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CN119861568B - A robust predictive cooperative control method and system for ASV-AUV hybrid clusters - Google Patents

A robust predictive cooperative control method and system for ASV-AUV hybrid clusters

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CN119861568B
CN119861568B CN202510033450.9A CN202510033450A CN119861568B CN 119861568 B CN119861568 B CN 119861568B CN 202510033450 A CN202510033450 A CN 202510033450A CN 119861568 B CN119861568 B CN 119861568B
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moment
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CN119861568A (en
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胡满江
崔峥嵘
边有钢
高铭
秦洪懋
杨泽宇
李洋
丁荣军
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Hunan University
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    • G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
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Abstract

The invention discloses an ASV-AUV hybrid cluster robust model prediction cooperative control method and system, which comprise the steps of 1, obtaining position state information and speed state information of any autonomous system in a hybrid cluster, wherein the autonomous system is divided into ASV and AUV, 2, setting expected position vectors corresponding to the autonomous system i according to cooperative tasks, calculating virtual control speed of the autonomous system at a kinematic layer by combining the position state information and the speed state information, 3, estimating interference at a dynamic layer according to the virtual control speed by adopting an interference observer, and calculating control input of the autonomous system by adopting a robust model prediction controller, and 4, calculating actual execution control quantity of a propulsion system at an execution layer by adopting a propeller model according to the control input. The invention can solve the problem of cooperative control of the ASV-AUV hybrid cluster system with uncertainty and improve the robustness and stability of system control.

Description

ASV-AUV hybrid cluster robust model prediction cooperative control method and system
Technical Field
The invention relates to the technical field of cross-domain coordination of autonomous systems, in particular to a prediction coordination control method and a prediction coordination control system for an ASV (Autonomous Surface Vehicle, autonomous water surface vehicle) -AUV (Autonomous UnderwaterVehicle ) hybrid cluster robust model.
Background
With the rapid development of intelligent technology and autonomous systems, the concept of cross-domain collaborative technology has grown and gradually become a place of global autonomous system technology competition. The cross-domain cooperative technology of the autonomous system mainly refers to cooperative control technology of different types of autonomous systems such as unmanned aerial vehicles, autonomous ground vehicles, autonomous surface boats, autonomous underwater robots and the like in different spatial domains such as air, ground and ocean. In the field of ocean engineering, an ASV-AUV hybrid cluster system consisting of an ASV and an AUV is application of a cross-domain cooperative technology. Through the cooperation of the upper space domain and the lower space domain of the water area, the ASV-AUV hybrid cluster system can be applied to more complex marine operation scenes, including emergency maritime rescue, marine topography, resource exploration and the like. Cooperative control is a key technology for realizing cross-domain cooperation, and a stable cooperative operation mode is formed by combining autonomous systems of two spatial domains with a preset specific structure.
Currently, main solutions to the problem of cooperative control include pilot-follower method, virtual structure method, artificial potential field method, behavior method, graph theory method, and the like. According to the method ideas, domestic and foreign scholars put forward some control methods for the problem of cooperative control of ASV and AUV, but mainly consider single-class clusters (ASV clusters or AUV clusters), and research on ASV-AUV hybrid clusters is relatively less. In practical application, due to uncertainty of interferences such as wind, sea waves, ocean currents and the like in a marine operation environment and influence of nonlinear dynamics characteristics and unmodeled uncertainty of an autonomous system, the robustness and stability of ASV-AUV hybrid cluster cooperative control are difficult to ensure in the prior art.
The patent document CN117850417A discloses a formation control method and a formation control system for a water surface unmanned ship and an autonomous underwater unmanned aircraft, and the formation control method comprises the following steps of respectively issuing a preset formation task to a USV and an AUV, arranging the USV and the AUV into water for sailing, calculating relative positions, designing an AUV reference course angle, a reference course speed and a longitudinal control force, designing a yaw direction control torque, calculating an error variable and an environment interference estimation error variable, and controlling the AUV propeller and a control surface to generate the calculated control force and torque to realize formation sailing of the USV and the AUV. The nonlinear disturbance observer provided by the invention can be used for estimating the influence caused by unknown environmental force and modeling uncertainty suffered by an aircraft. The invention only considers the cooperative formation control of a single USV and AUV, and an actual hybrid cluster system is generally composed of a plurality of USVs and AUVs, so that the invention is difficult to apply to the cooperative control of a large-scale number of clusters.
Patent document CN115268476B discloses a distributed cooperative control system and method for a water surface ship and an underwater vehicle, which adopts a modular design, an ASV (AUV) obtains information of the navigation states of the native and nearby AUV and ASV and formation structure instructions through a positioning and communication module, generates the navigation states and speed states at the next moment through a cooperative controller, performs point tracking control through an active disturbance point tracking controller and an actuator, forms internal circulation control due to high control frequency of the active disturbance point tracking control, and forms external circulation control due to low control frequency of the communication restriction. The dynamic equations considered by the invention are linear systems, whereas the actual AUV or ASV is typically a nonlinear system, so the invention is difficult to adapt to hybrid cluster systems with nonlinear dynamics.
The patent document CN114942646B discloses a three-dimensional space formation control method of a heterogeneous unmanned system, which comprises the following steps of establishing a three-dimensional formation communication topology model of the heterogeneous unmanned system, executing a course consistency control algorithm, executing a speed consistency control algorithm, executing a depth consistency control algorithm if an unmanned system node is an autonomous underwater vehicle, controlling a water surface unmanned ship serving as the unmanned system node to operate according to an output course angle and an output course speed, and controlling the autonomous underwater vehicle serving as the unmanned system node to operate according to the output course angle, the output course speed and the output course depth. The invention does not consider the dynamics models of unmanned ships and autonomous underwater vehicles on the water surface and does not consider the uncertainty of the models, so that the robustness and the stability of the invention in practical application are difficult to ensure.
Disclosure of Invention
The invention aims to provide an ASV-AUV hybrid cluster robust model prediction cooperative control method and system, which aim to solve the problem of cooperative control of an ASV-AUV hybrid cluster system with uncertainty and improve the robustness and stability of system control.
In order to achieve the above purpose, the present invention provides a prediction cooperative control method for an ASV-AUV hybrid cluster robust model, which is characterized by comprising:
Step 1, acquiring position state information eta i and speed state information xi i of any autonomous system i in a hybrid cluster, wherein the autonomous systems are divided into ASV and AUV;
Step 2, setting a desired position vector eta id corresponding to the autonomous system i according to the cooperative task, and calculating a virtual control speed zeta ic of the autonomous system i in a kinematic layer by combining position state information eta i and speed state information zeta i;
Step 3, estimating interference d i by adopting an interference observer at a dynamics layer according to the virtual control speed ζ ic, and calculating a control input tau i of the autonomous system i by a robust model predictive controller;
And 4, calculating the actual execution control quantity lambda i of the propulsion system by adopting a propeller model at an execution layer according to the control input tau i.
