementation, as a preferred embodiment of the present invention, the step S3 specifically includes:
s31, designing a fixed-time rapid terminal sliding mode surface on the basis of the limited-time terminal sliding mode surface, as follows:
wherein the content of the first and second substances,
represents the first derivative of x; l1，l2，k1Representing a sliding mode surface parameter; z represents a positive integer;
l1＞0,l2＞0；p1,q1are all positive odd numbers, and p1＞q1；
S32, when ζ is 0, integral conversion processing is performed on the time t required for the unmanned ship control system to converge to the equilibrium position from the initial state x (0), and the following is obtained:
s33, obtaining based on formula (7), that is, when N is 1, the fast terminal sliding mode convergence time is related to the system initial state and is finite time convergence; when N > 1, the convergence time is independent of the initial state of the system, and the upper convergence limit of the system convergence time is as follows:
the convergence rate of the designed novel fixed time terminal sliding mode surface in the state space except the original point meets the following requirements: when l is2When the value is more than 1, the larger the N value is, the larger the convergence speed of the sliding mode surface is, so that the unmanned ship formation control system is better designed on the premise of ensuring the system stability, and N is taken to be 3.
S4, designing a controller of the tracking control subsystem based on the designed fixed time quick terminal sliding mode surface and carrying out stability analysis;
in a specific implementation, as a preferred embodiment of the present invention, the step S4 specifically includes:
s41, obtaining the following tracking error dynamics between the piloted unmanned ship and the desired track based on equations (4) and (5):
wherein eta is0,d＝η0-ηd,χ0,d＝χ0-χdRespectively representing a position error vector and a velocity error vector after coordinate transformation, IeA simplified matrix is shown that is,
τdindicating a desired control input;
s42, taking N as 3, designing eta0,d,χ0,dThe fixed-time fast terminal slip-form face of (a), as follows:
s43, calculating the time derivative of the fixed-time fast terminal sliding mode surface as follows:
s44, designing a tracking control strategy based on a fixed-time fast terminal sliding mode by combining the theorem 1 as follows:
wherein λ is0,λ1,λ2Indicating a controller parameter, λ, of the tracking control subsystem0,λ1,λ2＞0，l1，l2Represents a sliding mode surface parameter, ζ represents a fixed time control parameter, and m, n represents a simplified parameter.
The theorem 1 in the step S44 is specifically as follows:
for a scalar system:
wherein, γ1,γ2Respectively representing a system parameter, gamma1,γ2> 0, p, q are two positive odd numbers, and p < q is satisfied, the scalar system (13) is stationary time stable, and the convergence time upper bound is satisfied:
theorem 1: when the piloting unmanned ship tracks the expected track, the external disturbance is not considered, the designed tracking control strategy (12) based on the fixed time fast terminal sliding mode can ensure that the piloting unmanned ship tracks the expected track within fixed time, and does not depend on the initial state of the piloting ship, and the upper bound of the convergence time is as follows:
Ts＝T0+T1 (25)
and (3) proving that: the proof of the arrival phase is as follows.
Designing a Lyapunov function:
combination of (11) and (12), pair V1Taking the derivative, we can get:
wherein the content of the first and second substances,
θ12n, and
from lemma 1, an upper bound on convergence time can be calculated:
thus, at a fixed time T1The designed fixed time terminal slip form surface ζ (t) can be reached. When the error vector eta0,d，χ0,dAssigned to the sliding mode surface, get ζ (t) equal to 0,
according to the design structure of the sliding mode, starting from an initial state x (0), the designed control system reaches the upper limit of the time required for converging to an equilibrium position after reaching the sliding stage:
so the upper bound of the convergence time is Ts＝T0+T1. A fixed time fast terminal sliding mode based tracking control strategy (12) designed for a tracking control subsystem can be realized at a fixed time TsThe inner-driving piloting unmanned ship accurately and quickly tracks the expected track, and the upper bound of the convergence time is independent of the initial state of the piloting unmanned ship.
And S5, designing a controller of the formation control subsystem based on the designed fixed-time quick terminal sliding mode surface and carrying out stability analysis.
