Gradient-dependent heterogeneous mobile robot distributed formation control method

Abstract

The invention belongs to the technical field of formation control, and discloses a gradient-dependent heterogeneous mobile robot distributed formation control method, which comprises the following steps of: establishing a relative kinematics model of an unmanned ground vehicle and an unmanned aerial vehicle by taking the unmanned ground vehicle as a leader and the unmanned aerial vehicle as a follower; based on an airborne camera on the unmanned aerial vehicle, obtaining relative visual kinematics representation of the unmanned ground vehicle characteristics relative to the unmanned aerial vehicle; establishing a comprehensive cost function based on target image information in a neighborhood acquired by an airborne camera, in combination with an expected formation, and in consideration of view field constraint, collision avoidance constraint and formation formation; according to the comprehensive cost function, a gradient-related distributed formation control strategy is designed and used for calculating the linear velocity and the angular velocity required by each unmanned ground vehicle in a neighborhood, and formation of an expected formation is completed; the problem that in the prior art, in the formation process, the reliability and safety of cooperative operation between robots are insufficient is solved, and the stability and safety of robot formation are improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of formation control, and in particular relates to a gradient-dependent distributed formation control method for heterogeneous mobile robots. Background Art

[0002] Heterogeneous multi-robot systems refer to multi-robot systems composed of different types of robots, such as drones and unmanned ground vehicles. These robots have different functions and mission capabilities, and can play their own advantages in different operation scenarios. In these systems, drones usually undertake more flexible aerial tasks, such as environmental monitoring and target recognition, while unmanned vehicles can perform ground operations, such as transportation and patrolling. Due to their complementarity, the collaborative operation of drones and unmanned ground vehicles has shown significant advantages in a variety of complex applications. Therefore, heterogeneous robot systems have gradually become an important means to improve efficiency and complete complex tasks in many fields. Traditional formation control methods, such as leader-follower methods, virtual structure methods, and behavior-based methods, usually rely on global positioning information or efficient communication mechanisms. However, these methods often fail to meet the requirements in environments without external positioning systems, especially in unstructured or unknown environments, where robots can only rely on local sensor data or information shared with other robots for positioning, resulting in limited positioning accuracy and reliability of collaborative operations.

[0003] In order to meet this challenge, image-based visual servoing methods have gradually become an effective solution. By using the camera carried by the robot, visual servoing can directly extract the relative position from the camera image plane, avoiding dependence on an external positioning system. This method obtains the relative position information between robots through real-time image processing, and adjusts the robot motion trajectory based on this information, thereby achieving high-precision formation control and target tracking. Compared with traditional methods, this method is particularly suitable for environments lacking global positioning information, and can show strong adaptability in dynamically changing tasks and environments. However, pure visual servoing still faces some challenges in the actual application of formation control, such as how to overcome the field of view constraints of the on-board camera to achieve visibility connectivity, how to avoid collisions between mobile robots, and how to ensure the stability of the formation morphology; therefore, there are problems of insufficient reliability and safety of collaborative operations between robots in the formation process in the prior art. Summary of the invention

[0004] In view of the deficiencies in the prior art, the purpose of the present invention is to provide a gradient-dependent distributed formation control method for heterogeneous mobile robots, which solves the problem of insufficient reliability and safety of collaborative operations between robots in the formation process in the prior art.

[0005] The purpose of the present invention can be achieved through the following technical solutions:

[0006] A gradient-dependent distributed formation control method for heterogeneous mobile robots comprises the following steps:

[0007] Taking the UGV as the leader and the UAV as the follower, a relative kinematic model of the UGV and the UAV is established;

[0008] Based on the onboard camera of the UAV, the relative visual kinematic representation of the features of the UGV relative to the UAV is obtained;

[0009] Based on the target image information in the neighborhood obtained by the airborne camera, combined with the desired formation, and considering the field of view constraints, collision avoidance constraints and formation formation, a comprehensive cost function is established;

[0010] According to the comprehensive cost function, a gradient-dependent distributed formation control strategy is designed and used to calculate the required linear velocity and angular velocity of each unmanned ground vehicle in the neighborhood to complete the formation of the desired formation.

[0011] The onboard camera is a monocular camera.