Further, in the step 3, the optimization problem of the robust model predictive controller is set as a formula (16-1), the constraint condition corresponding to the formula (16-1) is described as a formula (17-1), or the optimization problem of the robust model predictive controller is set as a formula (16-2), and the constraint condition corresponding to the formula (16-2) is described as a formula (17-2);
Wherein J i is an objective function to be optimized, τ i is τ i (t) which represents control input of an autonomous system i at a time t, N p is a prediction time domain, ζ i is ζ i (t) which represents actual speed of the autonomous system i at the time t, ζ i (s|t) is speed of the autonomous system i at the time t which predicts time step s, ζ ic (s|t) represents virtual control speed of the autonomous system i at the time t which predicts time step s, Q iζ is a weight matrix of speed tracking error, N c is a control time domain, R i2 is a weight matrix of control input quantity, τ i (s|t) is control input of the autonomous system i at the time t which predicts time step s, ζ i (s+ 1|t) is speed of the autonomous system i at the time t which predicts time step s+1, and g (ζ i(s|t),τi (s|t)) is a dynamic model nominal part of the autonomous system i at the time t which predicts time step s; Predicting the interference estimated by the time step s at the moment t for the autonomous system i; τ i (s|t) is the control input of the autonomous system i for predicting the time step s at the time t; τ i (s+ 1|t) represents the control input of the autonomous system predicting the time step s+1 at time t; the constraint set for controlling increment, zeta i(Np |t is the speed of the autonomous system i at the time t predicted time step N p, ψ i is the terminal constraint set of the speed state, and H (zeta i(s|t),τi (s|t)) is the function corresponding to the contraction constraint.
Further, the contraction constraint is based on the lyapunov method and the assist control amount design as the inequality constraint (18):
wherein V i represents a speed-dependent lyapunov function, which is set to formula (19);
Wherein e i＝ζi-ζic represents a speed tracking error of the autonomous system i at a time t, ζ ic is ζ ic (t), and is a virtual control speed of the autonomous system i at the time t;
Is that Representing a nonlinear auxiliary control quantity designed based on the Lyapunov method, which is represented by formula (20);
Wherein, the Representing the nominal portions of the inertia matrix, the coriolis and centrifugal force matrix, and the hydrodynamic damping matrix, respectively,For the interference estimated by the interference observer,For the virtual control acceleration of the autonomous system i, K iζ is the gain matrix.
Further, in step 2, the virtual control speed ζ ic is calculated by the Tube-MPC controller described in formula (5), In order to obtain the optimized speed control quantity through the solution of the optimization problem of the Tube-MPC controller, the corresponding constraint condition of the optimization problem is set as a formula (6),Feedback speed control amount for autonomous system i:
Wherein, the For the nominal position of the time step s+1 predicted by the autonomous system i at the time t, R i (s|t) is the rotation matrix of the time step s predicted by the autonomous system i at the time t; The nominal speed of the time step s is predicted for the autonomous system i at the instant t, For the nominal position of the time step s predicted by the autonomous system i at the instant t, L i (s|t) is the phase cost of the time step s predicted by the autonomous system i at the instant t, Η id (s|t) is the expected position of the autonomous system i at time t at time step s, Q i1 is the weight matrix of the position tracking error, R i1 is the weight matrix of the speed control quantity, N i(Np |t) is the terminal cost of the autonomous system i at time t prediction time step N p, For the nominal position of the autonomous system i at the time step N p predicted at the time t, η id(Np |t) is the expected position of the autonomous system i at the time t at the time step N p, and Q i2 is the weight matrix of the terminal position tracking error; For the actual position of autonomous system i at time t, For the nominal position of autonomous system i at time t,For the nominal speed of autonomous system i at time T, T is the sampling time,As a set of constraints for the actual position state,Represents a difference of Pontryagin in terms of the number of the samples,For a Tube invariant set of an actual kinematic model, y i is a feedback gain matrix, Λ i is a terminal constraint set of a position state, η i(s|t)、ηj (s|t) is an actual position of an autonomous system i and an autonomous system j at a time t predicted by a time step S respectively, η ijs is a safety distance limit between ASVs, η ijU is a safety distance limit between AUVs, if i e S, the autonomous system i is an ASV, if i e U, the autonomous system i is an AUV.
Further, when i ε U, a constraint described by the following equation (7) is added to the depth of AUV:
zi∈Zlim (7)
where Z lim is the depth constraint set of autonomous system i.
The invention also provides an ASV-AUV hybrid cluster robust model prediction cooperative control system, which comprises a hybrid cluster, water surface and underwater communication equipment, a state information sensor, a kinematic control unit, a disturbance observer unit, a dynamics control unit, a propeller unit and an execution and driving mechanism;
The water surface and underwater communication equipment is used for the ASV and AUV in the hybrid cluster to communicate with each other;
the state information sensor is used for acquiring position state information eta i and speed state information zeta i of the autonomous system i;
The kinematics control unit is used for setting a desired position vector eta id corresponding to the autonomous system i according to the cooperative task, and calculating a virtual control speed zeta ic of the autonomous system i at a kinematics layer by combining the position state information eta i and the speed state information zeta i;
the disturbance observer unit is used for estimating disturbance to ASV and AUV;
The dynamics control unit is used for calculating a control input tau i of the autonomous system i at a dynamics layer through the robust model predictive controller according to the virtual control speed zeta ic;
The propeller unit is used for constructing a propeller model, calculating the actual execution control quantity lambda i of the propulsion system by adopting the propeller model at the execution layer according to the control input tau i, and outputting an instruction to a specific execution and driving mechanism;
the execution and driving mechanism drives the ASV and the AUV to move according to the obtained instruction.