In a specific implementation, as a preferred embodiment of the present invention, the step S5 specifically includes:
s51, regarding system unmodeled dynamics and complex external disturbance in ship model of unmanned ship formation control subsystem as lumped uncertainty fiu(. to), designing an unmanned boat formation controller;
s52, dynamically rewriting the formation control error to be:
in the above formula, the first and second carbon atoms are,
Birepresenting internal disturbances following the unmanned ship, Bi＝B(ηi,νi)，B0(. represents an internal disturbance of the piloted unmanned ship, B0(·)＝B(η0,ν0)；
S53, let omegai,1To disturb fiuDesigning an observer with finite uncertaintyThe following were used:
wherein, ω isi,j:＝[ωi,j,1,ωi,j,2,ωi,j,3]T,(j＝0,1,2)，ξi,k:＝[ξi,k,1,ξi,k,2,ξi,k,3]T(k is 0,1) is the disturbance observer state; lambda [ alpha ]i,j＞0,(j＝3,4,5)，Zi＝diag(zi1,zi2,zi3) Design parameters for the observer;
s54, designing an observation error variable for the finite time uncertainty observer, which is as follows:
s55, obtaining the following result by differentiating the observation error variable:
s56, according to lemma 2, the observation error system (18) is stable for a finite time, and when the disturbance is effectively observed, we can obtain:
the theorem 2 in the step S56 specifically includes:
the following system is aimed at:
wherein l5,l6＞0，m1＞1，0＜m2Less than 1; the balance point of the system is stable in fixed time, and the upper bound of the convergence time can beIndependent of the initial state calculation, the following results are obtained:
s57, designing a fixed-time quick terminal sliding mode as follows:
s58, calculating the time derivative of the fixed-time fast terminal sliding mode surface as follows:
s59, designing a fixed-time fast terminal sliding-mode formation controller strategy based on a finite-time uncertain observer as follows:
wherein λ isi,jAnd j is greater than 0 (0, 1 and 2), m and n are positive odd numbers, and m is less than n.
Theorem 2: the designed finite time uncertain disturbance observer can effectively identify lumped uncertain items of the unmanned ship formation control system in finite time, and after observation, the designed formation control strategy based on the fixed time quick terminal sliding mode can accurately and quickly form a formation in fixed time.
And (3) proving that: a Lyapunov function is defined as follows:
derivation of this can yield:
according to the theorem 2, the upper bound of the convergence time can be calculated, the designed fast terminal sliding mode surface can arrive within the fixed time, and the proving process is similar to that of the theorem 1, and therefore, the description is omitted here.
In order to verify the effectiveness of the method, a simulation experiment is carried out, which specifically comprises the following steps:
a classical Cybership II test model is utilized to carry out a simulation experiment to verify the effectiveness of the designed unmanned ship formation control strategy with fixed time, and the parameters in the formation system are set as follows: the initial values of the expected track, the positions and the speeds of the pilot boat and the following boat are shown in the table 1; the values of the relevant parameters are shown in table 2;
initial values of the model of Table 1
TABLE 2 values of the parameters
The perturbations are as follows:
the simulation results are shown in fig. 2-9. The designed multi-unmanned boat formation can accurately track a desired track within 5s and maintain a desired formation. It is clear that the proposed control scheme can guarantee that the convergence time is less than the maximum value and can be calculated independently of the substituted initial state.
Finally, it should be noted that: the above embodiments are only used to illustrate the technical solution of the present invention, and not to limit the same; while the invention has been described in detail and with reference to the foregoing embodiments, it will be understood by those skilled in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some or all of the technical features may be equivalently replaced; and the modifications or the substitutions do not make the essence of the corresponding technical solutions depart from the scope of the technical solutions of the embodiments of the present invention.
Claims (8)
1. A multi-unmanned ship formation control method based on fixed time terminal sliding mode is characterized by comprising the following steps:
s1, establishing a kinematics and dynamics model of the unmanned ship control system;
s2, building an unmanned ship formation control framework based on the established unmanned ship control system kinematics and dynamics model;
s3, designing a fixed-time rapid terminal sliding mode surface based on the constructed unmanned ship formation control frame;
s4, designing a controller of the tracking control subsystem based on the designed fixed time quick terminal sliding mode surface and carrying out stability analysis;
and S5, designing a controller of the formation control subsystem based on the designed fixed-time quick terminal sliding mode surface and carrying out stability analysis.
