Gradient-related heterogeneous mobile robot distributed formation control method

Abstract

The application belongs to the technical field of formation control, and discloses a gradient-related heterogeneous mobile robot distributed formation control method, which comprises the following steps: taking an unmanned ground vehicle as a leader and a UAV as a follower, and establishing a relative kinematics model of the unmanned ground vehicle and the UAV; based on an airborne camera on the UAV, relative visual kinematics of a feature of the unmanned ground vehicle relative to the UAV is obtained; based on target image information in a neighborhood obtained by the airborne camera, a comprehensive cost function is established in combination with an expected formation and in consideration of field of view constraints, collision avoidance constraints and formation formation; according to the comprehensive cost function, a gradient-related distributed formation control strategy is designed and used to calculate linear velocities and angular velocities required by each unmanned ground vehicle in the neighborhood, so that the formation of the expected formation is completed; the problem of insufficient reliability and safety of collaborative work among robots in the formation process in the prior art is solved, and the stability and safety of the robot formation are improved.

Description

Technical Field

[0001] This invention belongs to the field of formation control technology, specifically relating to a gradient-dependent distributed formation control method for heterogeneous mobile robots. Background Technology

[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 each possess different functions and task capabilities, enabling them to leverage their respective strengths in different operational scenarios. In these systems, drones typically undertake more flexible aerial tasks, such as environmental monitoring and target recognition, while unmanned vehicles can perform ground operations, such as transportation and patrol. Due to their complementarity, collaborative operations between drones and unmanned ground vehicles have demonstrated significant advantages in various complex applications. Therefore, heterogeneous robot systems are gradually becoming an important means of improving efficiency and completing complex tasks in many fields. Traditional formation control methods, such as leader-follower methods, virtual structure methods, and behavior-based methods, typically rely on global positioning information or efficient communication mechanisms. However, these methods often fail to meet 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] To address this challenge, image-based visual servoing has gradually emerged as an effective solution. By utilizing the robot's onboard camera, visual servoing can directly extract relative positions from the camera's image plane, avoiding reliance on external positioning systems. This method acquires relative position information between robots through real-time image processing and adjusts the robot's trajectory accordingly, thereby achieving high-precision formation control and target tracking. Compared to traditional methods, this approach is particularly suitable for environments lacking global positioning information and exhibits strong adaptability in dynamically changing tasks and environments. However, pure visual servoing still faces some challenges in practical applications of formation control, such as overcoming the field-of-view constraints of onboard cameras to achieve visibility connectivity, avoiding collisions between mobile robots, and ensuring the stability of the formation. Therefore, existing technologies suffer from insufficient reliability and safety in robot-to-robot collaborative operations during formation processes. Summary of the Invention

[0004] To address the shortcomings of existing technologies, the present invention aims to provide a gradient-dependent distributed formation control method for heterogeneous mobile robots, which solves the problems of insufficient reliability and safety of robot-to-robot collaborative operation during the formation process in existing technologies.

[0005] The objective of this invention can be achieved through the following technical solutions:

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

[0007] With unmanned ground vehicles as the leader and drones as the followers, a relative kinematic model of unmanned ground vehicles and drones is established.

[0008] Based on the airborne camera on the drone, the relative visual kinematic representation of the features of the unmanned ground vehicle with respect to the drone is obtained;

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

[0010] Based on the comprehensive cost function, a gradient-dependent distributed formation control strategy is designed and used to calculate the linear and angular velocities required by each unmanned ground vehicle in the neighborhood, thereby completing the formation of the desired formation.

[0011] The airborne camera is a monocular camera.

[0012] Establishing a relative kinematic model between the unmanned ground vehicle and the drone involves the following steps:

[0013] Assuming the drone moves horizontally at a fixed altitude, the horizontal movements of both the drone and the unmanned ground vehicle can be placed on the same two-dimensional plane. The relative kinematic expression between the unmanned ground vehicle and the drone can be simplified as follows:

[0014]

[0015] In the formula, i = 1, 2, ..., N, This represents the position of the i-th unmanned ground vehicle relative to the drone. Let φ represent the relative angle between the i-th unmanned ground vehicle and the drone. a This indicates the drone's location in the world coordinate system. x a ,y a Let i represent the positions of the i-th unmanned ground vehicle and the i-th drone in the world coordinate system, respectively.