Further, the optimization problem of the robust model predictive controller in the dynamics control unit is set as a formula (16-1), the constraint condition corresponding to the formula (16-1) is described as a formula (17-1), or the optimization problem of the robust model predictive controller is set as a formula (16-2), and the constraint condition corresponding to the formula (16-2) is described as a formula (17-2);
Wherein J i is an objective function to be optimized, τ i is τ i (t) which represents control input of an autonomous system i at a time t, N p is a prediction time domain, ζ i is ζ i (t) which represents actual speed of the autonomous system i at the time t, ζ i (s|t) is speed of the autonomous system i at the time t which predicts time step s, ζ ic (s|t) represents virtual control speed of the autonomous system i at the time t which predicts time step s, Q iζ is a weight matrix of speed tracking error, N c is a control time domain, R i2 is a weight matrix of control input quantity, τ i (s|t) is control input of the autonomous system i at the time t which predicts time step s, ζ i (s+ 1|t) is speed of the autonomous system i at the time t which predicts time step s+1, and g (ζ i(s|t),τi (s|t)) is a dynamic model nominal part of the autonomous system i at the time t which predicts time step s; Predicting the interference estimated by the time step s at the moment t for the autonomous system i; τ i (s|t) is the control input of the autonomous system i for predicting the time step s at the time t; τ i (s+ 1|t) represents the control input of the autonomous system predicting the time step s+1 at time t; the constraint set for controlling increment, zeta i(Np |t is the speed of the autonomous system i at the time t predicted time step N p, ψ i is the terminal constraint set of the speed state, and H (zeta i(s|t),τi (s|t)) is the function corresponding to the contraction constraint.
Further, the contraction constraint may be designed based on the lyapunov method and the assist control amount as an inequality constraint (18):
wherein V i represents a speed-dependent lyapunov function, which is set to formula (19);
Wherein e i＝ζi-ζic represents a speed tracking error of the autonomous system i at a time t, ζ ic is ζ ic (t), and is a virtual control speed of the autonomous system i at the time t;
a nonlinear auxiliary control quantity designed for a lyapunov-based method, which is of formula (20);
Wherein, the Representing the nominal portions of the inertia matrix, the coriolis and centrifugal force matrix, and the hydrodynamic damping matrix, respectively,For the interference estimated by the interference observer,For the virtual control acceleration of the autonomous system i, K iξ is the gain matrix.
Further, in the kinematic control unit, the virtual control speed K ic is obtained by calculation by the Tube-MPC controller described in the formula (5), In order to obtain the optimized speed control quantity through the solution of the optimization problem of the Tube-MPC controller, the corresponding constraint condition of the optimization problem is set as a formula (6),Feedback speed control amount for autonomous system i:
Wherein, the For the nominal position of the time step s+1 predicted by the autonomous system i at the time t, R i (s|t) is the rotation matrix of the time step s predicted by the autonomous system i at the time t; The nominal speed of the time step s is predicted for the autonomous system i at the instant t, For the nominal position of the time step s predicted by the autonomous system i at the instant t, L i (s|t) is the phase cost of the time step s predicted by the autonomous system i at the instant t, Η id (s|t) is the expected position of the autonomous system i at time t at time step s, Q i1 is the weight matrix of the position tracking error, R i1 is the weight matrix of the speed control quantity, N i(Np |t) is the terminal cost of the autonomous system i at time t prediction time step N p, For the nominal position of the autonomous system i at the time step N p predicted at the time t, η id(Np |t) is the expected position of the autonomous system i at the time t at the time step N p, and Q i2 is the weight matrix of the terminal position tracking error; For the actual position of autonomous system i at time t, For the nominal position of autonomous system i at time t,For the nominal speed of autonomous system i at time T, T is the sampling time,As a set of constraints for the actual position state,Represents a difference of Pontryagin in terms of the number of the samples,For a Tube invariant set of an actual kinematic model, y i is a feedback gain matrix, Λ i is a terminal constraint set of a position state, η i(s|t)、ηj (s|t) is an actual position of an autonomous system i and an autonomous system j at a time t predicted by a time step S respectively, η ijs is a safety distance limit between ASVs, η ijU is a safety distance limit between AUVs, if i e S, the autonomous system i is an ASV, if i e U, the autonomous system i is an AUV.
Further, when i ε U, a constraint described by the following equation (7) is added to the depth of AUV:
zi∈Zlim (7)
where Z lim is the depth constraint set of autonomous system i.
The invention adopts a cascade control structure, the kinematic layer is responsible for calculating the virtual control speed according to the expected cooperative target, namely the expected position vector eta id, and the dynamic layer calculates the dynamic control input, namely the control input tau i according to the virtual control speed, so that the control precision can be improved, and the robustness of the system can be enhanced.
According to the invention, the actual kinematic model is constructed by considering the wind wave and ocean current constant velocity interference factors, the ideal kinematic model without environment velocity interference is regarded as the nominal kinematic model, and the virtual control velocity is calculated through the Tube-MPC controller, so that the robustness of the hybrid cluster system in the kinematic control layer is effectively improved.
The invention combines the disturbance observer with the robust model predictive control method, the disturbance observer enables the dynamic model prediction to be more accurate, the robust model predictive control method ensures the closed-loop stability of the control system, and the combination of the disturbance observer and the robust model predictive control method can obviously improve the performance and the stability of the control system in the face of uncertainty and disturbance. The invention outputs the execution control quantity of the system propeller, namely the execution control quantity lambda i, which meets the application requirements of practical engineering.
Drawings
Fig. 1 is a schematic illustration of a hybrid cluster of 5 ASVs and 5 AUVs in an embodiment of the present invention.
Fig. 2 is a flowchart of an ASV-AUV hybrid cluster robust model predictive cooperative control method according to an embodiment of the present invention.
Fig. 3 is a schematic diagram of an ASV-AUV hybrid cluster robust model predictive cooperative control framework in accordance with an embodiment of the present invention.
Fig. 4 is a schematic structural diagram of an ASV-AUV hybrid cluster robust model predictive cooperative control system.
Detailed Description
In the drawings, the same or similar reference numerals are used to denote the same or similar elements or elements having the same or similar functions. Embodiments of the present invention will be described in detail below with reference to the accompanying drawings.
In the description of the present invention, the terms "center", "longitudinal", "lateral", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", and the like indicate an orientation or a positional relationship based on that shown in the drawings, only for convenience of description and simplification of the description, and do not indicate or imply that the apparatus or element to be referred to must have a specific orientation, be configured and operated in a specific orientation, and therefore should not be construed as limiting the scope of protection of the present invention.
The hybrid cluster system provided by the embodiment of the present invention is composed of a plurality of autonomous systems, specifically, the autonomous systems are divided into K ASVs and N AUVs, the numbers of all autonomous systems are set to O, o= {1, 2. K+n, where the number of ASVs is defined as the set S, s= {1,2,.. the number of AUVs is defined as the set U, u= { k+1, k+2.
As shown in fig. 2, the main steps of the prediction cooperative control method for the ASV-AUV hybrid cluster robust model provided by the embodiment of the invention are as follows:
step 1, for any autonomous system i e O in the hybrid cluster, acquiring position state information η i and speed state information ζ i of the autonomous system i.