2. The fixed-time terminal sliding-mode-based multi-unmanned-boat formation control method according to claim 1, wherein the step S1 specifically comprises:
s11, establishing a kinematics and dynamics model of the unmanned ship, as follows:
wherein, B (η)i,vi)＝-C(vi)vi-D(vi)viThe navigation unmanned ship mathematical model is defined as i ═ 0, the following unmanned ship mathematical model is defined as i ═ 1,2, …, and n; etai＝[xi,yi,ψi]TFor the position and course of the unmanned ship in the geodetic coordinate system, vi＝[ui,vi,ri]TThe speeds of surging, drifting and yawing of the unmanned boat under an attached coordinate system are obtained; tau isi＝[τi1,τi2,τi3]TControl input for a pilot boat and a following boat; deltai＝MiRT(ψi)di(t)，di(t) is external perturbation; b (-) represents the hydrodynamic characteristics of the unmanned boat position under the unknown sea condition; g (η) represents the force and moment of buoyancy and gravity of the unmanned ship, and ideally, g (η) is 0; r (psi)i) For a rotation matrix, Mi＝Mi T0 is inertia matrix, C (v)i)＝-C(vi)TIs a Coriolis force matrix, D (v)i) Is a damping matrix;
s12, considering the following expected tracks based on the established unmanned ship kinematics and dynamics model:
wherein, E (η)d,vd)＝-C(vd)vd-D(vd)vd，ηd＝[xd,yd,ψd]TV and vd＝[ud,vd,rd]TRespectively the desired position vector and velocity vector, tau, for the unmanned boatd＝[τd1,τd2,τd3]TIs the desired control input.
3. The fixed-time terminal sliding-mode-based multi-unmanned-boat formation control method according to claim 1, wherein the step S2 specifically comprises:
s21, dividing the formation system into a tracking control subsystem and a formation control subsystem;
s22, the complex external interference suffered by the formation control subsystem is assumed to have an upper bound, namely, the complex external interference is satisfied
Introducing an auxiliary variable chii,χdThe following are:
wherein the content of the first and second substances,
a first derivative representing an unknown perturbation; ziRepresenting an external disturbance upper bound value; chi shapei＝[χi,1,χi,2,χi,3]T，χd＝[χd,1,χd,2,χd,3]T，RiAnd RdRepresenting an auxiliary rotation matrix, Ri＝R(ψi)，Rd＝R(ψd)；
S23, combining equations (1) - (3), the following coordinate transformation is obtained:
wherein, F (eta)i,χi) To simplify the matrix;
S(χi3) Representing an antisymmetric matrix; b (eta)i,Ri Tχi) Representing unmanned ship internal disturbances;
wherein, H (eta)d,χd) Representing a reduced matrix; h (eta)d,χd)＝S(χd3)χd+RdMd -1E(ηd,Rd Tχd)；S(χd3) Representing an antisymmetric matrix; e (eta)d,Rd Tχd) Representing an internal disturbance of the desired trajectory.
4. The fixed-time terminal sliding-mode-based multi-unmanned-boat formation control method according to claim 1, wherein the step S3 specifically comprises:
s31, designing a fixed-time rapid terminal sliding mode surface on the basis of the limited-time terminal sliding mode surface, as follows:
wherein the content of the first and second substances,
represents the first derivative of x; l1，l2，κ1Representing a sliding mode surface parameter; z represents a positive integer;
l1＞0,l2＞0；p1,q1are all positive odd numbers, and p1＞q1；
S32, when ζ is 0, integral conversion processing is performed on the time t required for the unmanned ship control system to converge to the equilibrium position from the initial state x (0), and the following is obtained:
s33, obtaining based on formula (7), that is, when N is 1, the fast terminal sliding mode convergence time is related to the system initial state and is finite time convergence; when N > 1, the convergence time is independent of the initial state of the system, and the upper convergence limit of the system convergence time is as follows:
5. the fixed-time terminal sliding-mode-based multi-unmanned-boat formation control method according to claim 1, wherein the step S4 specifically comprises:
s41, obtaining the following tracking error dynamics between the piloted unmanned ship and the desired track based on equations (4) and (5):
wherein eta is0,d＝η0-ηd,χ0,d＝χ0-χdRespectively representing a position error vector and a velocity error vector after coordinate transformation, IeA simplified matrix is shown that is,
τdindicating a desired control input;
s42, taking N as 3, designing eta0,d,χ0,dThe fixed-time fast terminal slip-form face of (a), as follows:
s43, calculating the time derivative of the fixed-time fast terminal sliding mode surface as follows:
s44, designing a tracking control strategy based on a fixed-time fast terminal sliding mode by combining the theorem 1 as follows:
wherein λ is0,λ1,λ2Indicating a controller parameter, λ, of the tracking control subsystem0,λ1,λ2＞0，l1，l2Represents a sliding mode surface parameter, ζ represents a fixed time control parameter, and m, n represents a simplified parameter.