[0012] Establishing the relative kinematic model of the unmanned ground vehicle and the unmanned aerial vehicle includes the following steps:

[0013] Assuming that the UAV moves horizontally at a fixed height, the horizontal movement of the UAV and the UGV can be placed in the same two-dimensional plane, and the relative kinematic expression between the UGV and the UAV can be simplified as follows:

[0014]

[0015] Where i = 1, 2, ..., N, represents the position of the i-th UGV relative to the UAV, represents the relative angle between the i-th UGV and the UAV, φ a Indicates the position of the drone in the world coordinate system, x a ,y a Respectively represent the positions of the i-th unmanned ground vehicle and the unmanned aerial vehicle in the world coordinate system;

[0016] Then, by taking the first-order differential of equation (1), we can obtain the relative kinematic model of the unmanned ground vehicle and the unmanned aerial vehicle:

[0017]

[0018] In the formula, are the first-order differentials of the relative position and angle between the i-th unmanned ground vehicle and the UAV, ω a are the angular velocities of the i-th UGV and UAV, ν gi ,νa are the linear velocities of the i-th unmanned ground vehicle and the i-th unmanned aerial vehicle, respectively.

[0019] Based on the onboard camera on the UAV, the relative visual kinematic representation of the features of the UGV relative to the UAV is obtained, which specifically includes the following steps:

[0020] Get the camera parameter A of the onboard camera;

[0021] The conversion relationship between the three-dimensional coordinate representation of the unmanned ground vehicle features in the airborne camera coordinate system and the two-dimensional coordinate representation of the camera image plane is:

[0022]

[0023] In the formula, is the two-dimensional coordinate representation of the unmanned ground vehicle feature in the camera image plane, A is the camera parameter, Represents the three-dimensional coordinate representation of the unmanned ground vehicle features in the onboard camera coordinate system;

[0024] The relative visual kinematics of the UGV feature relative to the UAV can be expressed as:

[0025]

[0026] In the formula, [m i ,n i ] Τ is the two-dimensional coordinate representation of the feature of the i-th unmanned ground vehicle in the camera image plane, f m ,f n Represents the pixel length of the focal length on the m-axis and n-axis, f mn represents the tilt coefficient between the m-axis and the n-axis, represents the position of the principal point of the camera image plane;

[0027] Where H represents the flight altitude of the UAV, and h is the height of the target feature of the unmanned ground vehicle from the ground;

[0028] Taking the first-order differential of equation (4) and substituting equation (2) into it, we can obtain the velocity expression of the unmanned ground vehicle feature in the camera image plane:

[0029]

[0030] In the formula, is the coordinate representation of the feature of the i-th unmanned ground vehicle in the normalized camera image plane.

[0031] Combined with the desired formation, and considering the field of view constraints, collision avoidance constraints and formation formation, a comprehensive cost function is established, which specifically includes the following steps:

[0032] Determine the desired formation and convert the desired formation into indicators on the camera image plane;

[0033] Based on the field of view constraint, design the field of view constraint cost function V i ;

[0034] Based on the collision avoidance constraint, design the collision avoidance constraint cost function A ij ;

[0035] Based on formation formation, design formation cost function F i ;

[0036] Combined with the field of view constraint cost function V i , collision avoidance constraint cost function A ij and formation cost function F i , establish a comprehensive cost function.

[0037] Based on the field of view constraint, design the field of view constraint cost function V i , the specific steps are as follows:

[0038] The constraint condition of the field of view constraint is to ensure that the features of the unmanned ground vehicle are always within the field of view of the UAV’s onboard camera during the formation process, that is, m min <m<m max ,n min <n<n max ;

[0039] Design the field of view constraint cost function V i The requirements are:

[0040] 1) V i is a continuously differentiable convex function;

[0041] 2) When hour,

[0042] 3)

[0043] in, Represented as l i ;

[0044] Based on the field of view constraint cost function V i According to the requirements, the field of view constraint cost function V is designed. i for:

[0045]

[0046] Among them, d<min(m max -m0,n max -n0).