Specifically, if i e S, the autonomous system i is ASV, the position states η i＝[xi,yi,ψi]T,xi、yi and ψ i represent the x-axis position, the y-axis position and the yaw angle of the autonomous system i in the geodetic coordinate system, respectively, and the speed states ζ i＝[ui,vi,ri]T,ui、vi and r i represent the forward speed, the lateral speed and the yaw angle speed in the carrier coordinate system, respectively.
If i is E U, the autonomous system i is AUV, and the position state isxi、yi、zi、Θ i and ψ i represent the x-axis position, y-axis position, z-axis position, roll angle, pitch angle and yaw angle, respectively, of the autonomous system i in the geodetic coordinate system, and speed states ζi＝[ui,vi,wi,pi,qi,ri]T,ui、vi、wi、pi、qi and r i represent the forward speed, lateral speed, vertical speed, roll angle speed, pitch angle speed and yaw angle speed, respectively, in the carrier coordinate system.
Taking 5 asvs+5 AUVs as an example, as shown in fig. 1, the ASV-AUV hybrid cluster of the present invention is shown.
And 2, setting a desired position vector eta id corresponding to the autonomous system i according to the cooperative task, and calculating a virtual control speed zeta ic of the autonomous system i in a kinematic layer by combining the position state information eta i and the speed state information zeta i.
In one embodiment, the actual kinematic model and the nominal kinematic model of the autonomous system i, i.e., the Tube-MPC controller, are built at the kinematic layer for calculating the virtual control speed ζ ic of the autonomous system i.
For example, the actual kinematic model of the autonomous system i may be set as formula (1):
ηi(t+1)＝ηi(t)+Ri(t)Tζi(t)+ξi(t) (1)
Wherein, the For the actual position of autonomous system i at time t +1,For the actual position of autonomous system i at time t,For a constrained set of actual position states, T is the sampling time, R i (T) is the rotation matrix of autonomous system i at time T,For the actual speed of the autonomous system i at time t,As a set of constraints for the actual speed state,For the environmental velocity interference term caused by wind waves, ocean currents and other interference factors,Is the corresponding set of interference items.
The nominal kinematic model may be set to formula (2):
Wherein, the For the nominal position of autonomous system i at time t +1,For the nominal position of autonomous system i at time t,Is the nominal speed of autonomous system i at time t.
The nominal system and the actual system satisfy the relationship described by equation (3):
Wherein, the Tube invariant set, which is the actual kinematic model, represents Minkowski and.
To meet the actual system, the Tube-MPC controller feeds back the speed control quantitySet to formula (4):
Wherein gamma i is a feedback gain matrix, which can be found by the Li-Ka equation, eta i and Η i (t) respectively,Η i (t) represents the actual position of the autonomous system i at time t,The nominal position of the autonomous system i at time t is shown.
For the nominal kinematics model part, the Tube-MPC controller solves the optimization speed control quantity through the optimization problem described by the formula (5)The optimization problem correspondence constraint is set to expression (6).
Wherein, the
Where s represents the predicted time step, N p is the predicted time domain, N c is the control time domain,For the nominal speed of the autonomous system i at time t, the predicted time step s, L i (s|t) is the phase cost of the autonomous system i at time t,For the nominal position of the autonomous system i at time t predicted time step s, η id (s|t) is the desired position of the autonomous system i at time t at time step s, Q i1 is the weight matrix of the position tracking error, Q i2 is the weight matrix of the terminal position tracking error, R i1 is the weight matrix of the speed control quantity, N i(Np |t) is the terminal cost of the autonomous system i at time t predicted time step N p,For the nominal position of the autonomous system i at time t predicted at time step N p, η id(Np |t) is the desired position of the autonomous system i at time t at time step N p.
Wherein, the For the nominal position of the time step s+1 predicted by the autonomous system i at the time t, R i (s|t) is the rotation matrix of the time step s predicted by the autonomous system i at the time t; For the nominal speed of autonomous system i at time t, Represents a difference of Pontryagin in terms of the number of the samples,For a Tube invariant set of an actual kinematic model, y i is a feedback gain matrix, Λ i is a terminal constraint set of a position state, η i(s|t)、ηj (s|t) is an actual position of an autonomous system i and an autonomous system j at a time t predicted by a time step s respectively, η ijs is a safe distance limit between ASVs, and η ijU is a safe distance limit between AUVs.
In particular, if i e U, the autonomous system i is AUV, and to avoid conflict with ASV operation, a constraint described by the following formula (7) is added to the depth of AUV:
zi∈Zlim (7)
where Z lim is the depth constraint set of autonomous system i.
The virtual speed control amount ζ ic corresponding to the final Tube-MPC controller is expressed as:
And 3, estimating disturbance d i by using a disturbance observer at a dynamics layer according to the virtual control speed ζ ic, and calculating a control input tau i of the autonomous system i by using a robust model predictive controller.
In one embodiment, the dynamics model corresponding to the autonomous system i is set to formula (8):
ζi(t+1)＝ζi(t)+g(ζi(t),τi(t))+di(t) (8)
Where g (ζ i(t),τi (t)) is the nominal part of the dynamics model of the autonomous system i, τ i (t) is the control input of the autonomous system i, including control forces and control moments, and d i (t) is the disturbance caused by wind, ocean currents, waves, modeling uncertainties, etc.
Taking a specific AUV dynamics model as an example, the method is shown in the formula (9):
Wherein, the Representing acceleration, M i representing the inertial matrix, C i(ζi) representing the coriolis and centrifugal force matrices, D i(ζi) representing the hydrodynamic damping matrix, τ i representing the control input, τ id representing the unknown external disturbance over time.
The matrix is decomposed as described above and, Representing the nominal part of the inertia matrix, the coriolis and centrifugal force matrices, respectively, the hydrodynamic damping matrix, Δm i、ΔCi(ζi)、ΔDi(ζi) representing the uncertainty part of the inertia matrix, the coriolis and centrifugal force matrices, respectively, the hydrodynamic damping matrix.
The original kinetic model can be described as formula (10):
In another embodiment, the raw kinetic model can also be described as formula (11):
wherein g (ζ i,τi) is g (ζ i(t),τi (t)) representing a nominal part of the kinetic model, which is represented by formula (12), and the disturbance d i is represented by formula (13):
the interference d i can be estimated by an interference observer, and the estimated interference is noted as
There are many types of disturbance observers, for example extended state observer (Extended State Observer, ESO), estimates of speedEstimated value of interferenceRepresented by formulas (14), (15), respectively:
Where γ i1 and γ i2 are both gain matrices of the observer.