6. The fixed-time terminal sliding-mode-based multi-unmanned-boat formation control method according to claim 5, wherein the theorem 1 in the step S44 is as follows:
for a scalar system:
wherein, γ1,γ2Respectively representing a system parameter, gamma1,γ2> 0, p, q are two positive odd numbers, and p < q is satisfied, the scalar system (13) is stationary time stable, and the convergence time upper bound is satisfied:
7. the fixed-time terminal sliding-mode-based multi-unmanned-boat formation control method according to claim 1, wherein the step S5 specifically comprises:
s51, regarding system unmodeled dynamics and complex external disturbance in ship model of unmanned ship formation control subsystem as lumped uncertainty fiu(. to), designing an unmanned boat formation controller;
s52, dynamically rewriting the formation control error to be:
in the above formula, the first and second carbon atoms are,
Birepresenting internal disturbances following the unmanned ship, Bi＝B(ηi,νi)，B0(. represents an internal disturbance of the piloted unmanned ship, B0(·)＝B(η0,ν0)；
S53, let omegai,1To disturb fiuThe finite time uncertainty observer is designed as follows:
wherein, ω isi,j:＝[ωi,j,1,ωi,j,2,ωi,j,3]T,(j＝0,1,2)，ξi,k:＝[ξi,k,1,ξi,k,2,ξi,k,3]T(k is 0,1) is the disturbance observer state; lambda [ alpha ]i,j＞0,(j＝3,4,5)，Zi＝diag(zi1,zi2,zi3) Design parameters for the observer;
s54, designing an observation error variable for the finite time uncertainty observer, which is as follows:
s55, obtaining the following result by differentiating the observation error variable:
s56, according to lemma 2, the observation error system (18) is stable for a finite time, and when the disturbance is effectively observed, we can obtain:
s57, designing a fixed-time quick terminal sliding mode as follows:
s58, calculating the time derivative of the fixed-time fast terminal sliding mode surface as follows:
s59, designing a fixed-time fast terminal sliding-mode formation controller strategy based on a finite-time uncertain observer as follows:
wherein λ isi,jAnd j is greater than 0 (0, 1 and 2), m and n are positive odd numbers, and m is less than n.
8. The method for controlling formation of multiple unmanned boats based on fixed time terminal sliding mode according to claim 1, wherein the lemma 2 in the step S56 specifically includes:
the following system is aimed at:
wherein l5,l6＞0，m1＞1，0＜m2Less than 1; the balance point of the system is stable in fixed time, and the upper bound of the convergence time can be obtained by calculation independent of the initial state:
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202110144673.4A CN112965375A (en) | 2021-02-02 | 2021-02-02 | Multi-unmanned-boat formation control method based on fixed-time terminal sliding mode |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202110144673.4A CN112965375A (en) | 2021-02-02 | 2021-02-02 | Multi-unmanned-boat formation control method based on fixed-time terminal sliding mode |
Publications (1)
| Publication Number | Publication Date |
|---|---|
| CN112965375A true CN112965375A (en) | 2021-06-15 |
Family
ID=76271955
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN202110144673.4A Pending CN112965375A (en) | 2021-02-02 | 2021-02-02 | Multi-unmanned-boat formation control method based on fixed-time terminal sliding mode |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN112965375A (en) |
Cited By (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN113268059A (en) * | 2021-04-20 | 2021-08-17 | 大连海事大学 | Multi-unmanned-boat formation control method based on finite-time extended state observer |
| CN113741468A (en) * | 2021-09-08 | 2021-12-03 | 哈尔滨工程大学 | Finite time fault-tolerant control method for distributed unmanned ship formation |
| CN113835338A (en) * | 2021-09-08 | 2021-12-24 | 哈尔滨工程大学 | Limited time tracking control method and device of under-actuated unmanned ship based on integral sliding mode |
| CN114296449A (en) * | 2021-12-13 | 2022-04-08 | 广东海洋大学 | Water surface unmanned ship track rapid tracking control method based on fixed time H-infinity control |
Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN110377034A (en) * | 2019-07-09 | 2019-10-25 | 哈尔滨工程大学 | A kind of waterborne vessel track following Global robust sliding-mode control based on dragonfly algorithm optimization |
| CN110928310A (en) * | 2019-12-12 | 2020-03-27 | 大连海事大学 | Unmanned ship navigation following fixed time formation control method |
-
2021
- 2021-02-02 CN CN202110144673.4A patent/CN112965375A/en active Pending
Patent Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN110377034A (en) * | 2019-07-09 | 2019-10-25 | 哈尔滨工程大学 | A kind of waterborne vessel track following Global robust sliding-mode control based on dragonfly algorithm optimization |