[0047] Based on the collision avoidance constraint, design the collision avoidance constraint cost function Aij , the specific steps are as follows:

[0048] The constraint condition of the collision avoidance constraint is: to ensure that the distance between each unmanned ground vehicle in the formation process is always kept at a safe distance, which is mapped to the camera image plane as

[0049] Among them, l s is the safe pixel distance that each unmanned ground vehicle feature needs to maintain in the camera image plane;

[0050] Design collision avoidance constraint cost function A ij The requirements are:

[0051] 1) A ij is a continuously differentiable convex function;

[0052] 2) When If and only if

[0053] 3)

[0054] Introducing Virtual Guide Points As a dynamic collision avoidance mechanism, virtual guidance points Designed for:

[0055]

[0056] In the formula,

[0057] Then the collision avoidance constraint cost function A ij Designed for:

[0058]

[0059] In the formula,

[0060] Based on formation formation, design formation cost function F i , the specific steps are as follows:

[0061] Design formation cost function F i The requirements are:

[0062] 1) F i is a continuously differentiable convex function;

[0063] 2) When and only when

[0064] 3)

[0065] Based on the design requirements, design the formation cost function F ifor:

[0066]

[0067] In the formula,

[0068] Combined with the field of view constraint cost function V i , collision avoidance constraint cost function A ij and formation cost function F i , establish a comprehensive cost function, the specific steps are as follows:

[0069] Assume that there are N unmanned ground vehicles in the formation mission, and the field of view of the onboard camera is Then the comprehensive cost function is established as:

[0070]

[0071] In the formula, κ v ,κ a ,κ f They are the corresponding correlation coefficients of field of view constraint, collision avoidance constraint and expected formation formation, and all the coefficients are positive.

[0072] According to the comprehensive cost function, a gradient-related distributed formation control strategy is designed and used to calculate the linear velocity and angular velocity required by each unmanned ground vehicle in the neighborhood. The linear velocity and angular velocity of each unmanned ground vehicle in the neighborhood are calculated:

[0073]

[0074] In the formula, sgn(χ) is a sign function, when χ≥0, sgn(χ)=1, otherwise, sgn(χ)=-1.

[0075] Beneficial effects of the present invention:

[0076] During the formation process, the present invention can effectively ensure the field of view constraint and ensure the visibility of the onboard camera's field of view. At the same time, it avoids collisions between unmanned ground vehicles through a collision avoidance cost function, thereby improving the stability and safety of the robot formation and solving the problem of insufficient reliability and safety of collaborative operations between robots in the formation process in the prior art. BRIEF DESCRIPTION OF THE DRAWINGS

[0077] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, for ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0078] Figure 1is a design flow chart of the formation control method of the present invention;

[0079] Figure 2 A schematic diagram of the distribution of unmanned aerial vehicles and unmanned ground vehicles of the present invention;

[0080] Figure 3 It is a schematic diagram of the convergence of the comprehensive cost function of the present invention in simulation;

[0081] Figure 4 It is a schematic diagram of the trajectory projected on the ground during the simulation formation process of the present invention;

[0082] Figure 5 It is a schematic diagram of the three-dimensional trajectory of the present invention in the process of simulating formation;

[0083] Figure 6 A schematic diagram of the position of each unmanned ground vehicle on the camera image plane at the sampling moment during the simulation formation process of the present invention;

[0084] Figure 7 It is a schematic diagram of the convergence process of the position error of the unmanned ground vehicle g1 in the simulation of the present invention;

[0085] Figure 8 It is a schematic diagram of the position error convergence process of the unmanned ground vehicle g2 in the simulation of the present invention;

[0086] Fig. 9 It is a schematic diagram of the position error convergence process of the unmanned ground vehicle g3 in the simulation of the present invention;

[0087] Fig.10 It is a schematic diagram of the position error convergence process of the unmanned ground vehicle g4 in the simulation of the present invention;

[0088] Fig.11 It is a schematic diagram of the image error convergence process of the unmanned ground vehicle g1 in the simulation of the present invention;

[0089] Fig.12 It is a schematic diagram of the image error convergence process of the unmanned ground vehicle g2 in the simulation of the present invention;

[0090] Fig.13 It is a schematic diagram of the image error convergence process of the unmanned ground vehicle g3 in the simulation of the present invention;

[0091] Fig.14 Schematic diagram of the image error convergence process of the unmanned ground vehicle g4 in simulation according to the present invention. DETAILED DESCRIPTION

[0092] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0093] like Figures 1 to 14 As shown, a gradient-dependent distributed formation control method for heterogeneous mobile robots includes the following steps:

[0094] Taking the UGV as the leader and the UAV as the follower, a relative kinematic model of the UGV and the UAV is established;

[0095] Based on the onboard camera of the UAV, the relative visual kinematic representation of the features of the UGV relative to the UAV is obtained;

[0096] Based on the target image information in the neighborhood obtained by the airborne camera, combined with the desired formation, and considering the field of view constraints, collision avoidance constraints and formation formation, a comprehensive cost function is established;

[0097] According to the comprehensive cost function, a gradient-dependent distributed formation control strategy is designed and used to calculate the required linear and angular velocities of each unmanned ground vehicle in the neighborhood to complete the formation of the desired formation.