[0016] Taking the first differential of equation (1), we obtain the relative kinematic model of the unmanned ground vehicle and the drone:

[0017]

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

[0019] Based on the onboard camera of the UAV, the relative visual kinematic representation of the features of the unmanned ground vehicle with respect to the UAV is obtained, specifically including the following steps:

[0020] Obtain camera parameter A from the airborne camera;

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

[0022]

[0023] In the formula, Let A be the two-dimensional coordinate representation of the features of the unmanned ground vehicle in the camera image plane, where A represents the camera parameters. The three-dimensional coordinate representation of the features of the unmanned ground vehicle in the coordinate system of the airborne camera;

[0024] The relative visual kinematics of the unmanned ground vehicle characteristics with respect to the drone can be expressed as:

[0025]

[0026] In the formula, [m i ,n i ] Τ Let f be the two-dimensional coordinate representation of the features of the i-th unmanned ground vehicle in the camera image plane. m ,f n f represents the pixel length along the m-axis and n-axis, respectively. mn This represents the skewness coefficient between the m-axis and the n-axis. Indicates the position of the principal point on the camera image plane;

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

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

[0029]

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

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

[0032] Determine the desired formation and translate it into an index 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 collision avoidance constraints, design the collision avoidance constraint cost function A. ij ;

[0035] Based on formation, design the 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 for 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, i.e., m min <m<m max ,n min <n<n max ;

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

[0040] 1)V i It 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 Design the field-of-view constraint cost function V according to the requirements. i for:

[0045]

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

[0047] Based on collision avoidance constraints, design the collision avoidance constraint cost function A.ij The specific steps are as follows:

[0048] The collision avoidance constraint is to ensure that the distance between each unmanned ground vehicle remains safe throughout the formation process, which is mapped onto the camera image plane as follows.

[0049] Among them, l s 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 It is a continuously differentiable convex function;

[0052] 2) When If and only if

[0053] 3)

[0054] Introducing virtual boot points As a dynamic collision avoidance mechanism, virtual guidance points Designed as follows:

[0055]

[0056] In the formula,

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

[0058]

[0059] In the formula,

[0060] Based on formation, design the 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 It is a continuously differentiable convex function;

[0063] 2) When, if and only if

[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 The comprehensive cost function is established through the following steps:

[0069] Assuming there are N unmanned ground vehicles in the formation mission, and the field of view of the airborne camera is... The comprehensive cost function is then established as follows:

[0070]

[0071] In the formula, κ v ,κ a ,κ f These are the correlation coefficients formed by the field of view constraint, collision avoidance constraint, and desired formation, respectively, and all coefficients are positive.

[0072] Based on 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. The linear and angular velocities of each unmanned ground vehicle in the neighborhood are then calculated.

[0073]

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

[0075] The beneficial effects of this invention are:

[0076] During formation, this invention can effectively guarantee the field of view constraint, ensure the visibility connectivity of the airborne 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 robot formation and solving the problem of insufficient reliability and safety of robot collaborative operation in the formation process in the prior art. Attached Figure Description

[0077] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, for those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0078] Figure 1This is a flowchart illustrating the design of the formation control method of the present invention.

[0079] Figure 2 This is a schematic diagram showing the distribution of the drone and unmanned ground vehicle of the present invention;

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

[0081] Figure 4 This is a schematic diagram of the trajectory projected onto the ground during the simulated formation process of the present invention;

[0082] Figure 5 This is a schematic diagram of the three-dimensional trajectory during the simulated formation process of the present invention;

[0083] Figure 6 This is a schematic diagram showing the position of each unmanned ground vehicle on the camera image plane at the sampling moment during the simulated formation process of the present invention;

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

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

[0086] Figure 9 This is a schematic diagram illustrating the convergence process of the unmanned ground vehicle g3 position error in the simulation of this invention;

[0087] Figure 10 This is a schematic diagram illustrating the convergence process of the unmanned ground vehicle g4 position error in the simulation of this invention;

[0088] Figure 11 This is a schematic diagram illustrating the image error convergence process of the unmanned ground vehicle g1 in the simulation of this invention;

[0089] Figure 12 This is a schematic diagram illustrating the image error convergence process of the unmanned ground vehicle g2 in the simulation of this invention;

[0090] Figure 13 This is a schematic diagram illustrating the image error convergence process of the unmanned ground vehicle g3 in the simulation of this invention;

[0091] Figure 14 This is a schematic diagram illustrating the image error convergence process of the unmanned ground vehicle g4 in the simulation of this invention. Detailed Implementation

[0092] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort 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] With unmanned ground vehicles as the leader and drones as the followers, a relative kinematic model of unmanned ground vehicles and drones is established.

[0095] Based on the airborne camera on the drone, the relative visual kinematic representation of the features of the unmanned ground vehicle with respect to the drone is obtained;

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

[0097] Based on the comprehensive cost function, a gradient-dependent 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, so as 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 connectivity of the airborne camera's field of view, and at the same time avoid collisions between unmanned ground vehicles through the collision avoidance cost function, thereby improving the stability and safety of robot formation and solving the problem of insufficient reliability and safety of robot collaborative operation in the formation process in the prior art.

[0099] The airborne camera is a monocular camera. Since monocular cameras are not only lower in cost, but also smaller and lighter, making them easier and more flexible to install on drones, monocular cameras are the preferred airborne camera solution in this application. At the same time, compared with multi-camera systems, data processing and calculation of monocular cameras are relatively simpler, reducing the demand for hardware resources and computing power.

[0100] Establishing a relative kinematic model between the unmanned ground vehicle and the drone involves the following steps:

[0101] Assuming the drone moves horizontally at a fixed altitude, the horizontal movements of both the drone and the unmanned ground vehicle can be placed on the same two-dimensional plane. The relative kinematic expression between the unmanned ground vehicle and the drone can be simplified as follows:

[0102]

[0103] In the formula, i = 1, 2, ..., N, This represents the position of the i-th unmanned ground vehicle relative to the drone. Let φ represent the relative angle between the i-th unmanned ground vehicle and the drone. a This indicates the drone's location in the world coordinate system. x a ,y a Let i represent the positions of the i-th unmanned ground vehicle and the i-th drone in the world coordinate system, respectively.

[0104] Taking the first differential of equation (1), we obtain the relative kinematic model of the unmanned ground vehicle and the drone:

[0105]

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

[0107] Based on the onboard camera of the UAV, the relative visual kinematic representation of the features of the unmanned ground vehicle with respect to the UAV is obtained, specifically including the following steps:

[0108] Obtain camera parameter A from the airborne 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 transformation relationship between the three-dimensional coordinate representation of unmanned ground vehicle features in the airborne camera coordinate system and the two-dimensional coordinate representation in the camera image plane is as follows:

[0111]

[0112] In the formula, Let A be the two-dimensional coordinate representation of the features of the unmanned ground vehicle in the camera image plane, where A represents the camera parameters. The three-dimensional coordinate representation of the features of the unmanned ground vehicle in the coordinate system of the airborne camera;

[0113] The relative visual kinematics of the unmanned ground vehicle characteristics with respect to the drone can be expressed as:

[0114]

[0115] In the formula, [m i ,ni ] Τ Let f be the two-dimensional coordinate representation of the features of the i-th unmanned ground vehicle in the camera image plane. m ,f n f represents the pixel length along the m-axis and n-axis, respectively. mn This represents the skewness coefficient between the m-axis and the n-axis. Indicates the position of the principal point on the camera image plane;

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

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

[0118]

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

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

[0121] Determine the desired formation and translate it into an index 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 collision avoidance constraints, design the collision avoidance constraint cost function A. ij ;

[0124] Based on formation, design the 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 for 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, i.e., m min <m<m max ,n min <n<n max ;

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

[0129] 1)V i It 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 Design the field-of-view constraint cost function V according to the requirements. i for:

[0134]

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

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

[0137] The collision avoidance constraint is to ensure that the distance between each unmanned ground vehicle remains safe throughout the formation process, which is mapped onto the camera image plane as follows.