| CN110928310A (en) * | 2019-12-12 | 2020-03-27 | 大连海事大学 | Unmanned ship navigation following fixed time formation control method |
Non-Patent Citations (2)
| Title |
|---|
| 李贺: "领航-跟随水面无人船编队固定时间控制研究", 中国学术期刊电子杂志社, no. 2021, pages 6 - 11 * |
| 王崇等: "一类非线性系统的新型固定时间滑模控制", 电光与控制, vol. 27, no. 2020, pages 47 - 53 * |
Cited By (8)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN113268059A (en) * | 2021-04-20 | 2021-08-17 | 大连海事大学 | Multi-unmanned-boat formation control method based on finite-time extended state observer |
| CN113268059B (en) * | 2021-04-20 | 2024-03-29 | 大连海事大学 | Multi-unmanned-ship formation control method based on limited-time extended state observer |
| CN113741468A (en) * | 2021-09-08 | 2021-12-03 | 哈尔滨工程大学 | Finite time fault-tolerant control method for distributed unmanned ship formation |
| CN113835338A (en) * | 2021-09-08 | 2021-12-24 | 哈尔滨工程大学 | Limited time tracking control method and device of under-actuated unmanned ship based on integral sliding mode |
| CN113741468B (en) * | 2021-09-08 | 2023-11-14 | 哈尔滨工程大学 | Finite time fault-tolerant control method for formation of distributed unmanned ship |
| CN113835338B (en) * | 2021-09-08 | 2024-03-01 | 哈尔滨工程大学 | Finite time tracking control method and device for under-actuated unmanned ship with integral sliding mode |
| CN114296449A (en) * | 2021-12-13 | 2022-04-08 | 广东海洋大学 | Water surface unmanned ship track rapid tracking control method based on fixed time H-infinity control |
| CN114296449B (en) * | 2021-12-13 | 2022-08-02 | 广东海洋大学 | Water surface unmanned ship track rapid tracking control method based on fixed time H-infinity control |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN112965375A (en) | Multi-unmanned-boat formation control method based on fixed-time terminal sliding mode | |
| CN110928310B (en) | Unmanned ship navigation following fixed time formation control method | |
| CN110879599B (en) | Fixed time formation control method based on finite time disturbance observer | |
| Peng et al. | Cooperative dynamic positioning of multiple marine offshore vessels: A modular design | |
| CN111752280B (en) | Multi-unmanned ship formation fixed time control method based on finite time uncertainty observer | |
| Ihle et al. | Passivity-based designs for synchronized path-following | |
| CN110262494B (en) | Collaborative learning and formation control method for isomorphic multi-unmanned ship system | |
| CN104898688A (en) | UUV four degree-of-freedom dynamic positioning adaptive anti-interference sliding mode control system and control method | |
| CN113268059A (en) | Multi-unmanned-boat formation control method based on finite-time extended state observer | |
| CN110377036A (en) | A kind of unmanned water surface ship Track In Track set time control method constrained based on instruction | |
| Qu et al. | Finite-time sideslip observer-based synchronized path-following control of multiple unmanned underwater vehicles | |
| Witkowska | Dynamic positioning system with vectorial backstepping controller | |
| Dai et al. | Finite-time trajectory tracking for marine vessel by nonsingular backstepping controller with unknown external disturbance | |
| CN117311142A (en) | DP ship motion control and thrust distribution cooperative control method integrating particle swarm optimization and neural network predictive control | |
| CN114967714A (en) | Anti-interference motion control method and system for autonomous underwater robot | |
| Xu et al. | Anti-disturbance fault-tolerant formation containment control for multiple autonomous underwater vehicles with actuator faults | |
| CN114397821A (en) | Multi-surface ship distributed formation robust control method based on preset performance | |
| CN112578797A (en) | Ship formation control method based on distributed guidance under switching topology | |
| Meng et al. | Nonlinear sliding mode formation control for underactuated surface vessels | |
| CN114296449B (en) | Water surface unmanned ship track rapid tracking control method based on fixed time H-infinity control | |
| Soylu et al. | Robust control of underwater vehicles with fault-tolerant infinity-norm thruster force allocation | |
| Zhu et al. | Containment control of underactuated ships with environment disturbances and parameter uncertainties | |
| CN109062232B (en) | Seabed seismic wave detection flight node distributed finite time anti-shake configuration inclusion control method | |
| CN109240081B (en) | Finite time configuration containing fault-tolerant control method of ocean bottom seismic demodulation flight node considering error constraint | |
| Dong et al. | Performance-Guaranteed Adaptive Optimized Control of Intelligent Surface Vehicle Using Reinforcement Learning |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination |