Non-convex distance constraint convexification method and system for cooperative control of unmanned transport equipment

Abstract

This application discloses a method and system for transforming non-convex distance constraints into convex constraints in the cooperative control of unmanned transport equipment, belonging to the field of unmanned transport equipment control technology. The method includes: linearizing the unmanned transport equipment model by constructing a nonlinear model of the unmanned transport equipment in a formation and performing Jacobian linearization on the constructed nonlinear model; constructing non-convex distance constraints by establishing non-convex communication maintenance constraints and collision avoidance constraints based on the position, communication distance, and safety distance of each unmanned transport equipment; and transforming the non-convex distance constraints into convex constraints by using a non-convex constraint convexification algorithm to convert the established non-convex communication maintenance constraints and collision avoidance constraints into convex constraints. This application's method of transforming non-convex distance constraints into convex constraints in the cooperative motion control problem of unmanned transport equipment is beneficial for finding the globally optimal solution of control input that simultaneously satisfies the communication maintenance and collision avoidance requirements, thereby enabling the simultaneous realization of the communication maintenance and collision avoidance requirements during the cooperative motion process of unmanned transport equipment.

Description

Technical Field

[0001] This application belongs to the field of unmanned transport equipment control technology, specifically relating to a non-convex distance constraint convexification method and system for collaborative control of unmanned transport equipment. Background Technology

[0002] When unmanned vehicles such as autonomous vehicles, drones, and UUVs (unmanned underwater vehicles) perform complex tasks, coordinated motion control plays a crucial role, and this motion control must meet distance constraints. The communication distance between unmanned vehicles is limited. If the distance exceeds this communication distance, unmanned vehicles will be unable to obtain status information from other unmanned vehicles, thus failing to maintain the pre-set desired formation. Therefore, the distance between unmanned vehicles must be controlled within the communication distance, i.e., the communication maintenance requirement. Furthermore, if the distance between unmanned vehicles is too small, collisions will occur, damaging their structure and function. Therefore, the distance between unmanned vehicles must be controlled above a safe distance, i.e., the collision avoidance requirement.

[0003] In summary, it is essential to maintain the distance between various pieces of equipment in unmanned transport vehicle coordination within communication range and above safe distance. In other words, the formation movement control of unmanned transport vehicles must simultaneously meet both communication maintenance and collision avoidance requirements.

[0004] Current technologies cannot simultaneously meet the communication maintenance and collision avoidance requirements during the coordinated movement of unmanned vehicles. Existing methods for addressing this problem mainly include the potential field method and the constraint method. With the potential field method, when the speed of the unmanned vehicles is relatively high, their motion becomes unstable, affecting the formation's motion control performance. For the constraint method, existing methods use the positions of the unmanned vehicles to construct non-convex constraints on distance, making the problem of finding control inputs that satisfy these constraints a non-convex optimization problem. Generally, non-convex optimization problems do not have a global optimum, and it is even difficult to find a local optimum; therefore, it is difficult to find a globally optimal solution for control inputs that satisfy non-convex constraints.

[0005] Existing technology 1:

[0006] AUV (Autonomous Underwater Vehicle) is a branch of UUV. To achieve consistent control of AUV formations, existing technology 1 (Li, S., and Wang X. "Finite-time consensus and collision avoidance control algorithms for multiple AUVs." Automatica 49.11(2013):3359-3367) divides the area where each AUV is located into a communication zone, a holding zone, a collision zone, and a collision avoidance zone. It also uses the potential field method to design the communication holding potential function and the collision avoidance potential function to control the distance between AUVs within the communication distance and above the safe distance.

[0007] The drawback of the existing technology is that it uses the potential field method. When the speed of the AUV is high, the motion of the AUV will be extremely unstable, which will seriously affect the motion control performance of the AUV.

[0008] Existing technology 2:

[0009] Existing technology 2 (C. Liu, Q. Hu, and T. Sun. "Distributed formation control of underactuated ships with connectivity preservation and collision avoidance." Ocean Engineering 263) fully utilizes the advantage of nonlinear model predictive control in handling constraints, transforming the communication preservation and collision avoidance requirements in the USV (unmanned surface vessel) formation tracking control process into an optimization problem with communication preservation constraints and collision avoidance constraints, so as to control the distance between each USV within the communication distance and above the safe distance.

[0010] The drawback of the existing technology 2 is that it uses a constraint method. The communication maintenance constraint and collision avoidance constraint are non-convex distance constraints constructed by the USV position, which makes it impossible to solve for the global optimal solution or local optimal solution of the control input that meets the requirements, thus affecting the tracking control performance of the USV formation. Summary of the Invention

[0011] The purpose of this application is to provide a method and system for transforming non-convex distance constraints into convex constraints for the cooperative control of unmanned transport equipment. This method transforms the non-convex constraints constructed based on the position, communication distance, and safety distance of the unmanned transport equipment during formation movement to meet the two major requirements of communication maintenance and collision avoidance into convex constraints. This provides convenience for solving the global optimal solution of the control input that meets these two requirements, thereby solving at least one of the technical problems involved in the background art.

[0012] To solve the above-mentioned technical problems, this application is implemented as follows:

[0013] This application provides a non-convex distance constraint convexification method for cooperative control of unmanned transport equipment, including the following steps:

[0014] Step S1: Linearization of unmanned transport equipment model. Construct a nonlinear model of unmanned transport equipment in the unmanned transport equipment formation, and perform Jacobi linearization on the constructed nonlinear model.

[0015] Step S2: Constructing non-convex distance constraints. Based on the position, communication distance, and safety distance of each unmanned transport vehicle, establish non-convex communication maintenance constraints and collision avoidance constraints.

[0016] Step S3: Convexify non-convex distance constraints. Use a region matching algorithm to transform the established non-convex communication preservation constraints and collision avoidance constraints into convex constraints.

[0017] In step S1, the nonlinear model is expressed as:

[0018]

[0019] In the formula, x i (t) represents the state of the i-th unmanned transport vehicle, τ i (t) is the control input, A i (t) and B i (t) is the coefficient matrix.

[0020] As a limitation of this invention, step S1, which involves Jacobi linearization of the constructed nonlinear model, specifically includes:

[0021] definition Assumption The equilibrium point is (x i (t0),τ i (t0)), then

[0022] Equation (1) is linearized using Jacobi linearization, as shown in the following equation:

[0023]

[0024] In the formula, And A′ i and B′ i It is a constant matrix.

[0025] As a limitation of the present invention, in step S2, the non-convex communication maintenance constraint and collision avoidance constraint are expressed by the following formula:

[0026] ||F(x i (t)-x j(t))||2≤d cp (3)

[0027] ||F(x i (t)-x j (t))||2≥d ca (4)

[0028] In the formula, x i (t) and x j (t) represents the states of unmanned transport vehicles numbered i and j in the unmanned transport vehicle formation, respectively, and d cp With d ca These represent the communication distance and the security distance, respectively, and F is the coefficient matrix.

[0029] As a limitation of this invention, in step S3, a non-convex constraint convexification algorithm is used to transform the established non-convex communication preservation constraints and collision avoidance constraints into convex constraints, specifically including:

[0030] by and They represent x respectively i (t) and x j The nominal value of (t) is then and Represented as:

[0031]

[0032]

[0033] definition Then formula (3) can be approximately described by the convex communication holding constraint shown in formula (6) below:

[0034]

[0035] Distributed model predictive control is employed, with convex communication preserving constraint representation within the prediction time domain N:

[0036]

[0037]

[0038]

[0039] in, It is the control input sequence for predicting the i-th unmanned transport vehicle within the time domain N, and The possible values ​​are as follows:

[0040]

[0041] The convex collision avoidance constraint in the prediction time domain N is expressed as:

[0042]

[0043]

[0044] This application also provides a non-convex distance constraint convexification system for implementing the method of cooperative control of unmanned transport equipment, comprising:

[0045] The unmanned transport equipment model linearization module is used to construct a nonlinear model of the unmanned transport equipment in the unmanned transport equipment formation and to perform Jacobian linearization on the constructed nonlinear model.

[0046] A non-convex distance constraint construction module is used to establish non-convex communication maintenance constraints and collision avoidance constraints based on the position, communication distance, and safety distance of each unmanned transport vehicle; and

[0047] The non-convex distance constraint convexification module is used to transform the established non-convex communication preservation constraints and collision avoidance constraints into convex constraints using a non-convex constraint convexification algorithm.

[0048] This application proposes a method to transform non-convex distance constraints into convex constraints in the cooperative motion control problem of unmanned transport equipment. This method is beneficial for finding the globally optimal control input solution that allows the distances between each piece of equipment in the unmanned transport equipment formation to simultaneously meet the communication maintenance and collision avoidance requirements. Thus, the communication maintenance and collision avoidance requirements during the cooperative motion of unmanned transport equipment can be achieved simultaneously. Attached Figure Description

[0049] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort, wherein:

[0050] Figure 1 A flowchart illustrating the non-convex distance constraint convexification method for collaborative control of unmanned transport equipment provided in this application embodiment;

[0051] Figure 2 This is an overall framework diagram of the convexification system for the non-convex distance constraint of UUV provided in the embodiments of this application.

[0052] In the diagram, 1 is the unmanned transport equipment model linearization module; 2 is the non-convex distance constraint construction module; and 3 is the non-convex distance constraint convexification module. Detailed Implementation

[0053] Please see Figure 1As shown, the unmanned transport vehicle in this embodiment of the invention is a UUV, and a non-convex distance constraint convexification method for UUV motion control problem is provided, including the following steps:

[0054] Step S1, Linearization of Unmanned Vehicle Model: Assume that the nonlinear model of each UUV in the four-degree-of-freedom UUV formation is the same, and the nonlinear model of the i-th UUV is as follows:

[0055]

[0056] In the formula, x i (t)=[η i (t), ξ i (t)] T This is the state of the i-th UUV, η i (t)=[x i (t), y i (t), z i (t), ψ i (t)] T It is the pose of the i-th UUV, ξ i (t)=[u i (t), v i (t), w i (t), r i (t)] T τ is the velocity of the i-th UUV. i (t) is the control input; A i (t) and B i (t) is the coefficient matrix, and And J i (ψ i (t)), M i C i (ξ i (t)) and D i (ξ i (t) represents the coordinate transformation matrix, inertial matrix, rigid body centrifugal and Coriolis force matrix, and hydrodynamic damping matrix of the i-th UUV from the body coordinate system to the inertial coordinate system.

[0057] definition Assumption The equilibrium point is (x i (t0), τ i (t0)), then Therefore, the linearized form of formula (10) using Jacobi linearization is as follows:

[0058]

[0059] in And A′ i and B′ i It is a constant matrix.

[0060] Step S2, Non-convex distance constraint construction: To ensure communication and safety among UUVs in the UUV formation, non-convex communication maintenance constraints and collision avoidance constraints are established based on the position, communication distance, and safety distance of each UUV, as shown below:

[0061] ||F(x i (t)-x j (t))||2≤d cp (12)

[0062] ||F(x i (t)-x j (t))||2≥d ca (13)

[0063] In the formula, x i (t) and x j (t) represents the states of UUVs numbered i and j in the UUV formation, respectively, and d cp =35m and d ca =1.5m are the communication distance and the safety distance, respectively. F is a coefficient matrix with values ​​of [1,0,0,0,0,0,0,0;0,1,0,0,0,0,0,0;0,0,1,0,0,0,0,0;0,0,0,0,0,0,0;0,0,0,0,0,0,0;0,0,0,0,0,0,0;0,0,0,0,0,0,0;0,0,0,0,0,0,0;0,0,0,0,0,0,0,0;0,0,0,0,0,0,0,0].

[0064] Step S3, Convexification of Non-convex Distance Constraints: In order to facilitate the solution of the global optimal solution of the control input that ensures both communication maintenance and collision avoidance of the UUV formation, the non-convex distance constraints in formulas (12) and (13) are transformed into convex constraints using a non-convex constraint convexification algorithm. The specific steps include the following:

[0065] by and They represent x respectively i (t) and x j The nominal value of (t) is then and It can be represented as:

[0066]

[0067]

[0068] definition Then formula (13) can be approximately described by the convex communication holding constraint shown in formula (15):

[0069]

[0070] Furthermore, when using distributed model predictive control, the convex communication holding constraint in the prediction time domain N=10 can be expressed as:

[0071]

[0072]

[0073]

[0074] in, It is the control input sequence for predicting the i-th UUV within the time domain N=10, and The possible values ​​are as follows:

[0075]

[0076] Similarly, the convex collision avoidance constraint in the time domain N=10 can be expressed as follows:

[0077]

[0078]

[0079] Combined Figure 2 As shown, this application also provides a non-convex distance constraint convexification system for implementing the motion control of unmanned transport equipment using the method described above, including an unmanned transport equipment model linearization module 1, a non-convex distance constraint construction module 2, and a non-convex distance constraint convexification module 3.

[0080] The unmanned transport equipment model linearization module 1 is used to construct a nonlinear model of the unmanned transport equipment in the unmanned transport equipment formation and to perform Jacobian linearization on the constructed nonlinear model.

[0081] The non-convex distance constraint construction module 2 is used to establish non-convex communication maintenance constraints and collision avoidance constraints based on the position, communication distance, and safety distance of each unmanned transport vehicle; and

[0082] The non-convex distance constraint convexification module 3 is used to transform the established non-convex communication preservation constraints and collision avoidance constraints into convex constraints using a non-convex constraint convexification algorithm.

[0083] The implementation methods of the above functional modules can be found in the content on the convexification method of non-convex distance constraints for motion control of unmanned transport equipment, and will not be repeated here.

[0084] This application proposes a method to transform the non-convex distance constraint in the cooperative motion control problem of unmanned transport equipment into a convex constraint. This method is beneficial for finding the globally optimal control input solution that allows the distance between each piece of equipment in the unmanned transport equipment formation to simultaneously meet the communication maintenance and collision avoidance requirements. Thus, the communication maintenance and collision avoidance requirements during the cooperative motion of unmanned transport equipment can be achieved simultaneously.

[0085] It should be noted that, in this document, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Unless otherwise specified, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes that element.

[0086] Furthermore, it should be noted that the scope of the methods and systems in the embodiments of this application is not limited to performing functions in the order shown or discussed, but may also include performing functions in a substantially simultaneous manner or in the reverse order, depending on the functions involved. For example, the described methods may be performed in a different order than described, and various steps may be added, omitted, or combined. In addition, features described with reference to certain examples may be combined in other examples.

[0087] The embodiments of this application have been described above with reference to the accompanying drawings. However, this application is not limited to the specific embodiments described above. The specific embodiments described above are merely illustrative and not restrictive. Those skilled in the art can make many other forms under the guidance of this application without departing from the spirit and scope of the claims, and all of these forms are within the protection scope of this application.

Claims

1. A method for convexifying non-convex distance constraints in the cooperative control of unmanned transport equipment, characterized in that, Includes the following steps: Step S1: Linearization of unmanned transport equipment model. Construct a nonlinear model of unmanned transport equipment in the unmanned transport equipment formation, and perform Jacobi linearization on the constructed nonlinear model. Step S2: Constructing non-convex distance constraints. Based on the position, communication distance, and safety distance of each unmanned transport vehicle, establish non-convex communication maintenance constraints and collision avoidance constraints. Step S3: Convexification of Non-convex Distance Constraints. A non-convex constraint convexification algorithm is used to transform the established non-convex communication preservation constraints and collision avoidance constraints into convex constraints. Specifically, this includes: by and They represent and The nominal value, then and Represented as: definition Then, formula (3) can be approximately described by the convex communication holding constraint shown in formula (6): Distributed model predictive control is employed in the prediction time domain. Convex communication retains constraint representation: in, It is a prediction time domain Inner The control input sequence of an unmanned transport vehicle, and The possible values ​​are as follows: Prediction Time Domain The convex collision avoidance constraint within is represented as: 。 2. The method according to claim 1, characterized in that, In step S1, the nonlinear model is expressed as: In the formula, It is the first The status of an unmanned transport vehicle. It is a control input. and It is a coefficient matrix.

3. The method according to claim 2, characterized in that, In step S1, the constructed nonlinear model is Jacobi linearized, specifically including: definition Assuming The equilibrium point is ,So ; Formula (1) is linearized using Jacobi linearization, as shown in the following equation: In the formula, , ,and and It is a constant matrix.

4. The method according to claim 3, characterized in that, In step S2, the non-convex communication maintenance constraint and collision avoidance constraint are expressed by the following formula: In the formula, and These are the unmanned transport equipment formations, numbered respectively. and The status of unmanned transport equipment and These are communication distance and safe distance. It is a coefficient matrix.

5. A non-convex distance constraint convexification system for implementing the method described in any one of claims 1-4 for cooperative control of unmanned transport equipment, characterized in that, include: The unmanned transport equipment model linearization module is used to construct a nonlinear model of the unmanned transport equipment in the unmanned transport equipment formation and to perform Jacobian linearization on the constructed nonlinear model. A non-convex distance constraint construction module is used to establish non-convex communication maintenance constraints and collision avoidance constraints based on the position, communication distance, and safety distance of each unmanned transport vehicle; and The non-convex distance constraint convexification module is used to transform the established non-convex communication preservation constraints and collision avoidance constraints into convex constraints using a non-convex constraint convexification algorithm.

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