In one embodiment, the optimization problem of the robust model predictive controller is set to equation (16-1), and the constraint corresponding to equation (16-1) is described as equation (17-1):
Wherein N p is a prediction time domain, N c is a control time domain, Q iζ is a weight matrix of a speed tracking error, and R i2 is a weight matrix of a control input amount.
In another embodiment, the optimization problem of the robust model predictive controller is set as equation (16-2), and the constraint corresponding to equation (16-2) is described as equation (17-2):
Wherein J i is an objective function to be optimized, τ i is τ i (t) which represents control input of an autonomous system i at a time t, N p is a prediction time domain, ζ i is ζ i (t) which represents actual speed of the autonomous system i at the time t, ζ i (s|t) is speed of the autonomous system i at the time t which predicts time step s, ζ ic (s|t) represents virtual control speed of the autonomous system i at the time t which predicts time step s, Q iζ is a weight matrix of speed tracking error, N c is a control time domain, R i2 is a weight matrix of control input quantity, τ i (s|t) is control input of the autonomous system i at the time t which predicts time step s, ζ i (s+ 1|t) is speed of the autonomous system i at the time t which predicts time step s+1, and g (ζ i(s|t),τi (s|t)) is a dynamic model nominal part of the autonomous system i at the time t which predicts time step s; Predicting the interference estimated by the time step s at the moment t for the autonomous system i; τ i (s|t) is the control input of the autonomous system i for predicting the time step s at the time t; τ i (s+ 1|t) represents the control input of the autonomous system predicting the time step s+1 at time t; The method comprises the steps of controlling a constraint set of increment, predicting the speed of a time step N p at a moment t by using a zeta i(Np |t as an autonomous system i, using a terminal constraint set of a speed state by using a psi i, and using H (zeta i(s|t),τi (s|t)) as a function corresponding to a contraction constraint for guaranteeing the closed loop stability of the system.
Preferably, an alternative to the shrinkage constraint is to design the inequality constraint (18) based on the lyapunov method and the auxiliary control amount as follows:
wherein V i represents a speed-dependent Lyapunov function, Nonlinear auxiliary control quantity designed for the Lyapunov method.
Specifically, the nonlinear auxiliary control quantity is designed based on a Lyapunov function, and the stability can be demonstrated by the Lyapunov method. Taking nonlinear back-step control as an example, let e i＝ζi-ζic represent a velocity tracking error according to the AUV dynamics model described by the above formula (11), the following lisapunov function (19) is defined:
To derive it from
Thus, a nonlinear backstepping control described by the following equation (20) can be designed:
where K iζ is the gain matrix.
Based on the optimization problem (16) and constraint (17) described above, the control input τ i to the autonomous system i can be solved.
And 4, determining the execution control quantity corresponding to the autonomous system i through the propeller model described in the formula (21).
τi＝Kih(λi) (21)
Where K i is the propulsion system conversion factor, λ i is the execution control amount, and h (λ i) is the correlation function of the execution control amount.
Motion control of autonomous systems ultimately needs to be achieved depending on the particular propulsion system. The present invention thus determines the corresponding execution control amount based on the propeller model.
Specifically, taking under-actuated ASV and AUV as examples, the propeller of the system mainly comprises a propeller and a steering engine, and the corresponding propeller thrust and steering engine torque are obtained by the components of the control input τ i. For ASV, the control quantity of the propeller execution is the rotating speed n i, and the control quantity of the steering engine execution is the horizontal rudder angle delta si.
The thrust model of the propeller is of formula (22):
Wherein, the For the thrust of the propeller,For controlling the component of the input τ i in the direction of the system forward speed u i, K iT is the thrust coefficient.
The horizontal moment model of the steering engine is represented by formula (23):
Wherein, the Is the horizontal moment of the steering engine,For controlling the horizontal component of the input tau i,For a dimensional horizontal rudder angle coefficient, u i is the forward speed of the autonomous system i.
For the AUV, the propeller execution control quantity is the rotating speed n i, and the steering engine execution control quantity is the horizontal rudder angle delta si and the vertical rudder angle delta ri.
The propeller thrust model and steering engine horizontal moment model are similar to ASV, and the steering engine vertical moment model is (24):
Wherein, the Is the vertical moment of the steering engine,For controlling the component of the input τ i in the vertical direction,Is a factor of vertical rudder angle coefficient.
The execution control amount of the system, namely the propeller rotating speed n i, the horizontal rudder angle delta si and the vertical rudder angle delta ri, can be determined based on the propeller model.
Other full-drive or overdrive type ASV and AUV systems may construct a propeller model in a similar manner to determine the corresponding amount of execution control.
In order to realize the above method, the present patent further provides an ASV-AUV hybrid cluster robust model prediction cooperative control system, as shown in fig. 3 and 4, which includes an ASV/AUV entity, a water surface and underwater communication device, a status information sensor, a kinematic control unit, a disturbance observer unit, a dynamics control unit, a propeller unit, and an execution and driving mechanism.
The system comprises a water surface and underwater communication device, a state information sensor, a kinematics control unit, a position state information processor, a disturbance observer unit, a dynamics control unit and a driver control unit, wherein the water surface and underwater communication device can adopt radio communication devices, underwater sound communication machines, buoys and other available communication devices for communication between ASVs and AUVs in a mixed cluster, the state information sensor can adopt inertial navigation devices, attitude sensors, doppler velocimeters, depth meters and other available sensor devices for acquiring state information such as positions and speeds of the ASVs and the AUVs, the kinematics control unit is used for setting a desired position vector eta id corresponding to the autonomous system i according to a cooperative task, combining the position state information eta i and the speed state information zeta i, calculating a virtual control speed zeta ic of the autonomous system i at a kinematics layer, the disturbance observer unit is used for estimating disturbance of the ASVs and the AUVs, the dynamics control unit is used for calculating a control input tau i of the autonomous system i through a robust model prediction controller at a dynamics layer according to the virtual control speed zeta ic, the thruster unit is used for calculating an actual execution control quantity lambda AU i of the propulsion system at an execution layer through the thruster model according to the control input tau i, and outputting the actual execution control quantity lambda AU i to a specific command and an execution command to an execution mechanism and a driving mechanism of the ASVs and a driving mechanism according to the execution command and a driving mechanism.
In one embodiment, the optimization problem of the robust model predictive controller in the dynamics control unit is set as formula (16-1), the constraint corresponding to formula (16-1) is described as formula (17-1), or the optimization problem of the robust model predictive controller is set as formula (16-2), and the constraint corresponding to formula (16-2) is described as formula (17-2).