[0098] Through the above steps, during the formation process, the present invention can effectively ensure the field of view constraint, ensure the visibility of the onboard camera's field of view, and avoid collisions between unmanned ground vehicles through the collision avoidance cost function, thereby improving the stability and safety of the robot formation and solving the problem of insufficient reliability and safety of collaborative operations between robots in the formation process in the prior art.

[0099] The onboard camera uses a monocular camera; since the monocular camera is not only low in cost, but also small in size and light in weight, it is more convenient and flexible to install on the drone. Therefore, the monocular camera is the preferred solution for the onboard camera of this application; at the same time, compared with the multi-camera system, the data processing and calculation of the monocular camera are relatively simple, reducing the demand for hardware resources and computing power.

[0100] Establishing the relative kinematic model of the unmanned ground vehicle and the unmanned aerial vehicle includes the following steps:

[0101] Assuming that the UAV moves horizontally at a fixed height, the horizontal movement of the UAV and the UGV can be placed in the same two-dimensional plane, and the relative kinematic expression between the UGV and the UAV can be simplified as follows:

[0102]

[0103] Where i = 1, 2, ..., N, represents the position of the i-th UGV relative to the UAV, represents the relative angle between the i-th UGV and the UAV, φ a Indicates the position of the drone in the world coordinate system, x a ,y a Respectively represent the positions of the i-th unmanned ground vehicle and the unmanned aerial vehicle in the world coordinate system;

[0104] Then, by taking the first-order differential of equation (1), we can obtain the relative kinematic model of the unmanned ground vehicle and the unmanned aerial vehicle:

[0105]

[0106] In the formula, are the first-order differentials of the relative position and angle between the i-th unmanned ground vehicle and the UAV, ω a are the angular velocities of the i-th unmanned ground vehicle and the UAV, ν a are the linear velocities of the i-th unmanned ground vehicle and the i-th unmanned aerial vehicle, respectively.

[0107] Based on the onboard camera on the UAV, the relative visual kinematic representation of the features of the UGV relative to the UAV is obtained, which specifically includes the following steps:

[0108] Get the camera parameter A of the onboard camera;

[0109] In this application, in the two-dimensional coordinate system of the camera image plane, the m-axis is the horizontal axis of the airborne camera image plane, and the n-axis is the vertical axis of the airborne camera image plane;

[0110] The conversion relationship between the three-dimensional coordinate representation of the unmanned ground vehicle features in the airborne camera coordinate system and the two-dimensional coordinate representation of the camera image plane is:

[0111]

[0112] In the formula, is the two-dimensional coordinate representation of the unmanned ground vehicle feature in the camera image plane, A is the camera parameter, Represents the three-dimensional coordinate representation of the unmanned ground vehicle features in the onboard camera coordinate system;

[0113] The relative visual kinematics of the UGV feature relative to the UAV can be expressed as:

[0114]

[0115] In the formula, [m i ,ni ] Τ is the two-dimensional coordinate representation of the feature of the i-th unmanned ground vehicle in the camera image plane, f m ,f n Represents the pixel length of the focal length on the m-axis and n-axis, f mn represents the tilt coefficient between the m-axis and the n-axis, represents the position of the principal point of the camera image plane;

[0116] Where H represents the flight altitude of the UAV, and h is the height of the target feature of the unmanned ground vehicle from the ground;

[0117] Taking the first-order differential of equation (4) and substituting equation (2) into it, we can obtain the velocity expression of the unmanned ground vehicle feature in the camera image plane:

[0118]

[0119] In the formula, is the coordinate representation of the feature of the i-th unmanned ground vehicle in the normalized camera image plane.

[0120] Combined with the desired formation, and considering the field of view constraints, collision avoidance constraints and formation formation, a comprehensive cost function is established, which specifically includes the following steps:

[0121] Determine the desired formation and convert the desired formation into indicators on the camera image plane;

[0122] Based on the field of view constraint, design the field of view constraint cost function V i ;

[0123] Based on the collision avoidance constraint, design the collision avoidance constraint cost function A ij ;

[0124] Based on formation formation, design formation cost function F i ;

[0125] Combined with the field of view constraint cost function V i , collision avoidance constraint cost function A ij and formation cost function F i , establish a comprehensive cost function.

[0126] Based on the field of view constraint, design the field of view constraint cost function V i , the specific steps are as follows:

[0127] The constraint condition of the field of view constraint is to ensure that the features of the unmanned ground vehicle are always within the field of view of the UAV’s onboard camera during the formation process, that is, m min <m<m max ,n min <n<n max ;

[0128] Design the field of view constraint cost function V i The requirements are:

[0129] 1) V i is a continuously differentiable convex function;

[0130] 2) When hour,

[0131] 3)

[0132] in, Represented as l i ;

[0133] Based on the field of view constraint cost function V i According to the requirements, the field of view constraint cost function V is designed. i for:

[0134]

[0135] Among them, d<min(m max -m0,n max -n0).

[0136] Based on the collision avoidance constraint, design the collision avoidance constraint cost function A ij , the specific steps are as follows:

[0137] The constraint condition of the collision avoidance constraint is: to ensure that the distance between each unmanned ground vehicle in the formation process is always kept at a safe distance, which is mapped to the camera image plane as

[0138] Among them, l s is the safe pixel distance that each unmanned ground vehicle feature needs to maintain in the camera image plane;

[0139] Design collision avoidance constraint cost function A ij The requirements are:

[0140] 1) A ij is a continuously differentiable convex function;

[0141] 2) When If and only if

[0142] 3)

[0143] Introducing Virtual Guide Points As a dynamic collision avoidance mechanism, virtual guidance points Designed for:

[0144]

[0145] In the formula,

[0146] Then the collision avoidance constraint cost function A ij Designed for:

[0147]

[0148] In the formula,

[0149] Based on formation formation, design formation cost function F i , the specific steps are as follows:

[0150] Design formation cost function F i The requirements are:

[0151] 1) F i is a continuously differentiable convex function;

[0152] 2) When and only when

[0153] 3)

[0154] Based on the design requirements, design the formation cost function F i for:

[0155]

[0156] In the formula,

[0157] Combined with the field of view constraint cost function V i , collision avoidance constraint cost function A ij and formation cost function F i , establish a comprehensive cost function, the specific steps are as follows:

[0158] Assume that there are N unmanned ground vehicles in the formation mission, and the field of view of the onboard camera is Then the comprehensive cost function is established as:

[0159]

[0160] In the formula, κ v ,κ a ,κ f They are the corresponding correlation coefficients of field of view constraint, collision avoidance constraint and expected formation formation, and all the coefficients are positive.

[0161] According to the comprehensive cost function, a gradient-related distributed formation control strategy is designed and used to calculate the linear velocity and angular velocity required by each unmanned ground vehicle in the neighborhood. The linear velocity and angular velocity of each unmanned ground vehicle in the neighborhood are calculated:

[0162]

[0163] In the formula, sgn(χ) is a sign function, when χ≥0, sgn(χ)=1, otherwise, sgn(χ)=-1.

[0164] Regarding the process of converting the expected formation into indicators on the camera image plane, this application takes the expected formation as an example that the unmanned ground vehicles are evenly distributed on a circle with the drone as the center and the expected distance as the radius. Based on the assumption that the drone moves horizontally at a fixed height, the expected position of each unmanned ground vehicle feature on the camera image plane should be set at a point with the principal point [m0,n0] Τ is the center of the circle and the expected image pixel distance l d The circumference of the circle with radius is the expected image coordinates =[m0+l d cos(2π i / N) / ,n0+l d sin(2π i / N)] Τ .

[0165] Figure 3 The changing trend of the comprehensive cost function S during the formation process is shown, which clearly shows that during the simulation, S gradually decreases over time and gradually converges to 0.

[0166] Figure 4 and Figure 5 Describe the heterogeneous robot system in X W O W Y W The trajectory diagram projected on the ground and the three-dimensional trajectory diagram show that when the sampling time reaches 20 seconds, the heterogeneous robot system has successfully achieved the pre-set expected formation; it is worth emphasizing that during this process, the unmanned ground vehicle not only did not have any collision, but also never left the field of view.