[0138] Among them, l s 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 It is a continuously differentiable convex function;

[0141] 2) When If and only if

[0142] 3)

[0143] Introducing virtual boot points As a dynamic collision avoidance mechanism, virtual guidance points Designed as follows:

[0144]

[0145] In the formula,

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

[0147]

[0148] In the formula,

[0149] Based on formation, design the 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 It is a continuously differentiable convex function;

[0152] 2) When, if and only if

[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 The comprehensive cost function is established through the following steps:

[0158] Assuming there are N unmanned ground vehicles in the formation mission, and the field of view of the airborne camera is... The comprehensive cost function is then established as follows:

[0159]

[0160] In the formula, κ v ,κ a ,κ f These are the correlation coefficients formed by the field of view constraint, collision avoidance constraint, and desired formation, respectively, and all coefficients are positive.

[0161] Based on 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. The linear and angular velocities of each unmanned ground vehicle in the neighborhood are then 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 desired formation into indicators on the camera image plane, this application describes the desired formation as an example where unmanned ground vehicles are uniformly distributed on a circle with the UAV as the center and the desired distance as the radius. Based on the assumption that the UAV moves horizontally at a fixed altitude, the desired position of each unmanned ground vehicle feature on the camera image plane should be set at a principal point [m0, n0]. Τ l is the center of the circle and the desired image pixel distance. d On the circumference of the circle with radius , i.e., the coordinates of the desired image For [m0+l d cos(2π i / N) / ,n0+l d sin(2π i / N)] Τ .

[0165] Figure 3 The study demonstrates the changing trend of the comprehensive cost function S during the formation process, clearly showing that S gradually decreases over time during the simulation and gradually converges towards 0.

[0166] Figure 4 and Figure 5 They respectively described heterogeneous robotic systems in X W O W Y W The trajectory diagrams projected onto the ground and the three-dimensional trajectory diagrams show that the heterogeneous robot system successfully achieved the pre-set desired formation when the sampling time reached 20 seconds. It is worth emphasizing that during this process, the unmanned ground vehicle not only did not experience any collisions, but also never left the field of view.

[0167] Figure 6 This shows the change in the position trajectory of the unmanned ground vehicle on the camera image plane. Obviously, after a sampling time of 20 seconds, the position of each unmanned ground vehicle on the camera image plane tends to stabilize and no longer moves. This means that the relative position of each unmanned ground vehicle and the drone has become fixed.

[0168] Figures 7 to 10The unmanned ground vehicles g1, g2, g3, and g4 were displayed in sequence in X W O W Y W The trajectory error curves on the plane all exhibit rapid convergence.

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

[0170] In the description of this specification, references to terms such as "an embodiment," "example," "specific example," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the invention. In this specification, illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.

[0171] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely illustrative of the principles of the invention. Various changes and modifications can be made to the present invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the claimed invention.