In one embodiment, the virtual control speed ζ ic is calculated by a Tube-MPC controller described by equation (5) in the kinematic control unit, In order to obtain the optimized speed control quantity through the solution of the optimization problem of the Tube-MPC controller, the corresponding constraint condition of the optimization problem is set as a formula (6),Is the feedback speed control quantity of the autonomous system i.
In the above embodiments:
1. In the technical solution, other types of disturbance observers than the Extended State Observer (ESO) mentioned in the example are equally applicable.
2. In constructing a robust model predictive controller, other constraints that can deduce the stability of the system can be used as contraction constraints in addition to the inequality constraint based on the lyapunov method.
3. In constructing the inequality constraint based on the Lyapunov method, besides using nonlinear backstepping control as the auxiliary control quantity, other nonlinear control strategies designed based on the Lyapunov method can also be used as effective auxiliary control quantity.
Unlike the prior art, there are three aspects:
1. the invention adopts a cascade control structure, the kinematic layer is responsible for calculating the virtual control speed according to the expected cooperative target, and the dynamic layer calculates dynamic control input according to the virtual control speed, so that the control precision can be improved, and the robustness of the system can be enhanced. Unlike conventional technology, the method of treating the kinematic model as ideal model (without considering the interference of environmental speed), the invention constructs the actual kinematic model of ASV and AUV by considering the interference factors of wind wave, ocean current and other speed, treats the ideal model as nominal kinematic model, and calculates the virtual control speed by the Tube-MPC controller, so that ASV and AUV can maintain the expected position under the speed interference, and the robustness of the hybrid cluster system in the kinematic control layer is effectively improved.
2. In the dynamic control layer, the invention combines the disturbance observer with the robust model predictive control method, and utilizes the robust model predictive controller to calculate dynamic control input on the basis of disturbance estimation. This combination significantly enhances the robustness and stability of the hybrid cluster system at the dynamics control level.
3. The invention considers the propeller model, determines the execution control quantity of the autonomous system execution layer, and is more close to the requirements of practical engineering application.
Finally, it should be pointed out that the above embodiments are only intended to illustrate the technical solution of the invention, not to limit it. It will be understood by those skilled in the art that modifications may be made to the technical solutions described in the foregoing embodiments or equivalents may be substituted for some of the technical features thereof, and that these modifications or substitutions may be made without departing from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims (8)

1.一种混合集群鲁棒模型预测协同控制方法，其特征在于，包括：1. A kind A hybrid cluster robust model predictive cooperative control method, characterized by comprising: 步骤1，获取混合集群中任意自主系统的位置状态信息和速度状态信息，自主系统分为和；Step 1: Obtain any autonomous system in the hybrid cluster Location status information and speed status information Autonomous systems are divided into and ; 步骤2，依据协同任务设定自主系统对应的期望位置向量，结合位置状态信息和速度状态信息，在运动学层计算自主系统的虚拟控制速度；Step 2: Set up the autonomous system based on the collaborative task. The corresponding expected position vector Combined with location status information and speed status information Computational autonomous systems at the kinematic level Virtual control speed ; 步骤3，根据虚拟控制速度，在动力学层采用干扰观测器估计干扰，通过鲁棒模型预测控制器计算自主系统的控制输入；Step 3, based on virtual control speed At the dynamics layer, an interference observer is used to estimate the interference. The autonomous system is calculated using a robust model predictive controller. control input ; 步骤4，根据控制输入，在执行层采用推进器模型计算出推进系统的实际执行控制量；Step 4, according to the control input At the execution layer, the actual control quantities of the propulsion system are calculated using a thruster model. ; 步骤3中鲁棒模型预测控制器的优化问题设置为式（16-1），式（16-1）对应的约束条件描述为式（17-1）；或者鲁棒模型预测控制器的优化问题设置为式（16-2），式（16-2）对应的约束条件描述为式（17-2）；In step 3, the optimization problem of the robust model predictive controller is set as Equation (16-1), and the constraint condition corresponding to Equation (16-1) is described as Equation (17-1); or the optimization problem of the robust model predictive controller is set as Equation (16-2), and the constraint condition corresponding to Equation (16-2) is described as Equation (17-2). （16-1） (16-1) （17-1） (17-1) （16-2） (16-2) （17-2） (17-2) 其中，为，表示自主系统在时刻的旋转矩阵；为，表示自主系统在时刻的控制输入；为预测时域；为，表示自主系统在时刻的实际速度；为自主系统在时刻预测时间步的速度；表示自主系统在时刻预测时间步的虚拟控制速度；为速度跟踪误差的权重矩阵；为控制时域；为控制输入量的权重矩阵；为自主系统在时刻预测时间步的控制输入；为自主系统在时刻预测时间步的速度；为自主系统在时刻预测时间步的动力学模型标称部分；为自主系统在时刻预测时间步估计的干扰；为实际速度状态的约束集合；为自主系统在时刻预测时间步的控制输入；为控制输入的约束集合；表示自主系统在时刻预测时间步的控制输入；为控制增量的约束集合；为自主系统在时刻预测时间步的速度；为速度状态的终端约束集合；为收缩约束对应的函数。in, for This indicates an autonomous system. At any moment rotation matrix; for This indicates an autonomous system. At any moment Control input; For prediction in the time domain; for This indicates an autonomous system. At any moment The actual speed; For autonomous systems At any moment Predicting time steps speed; Indicates autonomous system At any moment Predicting time steps Virtual control speed; This is the weighting matrix for the speed tracking error; To control the time domain; The weight matrix is used to control the input quantities; For autonomous systems At any moment Predicting time steps Control input; For autonomous systems At any moment Predicting time steps speed; For autonomous systems At any moment Predicting time steps The nominal part of the dynamic model; For autonomous systems At any moment Predicting time steps Estimated interference; The set of constraints for the actual velocity state; For autonomous systems At any moment Predicting time steps Control input; A set of constraints for controlling the input; Indicates that the autonomous system is at time Predicting time steps Control input; The set of constraints to control the increment; For autonomous systems At any moment Predicting time steps speed; The set of terminal constraints for velocity states; This is the function corresponding to the contraction constraint. 