[0167] Figure 6 The position trajectory changes of the unmanned ground vehicles in the camera image plane are presented. Obviously, after the sampling time of 20 seconds, the position of each unmanned ground vehicle in the camera image plane tends to be stable and no longer moves, which means that the relative position of each unmanned ground vehicle and the drone has been fixed.

[0168] Figures 7 to 10The unmanned ground vehicles g1, g2, g3, and g4 are shown in turn. W O W Y W The trajectory error curves of the plane all show the characteristics of rapid convergence.

[0169] Figures 11 to 14 The image feature error curves of the unmanned ground vehicles g1, g2, g3, and g4 in the camera image plane are shown respectively. These curves not only converge quickly, but also always remain within the threshold range of the camera image plane, thus ensuring the continued effectiveness of the field of view constraint.

[0170] In the description of this specification, the description with reference to the terms "one embodiment", "example", "specific example", etc. means that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic representation of the above terms does not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described can be combined in any one or more embodiments or examples in a suitable manner.

[0171] The above shows and describes the basic principles, main features and advantages of the present invention. It should be understood by those skilled in the art that the present invention is not limited by the above embodiments, and the above embodiments and descriptions are only for explaining the principles of the present invention. Without departing from the spirit and scope of the present invention, the present invention may have various changes and improvements, and these changes and improvements all fall within the scope of the present invention to be protected.

Claims

1. A gradient-dependent distributed formation control method for heterogeneous mobile robots, characterized in that: The following steps are involved: Taking the UGV as the leader and the UAV as the follower, a relative kinematic model of the UGV and the UAV is established; Based on the onboard camera of the UAV, the relative visual kinematic representation of the features of the UGV relative to the UAV is obtained; Based on the target image information in the neighborhood obtained by the airborne camera, combined with the desired formation, and considering the field of view constraints, collision avoidance constraints and formation formation, a comprehensive cost function is established; According to the comprehensive cost function, a gradient-dependent distributed formation control strategy is designed and used to calculate the required linear velocity and angular velocity of each unmanned ground vehicle in the neighborhood to complete the formation of the desired formation.

2. The gradient-dependent heterogeneous mobile robot distributed formation control method according to claim 1, characterized in that: The onboard camera is a monocular camera.

3. The gradient-dependent distributed formation control method for heterogeneous mobile robots according to claim 2 is characterized in that: Establishing the relative kinematic model of the unmanned ground vehicle and the unmanned aerial vehicle includes the following steps: Assuming that the UAV moves horizontally at a fixed height, the horizontal movement of the UAV and the UGV can be placed in the same two-dimensional plane, and the relative kinematic expression between the UGV and the UAV can be simplified as follows: Where i = 1, 2, ..., N, represents the position of the i-th UGV relative to the UAV, represents the relative angle between the i-th UGV and the UAV, φ a Indicates the position of the drone in the world coordinate system, x a ,y a Respectively represent the positions of the i-th unmanned ground vehicle and the unmanned aerial vehicle in the world coordinate system; Then, by taking the first-order differential of equation (1), we can obtain the relative kinematic model of the unmanned ground vehicle and the unmanned aerial vehicle: In the formula, are the first-order differentials of the relative position and angle between the i-th unmanned ground vehicle and the UAV, ω a are the angular velocities of the i-th unmanned ground vehicle and the UAV, ν a are the linear velocities of the i-th unmanned ground vehicle and the i-th unmanned aerial vehicle, respectively.

4. The gradient-dependent distributed formation control method for heterogeneous mobile robots according to claim 3 is characterized in that: Based on the onboard camera on the UAV, the relative visual kinematic representation of the features of the UGV relative to the UAV is obtained, which specifically includes the following steps: Get the camera parameter A of the onboard camera; The conversion relationship between the three-dimensional coordinate representation of the unmanned ground vehicle features in the airborne camera coordinate system and the two-dimensional coordinate representation of the camera image plane is: In the formula, is the two-dimensional coordinate representation of the unmanned ground vehicle feature in the camera image plane, A is the camera parameter, Represents the three-dimensional coordinate representation of the unmanned ground vehicle features in the onboard camera coordinate system; The relative visual kinematics of the UGV feature relative to the UAV can be expressed as: In the formula, [m i ,n i ] Τ is the two-dimensional coordinate representation of the feature of the i-th unmanned ground vehicle in the camera image plane, f m ,f n Represents the pixel length of the focal length on the m-axis and n-axis, f mn represents the tilt coefficient between the m-axis and the n-axis, represents the position of the principal point of the camera image plane; Where H represents the flight altitude of the UAV, and h is the height of the target feature of the unmanned ground vehicle from the ground; Taking the first-order differential of equation (4) and substituting equation (2) into it, we can obtain the velocity expression of the unmanned ground vehicle feature in the camera image plane: In the formula, is the coordinate representation of the feature of the i-th unmanned ground vehicle in the normalized camera image plane.