Claims

1. A gradient-related heterogeneous mobile robot distributed formation control method, characterized in that, The method comprises the following steps: Taking an unmanned ground vehicle as a leader and a UAV as a follower, a relative kinematics model of the unmanned ground vehicle and the UAV is established; Based on an onboard camera on the UAV, a relative visual kinematics expression of a feature of the unmanned ground vehicle relative to the UAV is obtained; Based on target image information in a neighborhood obtained by the onboard camera, a comprehensive cost function is established in combination with an expected formation and in consideration of field-of-view constraints, collision avoidance constraints and formation formation; According to the comprehensive cost function, a gradient-related distributed formation control strategy is designed and used to calculate linear velocities and angular velocities required by the unmanned ground vehicles in the neighborhood, so that the formation of the expected formation is completed; In combination with the expected formation and in consideration of field-of-view constraints, collision avoidance constraints and formation formation, a comprehensive cost function is established, specifically comprising the following steps: An expected formation is determined, and the expected formation is converted into an index on a camera image plane; Based on the field of view constraint, a field of view constraint cost function is designed ; Based on the collision avoidance constraint, a collision avoidance constraint cost function is designed ; Based on the formation of the formation, the formation cost function is designed ; combining field of view constraint cost function , collision avoidance constraint cost function and platoon cost function to establish a comprehensive cost function; Based on the field of view constraint, a field of view constraint cost function is designed The specific steps are as follows: The constraint condition of the field of view constraint is to ensure that the feature of the unmanned ground vehicle is always within the field of view of the camera on the unmanned aerial vehicle during the platoon process, that is ; Designing a field of view constraint cost function The requirements are that: 1) is a continuously differentiable convex function; 2) when time, ; 3） ； wherein is represented as ; Based on the field of view constraint cost function The field of view constraint cost function is designed as follows: ​ （6） wherein ; Based on the collision avoidance constraint, a collision avoidance constraint cost function is designed The specific steps are as follows: The constraint condition of the collision avoidance constraint is: ensuring that the distance between each unmanned ground vehicle in the platoon process is always kept at a safe distance, which is mapped to the camera image plane as ; wherein, safety pixel distance that each unmanned ground vehicle feature needs to maintain in the camera image plane; Designing a collision avoidance constraint cost function The requirements are: 1) is a continuously differentiable convex function; 2) when if and only if ; 3） ； Introducing virtual guidance points As a dynamic collision avoidance mechanism, virtual guidance points are designed to: （7） In the formulae, ; The collision avoidance constraint cost function is designed as: （8） In the formulae, ; Based on the formation of the formation, the formation cost function is designed The specific steps are as follows: Designing a platoon cost function The requirements are: 1) is a continuously differentiable convex function; 2) iff ; 3） ； Based on the design requirements, the platoon cost function is designed is: （9） In the formulae, ; combining the field of view constraint cost function , the collision avoidance constraint cost function , and the platoon cost function , to establish a comprehensive cost function, the specific steps are as follows: Suppose there are N vehicles in the platoon task, and the field of view of the on-board camera is Then the comprehensive cost function is established as: （10） In the formula, are the corresponding correlation coefficients of the field-of-view constraint, the collision avoidance constraint, and the desired formation formation, respectively, and the coefficients are all positive numbers. According to the comprehensive cost function, a gradient-related distributed formation control strategy is designed and used to calculate linear velocities and angular velocities required by the unmanned ground vehicles in the neighborhood, so that the linear velocities and the angular velocities of the unmanned ground vehicles in the neighborhood are calculated: （11） wherein , is a sign function, when , , otherwise, .

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

3. The gradient-related heterogeneous mobile robot distributed formation control method according to claim 2, wherein, The relative kinematics model of the unmanned ground vehicle and the UAV is established, specifically comprising the following steps: Supposing that the UAV moves horizontally at a fixed height, horizontal movements of the UAV and the unmanned ground vehicle can be placed in the same two-dimensional plane, and a relative kinematics expression of the unmanned ground vehicle and the UAV can be simplified as: （1） In the formula, , Indicates the first The position of the unmanned ground vehicle relative to the drone. Indicates the first The relative angle between the unmanned ground vehicle and the drone. This indicates the drone's location in the world coordinate system. They represent the first The positions of unmanned ground vehicles and drones in the world coordinate system; First-order differentiation is performed on formula (1) to obtain the relative kinematics model of the unmanned ground vehicle and the UAV: （2） wherein are the first order derivatives of the relative position and relative angle between the are the angular velocities of the first are the linear velocities of the first ​​​ 4. The gradient-related heterogeneous mobile robot distributed formation control method according to claim 3, wherein, Based on the onboard camera on the UAV, a relative visual kinematics expression of a feature of the unmanned ground vehicle relative to the UAV is obtained, specifically comprising the following steps: Acquiring camera parameters of an onboard camera A ; A conversion relationship between a three-dimensional coordinate expression of the feature of the unmanned ground vehicle on a camera coordinate system and a two-dimensional coordinate expression on a camera image plane is: （3） wherein is a two-dimensional coordinate representation of the unmanned ground vehicle feature in the camera image plane, is a camera parameter, is a three-dimensional coordinate representation of the unmanned ground vehicle feature in the on-board camera coordinate system; The relative visual kinematics of the unmanned ground vehicle relative to the UAV can be expressed as: （4） wherein is the first vehicle feature in a two-dimensional coordinate representation in the camera image plane, respectively denote the pixel length of the focal length in the axis and axis, denotes the tilt factor between the axis and axis, denotes the principal point position of the camera image plane; wherein represents the unmanned aerial vehicle flight height, is the unmanned ground vehicle target feature distance ground height; First-order differentiation is performed on formula (4), and formula (2) is substituted into formula (4) to obtain a velocity expression of the feature of the unmanned ground vehicle in the camera image plane: （5） In the formula, is the first Coordinate representation of the vehicle feature in the normalized camera image plane.

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