2.如权利要求1所述的混合集群鲁棒模型预测协同控制方法，其特征在于，收缩约束基于李雅普诺夫方法和辅助控制量设计如下不等式约束（18）：2. As described in claim 1 The hybrid cluster robust model predictive cooperative control method is characterized by the following inequality constraint (18) designed based on the Lyapunov method and auxiliary control quantity: （18） (18) 其中，代表与速度相关的李雅普诺夫函数，其设置为式（19）；in, The Lyapunov function, which is related to velocity, is set as equation (19). （19） (19) 其中，代表自主系统在时刻的速度跟踪误差，为，为自主系统在时刻的虚拟控制速度；in, Represents autonomous system At any moment Speed tracking error, for For autonomous systems At any moment Virtual control speed; 为，代表基于李雅普诺夫方法设计的非线性辅助控制量，其为式（20）； for , representing the nonlinear auxiliary control quantity designed based on the Lyapunov method, is given by equation (20). （20） (20) 其中，、、分别代表惯性矩阵、科里奥利力和离心力矩阵、流体动力学阻尼矩阵的标称部分，为由干扰观测器估计的干扰，为自主系统的虚拟控制加速度，为增益矩阵。in, , , These represent the nominal portions of the inertia matrix, the Coriolis force and centrifugal force matrices, and the fluid dynamics damping matrix, respectively. The interference estimated by the interference observer, For autonomous systems Virtual control acceleration, This is the gain matrix. 3.如权利要求1-2中任一项所述的混合集群鲁棒模型预测协同控制方法，其特征在于，步骤2中，虚拟控制速度通过式（5）描述的控制器计算获得，，为通过控制器的优化问题求解得到的优化速度控制量，优化问题对应约束条件设置为式（6），为自主系统的实际位置和标称位置之间的差异：3. The method of claim 1-2 The hybrid cluster robust model predictive cooperative control method is characterized in that, in step 2, the virtual control speed... Described by equation (5) The controller calculates and obtains this information. , To pass The optimized speed control quantity is obtained by solving the optimization problem of the controller, and the corresponding constraint condition of the optimization problem is set as Equation (6). For autonomous systems The difference between the actual location and the nominal location: （5） (5) （6） (6) 其中，为自主系统在时刻预测时间步的标称速度，为自主系统在时刻预测的时间步的标称位置，为自主系统在时刻预测时间步的阶段成本，，为自主系统在时刻在时间步的期望位置，为位置跟踪误差的权重矩阵，为速度控制量的权重矩阵，为自主系统在时刻预测时间步的终端成本，，为自主系统在时刻预测的时间步的标称位置，为自主系统在时刻在时间步的期望位置，为终端位置跟踪误差的权重矩阵；为自主系统在时刻的实际位置，为自主系统在时刻的标称位置，为自主系统在时刻的标称速度，为采样时间，为实际位置状态的约束集合，代表差，为实际运动学模型的不变集，为反馈增益矩阵，为位置状态的终端约束集合，、分别为自主系统和自主系统在时刻预测时间步的实际位置，为相互间的安全距离限制，为相互间的安全距离限制，若，则自主系统为，若，则自主系统为。in, For autonomous systems At any moment Predicting time steps The nominal speed, For autonomous systems At any moment Predicted time steps The nominal location, For autonomous systems At any moment Predicting time steps Stage costs, , For autonomous systems At any moment At time step The expected position This is the weight matrix for the position tracking error. This is the weight matrix for the speed control quantity. For autonomous systems At any moment Predicting time steps terminal cost, , For autonomous systems At any moment Predicted time steps The nominal location, For autonomous systems At any moment At time step The expected position This is the weight matrix for the terminal position tracking error; For autonomous systems At any moment The actual location, For autonomous systems At any moment The nominal location, For autonomous systems At any moment The nominal speed, Sampling time, The set of constraints for the actual position state. represent Difference, For actual kinematic models Invariant set For the feedback gain matrix, For the set of terminal constraints in position state, , Autonomous systems and autonomous systems At any moment Predicting time steps The actual location, for Mutual safety distance restrictions, for Mutual safety distance restrictions, if Then autonomous system for ,like Then autonomous system for . 4.如权利要求3所述的混合集群鲁棒模型预测协同控制方法，其特征在于，当时，对的深度添加如下式（7）描述的约束：4. As described in claim 3 The hybrid cluster robust model predictive cooperative control method is characterized in that, when At that time, The depth is subject to the constraint described in equation (7) below: （7） (7) 其中，为自主系统的深度约束集合。in, For autonomous systems The set of depth constraints. 5.一种混合集群鲁棒模型预测协同控制系统，其特征在于，包括混合集群、水面与水下通信设备、状态信息传感器、运动学控制单元、扰动观测器单元、动力学控制单元、推进器单元、执行与驱动机构；5. A kind A hybrid cluster robust model predictive cooperative control system is characterized by comprising a hybrid cluster, surface and underwater communication equipment, state information sensors, kinematic control unit, disturbance observer unit, dynamic control unit, thruster unit, and actuation and drive mechanism; 其中，水面与水下通信设备用于混合集群中的、相互之间通信；Among them, surface and underwater communication equipment is used in hybrid clusters. , Communication between each other; 状态信息传感器用于获取自主系统的位置状态信息和速度状态信息；Status information sensors are used to acquire information about autonomous systems. Location status information and speed status information ; 运动学控制单元用于依据协同任务设定自主系统对应的期望位置向量，结合位置状态信息和速度状态信息，在运动学层计算自主系统的虚拟控制速度；The kinematic control unit is used to set up the autonomous system according to the cooperative task. The corresponding expected position vector Combined with location status information and speed status information Computational autonomous systems at the kinematic level Virtual control speed ; 扰动观测器单元用于估计、所受扰动；The perturbation observer unit is used for estimation , The disturbance received; 动力学控制单元用于根据虚拟控制速度，在动力学层通过鲁棒模型预测控制器计算自主系统的控制输入；推进器单元用于构建推进器模型，用于根据控制输入，在执行层采用推进器模型计算出，并输出指令给具体的执行与驱动机构；The dynamic control unit is used to control the speed according to the virtual control speed. At the dynamics layer, a robust model predicts the controller to calculate the autonomous system. control input The thruster unit is used to construct the thruster model, which is used to determine the thruster based on the control input. At the execution layer, the thruster model is used to calculate... It also outputs instructions to the specific execution and driving mechanisms; 执行与驱动机构依据得到的指令驱动与运动；The execution and drive mechanism is driven according to the received instructions. and sports; 动力学控制单元中鲁棒模型预测控制器的优化问题设置为式（16-1），式（16-1）对应的约束条件描述为式（17-1）；或者，鲁棒模型预测控制器的优化问题设置为式（16-2），式（16-2）对应的约束条件描述为式（17-2）；The optimization problem of the robust model predictive controller in the dynamic control unit is set as Equation (16-1), and the constraint condition corresponding to Equation (16-1) is described as Equation (17-1); or, the optimization problem of the robust model predictive controller is set as Equation (16-2), and the constraint condition corresponding to Equation (16-2) is described as Equation (17-2). （16-1） (16-1) （17-1） (17-1) （16-2） (16-2) （17-2） (17-2) 其中，为，表示自主系统在时刻的旋转矩阵；为，表示自主系统在时刻的控制输入；为预测时域；为，表示自主系统在时刻的实际速度；为自主系统在时刻预测时间步的速度；表示自主系统在时刻预测时间步的虚拟控制速度；为速度跟踪误差的权重矩阵；为控制时域；为控制输入量的权重矩阵；为自主系统在时刻预测时间步的控制输入；为自主系统在时刻预测时间步的速度；为自主系统在时刻预测时间步的动力学模型标称部分；为自主系统在时刻预测时间步估计的干扰；为实际速度状态的约束集合；为自主系统在时刻预测时间步的控制输入；为控制输入的约束集合；表示自主系统在时刻预测时间步的控制输入；为控制增量的约束集合；为自主系统在时刻预测时间步的速度；为速度状态的终端约束集合；为收缩约束对应的函数。