5. The gradient-dependent distributed formation control method for heterogeneous mobile robots according to claim 4 is characterized in that: Combined with the desired formation, and considering the field of view constraints, collision avoidance constraints and formation formation, a comprehensive cost function is established, which specifically includes the following steps: Determine the desired formation and convert the desired formation into indicators on the camera image plane; Based on the field of view constraint, design the field of view constraint cost function V i ; Based on the collision avoidance constraint, design the collision avoidance constraint cost function A ij ; Based on formation formation, design formation cost function F i ; Combined with the field of view constraint cost function V i , collision avoidance constraint cost function A ij and formation cost function F i , establish a comprehensive cost function.

6. The gradient-dependent heterogeneous mobile robot distributed formation control method according to claim 5, characterized in that: Based on the field of view constraint, design the field of view constraint cost function V i , the specific steps are as follows: The constraint condition of the field of view constraint is to ensure that the features of the unmanned ground vehicle are always within the field of view of the UAV’s onboard camera during the formation process, that is, m min <m<m max ,n min <n<n max ; Design the field of view constraint cost function V i The requirements are: 1) V i is a continuously differentiable convex function; 2) When hour, 3) in, Represented as l i ; Based on the field of view constraint cost function V i According to the requirements, the field of view constraint cost function V is designed. i for: Among them, d<min(m max -m0,n max -n0).

7. The gradient-dependent distributed formation control method for heterogeneous mobile robots according to claim 6, characterized in that: Based on the collision avoidance constraint, design the collision avoidance constraint cost function A ij , the specific steps are as follows: The constraint condition of the collision avoidance constraint is: to ensure that the distance between each unmanned ground vehicle in the formation process is always kept at a safe distance, which is mapped to the camera image plane as Among them, l s is the safe pixel distance that each unmanned ground vehicle feature needs to maintain in the camera image plane; Design collision avoidance constraint cost function A ij The requirements are: 1) A ij is a continuously differentiable convex function; 2) When If and only if 3) Introducing Virtual Guide Points As a dynamic collision avoidance mechanism, virtual guidance points Designed for: In the formula, Then the collision avoidance constraint cost function A ij Designed for: In the formula, 8. The gradient-dependent heterogeneous mobile robot distributed formation control method according to claim 7, characterized in that: Based on formation formation, design formation cost function F i , the specific steps are as follows: Design formation cost function F i The requirements are: 1) F i is a continuously differentiable convex function; 2) When and only when 3) Based on the design requirements, design the formation cost function F i for: In the formula, 9. The gradient-dependent distributed formation control method for heterogeneous mobile robots according to claim 8, characterized in that: Combined with the field of view constraint cost function V i , collision avoidance constraint cost function A ij and formation cost function F i , establish a comprehensive cost function, the specific steps are as follows: Assume that there are N unmanned ground vehicles in the formation mission, and the field of view of the onboard camera is Then the comprehensive cost function is established as: In the formula, κ v ,κ a ,κ f They are the corresponding correlation coefficients of field of view constraint, collision avoidance constraint and expected formation formation, and all the coefficients are positive.

10. The gradient-dependent distributed formation control method for heterogeneous mobile robots according to claim 9, characterized in that: According to the comprehensive cost function, a gradient-related distributed formation control strategy is designed and used to calculate the linear velocity and angular velocity required by each unmanned ground vehicle in the neighborhood. The linear velocity and angular velocity of each unmanned ground vehicle in the neighborhood are calculated: In the formula, sgn(χ) is a sign function, when χ≥0, sgn(χ)=1, otherwise, sgn(χ)=-1.

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