in, for This indicates an autonomous system. At any moment rotation matrix; for This indicates an autonomous system. At any moment Control input; For prediction in the time domain; for This indicates an autonomous system. At any moment The actual speed; For autonomous systems At any moment Predicting time steps speed; Indicates autonomous system At any moment Predicting time steps Virtual control speed; This is the weighting matrix for the speed tracking error; To control the time domain; The weight matrix is used to control the input quantities; For autonomous systems At any moment Predicting time steps Control input; For autonomous systems At any moment Predicting time steps speed; For autonomous systems At any moment Predicting time steps The nominal part of the dynamic model; For autonomous systems At any moment Predicting time steps Estimated interference; The set of constraints for the actual velocity state; For autonomous systems At any moment Predicting time steps Control input; A set of constraints for controlling the input; Indicates that the autonomous system is at time Predicting time steps Control input; The set of constraints to control the increment; For autonomous systems At any moment Predicting time steps speed; The set of terminal constraints for velocity states; This is the function corresponding to the contraction constraint. 6.如权利要求5所述的ASV-AUV混合集群鲁棒模型预测协同控制系统，其特征在于，收缩约束基于李雅普诺夫方法和辅助控制量设计如下不等式约束（18）：6. The ASV-AUV hybrid cluster robust model predictive cooperative control system as described in claim 5, characterized in that the contraction constraint is designed based on the Lyapunov method and auxiliary control quantity using the following inequality constraint (18): （18） (18) 其中，代表与速度相关的李雅普诺夫函数，其设置为式（19）；in, The Lyapunov function, which is related to velocity, is set as equation (19). （19） (19) 其中，代表自主系统在时刻的速度跟踪误差，为，为自主系统在时刻的虚拟控制速度；in, Represents autonomous system At any moment Speed tracking error, for For autonomous systems At any moment Virtual control speed; 为基于李雅普诺夫方法设计的非线性辅助控制量，其为式（20）； For the nonlinear auxiliary control quantity designed based on the Lyapunov method, it is given by equation (20). （20） (20) 其中，、、分别代表惯性矩阵、科里奥利力和离心力矩阵、流体动力学阻尼矩阵的标称部分，为由干扰观测器估计的干扰，为自主系统的虚拟控制加速度，为增益矩阵。in, , , These represent the nominal portions of the inertia matrix, the Coriolis force and centrifugal force matrices, and the fluid dynamics damping matrix, respectively. The interference is estimated by the interference observer. For autonomous systems Virtual control acceleration, This is the gain matrix. 7.如权利要求5-6中任一项所述的混合集群鲁棒模型预测协同控制系统，其特征在于，运动学控制单元中，虚拟控制速度通过式（5）描述的控制器计算获得，，为通过控制器的优化问题求解得到的优化速度控制量，优化问题对应约束条件设置为式（6），为自主系统的实际位置和标称位置之间的差异：7. The claim 5-6 A hybrid cluster robust model predictive cooperative control system, characterized in that, in the kinematic control unit, virtual control velocity... Described by equation (5) The controller calculates and obtains this information. , To pass The optimized speed control quantity is obtained by solving the optimization problem of the controller, and the corresponding constraint condition of the optimization problem is set as Equation (6). For autonomous systems The difference between the actual location and the nominal location: （5） (5) （6） (6) 其中，为自主系统在时刻预测时间步的标称速度，为自主系统在时刻预测的时间步的标称位置，为自主系统在时刻预测时间步的阶段成本，，为自主系统在时刻在时间步的期望位置，为位置跟踪误差的权重矩阵，为速度控制量的权重矩阵，为自主系统在时刻预测时间步的终端成本，，为自主系统在时刻预测的时间步的标称位置，为自主系统在时刻在时间步的期望位置，为终端位置跟踪误差的权重矩阵；为自主系统在时刻的实际位置，为自主系统在时刻的标称位置，为自主系统在时刻的标称速度，为采样时间，为实际位置状态的约束集合，代表Pontryagin差，为实际运动学模型的不变集，为反馈增益矩阵，为位置状态的终端约束集合，、分别为自主系统和自主系统在时刻预测时间步的实际位置，为相互间的安全距离限制，为相互间的安全距离限制，若，则自主系统为，若，则自主系统为。in, For autonomous systems At any moment Predicting time steps The nominal speed, For autonomous systems At any moment Predicted time steps The nominal location, For autonomous systems At any moment Predicting time steps Stage costs, , For autonomous systems At any moment At time step The expected position This is the weight matrix for the position tracking error. This is the weight matrix for the speed control quantity. For autonomous systems At any moment Predicting time steps terminal cost, , For autonomous systems At any moment Predicted time steps The nominal location, For autonomous systems At any moment At time step The expected position This is the weight matrix for the terminal position tracking error; For autonomous systems At any moment The actual location, For autonomous systems At any moment The nominal location, For autonomous systems At any moment The nominal speed, Sampling time, The set of constraints for the actual position state. This represents poor performance in Pontryagin. For actual kinematic models Invariant set For the feedback gain matrix, For the set of terminal constraints in position state, , Autonomous systems and autonomous systems At any moment Predicting time steps The actual location, for Mutual safety distance restrictions, for Mutual safety distance restrictions, if Then autonomous system for ,like Then autonomous system for . 8.如权利要求7所述的混合集群鲁棒模型预测协同控制系统，其特征在于，当时，对的深度添加如下式（7）描述的约束：8. As described in claim 7 Hybrid cluster robust model predictive cooperative control system, characterized in that, when At that time, The depth is subject to the constraint described in equation (7) below: （7） (7) 其中，为自主系统的深度约束集合。in, For autonomous systems The set of depth constraints.
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