A multi-unmanned vehicle target encirclement method based on MPC-APF control

Abstract

The present disclosure provides a multi-unmanned vehicle target encirclement method based on MPC-APF control, which comprises the following steps: step 1: taking a rear axle-centered single vehicle model as a kinematics model, and constructing a vehicle motion state equation; step 2: establishing an artificial potential field APF in an environment, including a road boundary line APF and an obstacle APF; the obstacle APF is constructed by fusing the artificial potential field effects of the same direction and reverse motion obstacle vehicles on the unmanned vehicle; step 3: converting the target encirclement problem into a dynamic trajectory tracking problem, adding an APF penalty term designed based on an artificial potential field in an optimization objective function, and tracking and controlling a dynamic target trajectory by using model predictive control MPC according to the vehicle motion state equation. The present application can realize the encirclement of a dynamic target in a road environment with dynamic obstacles and avoid collisions with other social vehicles.

Description

Technical Field

[0001] This invention belongs to the technical field of target capture, specifically relating to a multi-unmanned vehicle target capture method based on MPC-APF control. Background Technology

[0002] Target encirclement is a strategy for multi-agent systems to collaboratively encircle dynamic or static targets. It is an important branch of multi-robot collaboration, focusing on how multiple robots can cooperate to effectively track and surround dynamic, suspicious targets. It has significant research value and practical applications in fields such as military reconnaissance, emergency rescue, and collaborative detection. Currently, encirclement tasks emphasize the encirclement control itself, neglecting the impact of environmental information. However, avoiding collisions with dynamic obstacles in the environment during the encirclement process is a crucial research area. Summary of the Invention

[0003] In view of this, the present invention provides a multi-unmanned vehicle target capture method based on model predictive control and artificial potential field method, which can capture dynamic targets in road environments with dynamic obstacles and avoid collisions with other vehicles.

[0004] To solve the above-mentioned technical problems, the present invention is implemented as follows.

[0005] A multi-unmanned vehicle target capture method based on MPC-APF control includes:

[0006] Step 1: Using the single-vehicle model centered on the rear axle as the kinematic model, construct the motion state equation of the unmanned vehicle;

[0007] Step 2: Establish the artificial potential field (APF) in the environment, including the road boundary line APF and the obstacle APF; the obstacle APF is constructed by integrating the artificial potential field effect of obstacle vehicles moving in the same direction and opposite direction on the unmanned vehicle.

[0008] The effective range of the APF (Advanced Potential Field) for vehicles moving in the same direction is defined as follows: Taking the center of the obstacle vehicle as the dividing point, design a forward triangular artificial potential field region and a backward triangular artificial potential field region. The furthest effective distance between the front and rear ends of these two artificial potential field regions along the S-axis in the Frenet coordinate system is defined, with the S-axis as the safety distance. Based on this, the speed is dynamically adjusted according to the speed of the driverless vehicle and the obstacle vehicle;

[0009] The effective range of the APF (Automatic Potential Field) for vehicles moving in the opposite direction is as follows: A forward rectangular artificial potential field region and a backward triangular artificial potential field region are designed, with the center of the obstacle vehicle as the dividing point; the maximum effective distance along the S-axis of the forward rectangular artificial potential field region is a set value. The furthest effective distance along the S-axis of the backward triangular artificial potential field region is the safe distance along the S-axis. Based on this, the speed is dynamically adjusted according to the speed of the driverless vehicle and the obstacle vehicle;

[0010] Step 3: Transform the target capture problem into a dynamic trajectory tracking problem. Add an APF penalty term based on artificial potential field design to the optimization objective function. Based on the motion state equation of the unmanned vehicle, use model predictive control (MPC) to track and control the dynamic target trajectory.

[0011] Preferably, in the design of the APF effective range of the same-direction obstacle vehicle, the furthest effective distance along the S-axis of the rearward triangular artificial potential field region is... Designed with an S-axis safety distance Based on this, dynamic adjustments are made according to the speed difference between the autonomous vehicle and the obstacle vehicle; the maximum effective distance along the S-axis of the forward triangular artificial potential field region. Designed with an S-axis safety distance Based on this, dynamic adjustments are made according to the sum of the speeds of the autonomous vehicle and the obstacle vehicles to reserve buffer space for the safe return of the autonomous vehicle to the road.

[0012] In the design of the APF effective range of the reverse-moving obstacle vehicle, the furthest effective distance along the S-axis of the rearward triangular artificial potential field region is... Designed with an S-axis safety distance Based on this, dynamic adjustments are made according to the speed difference between the driverless vehicle and the obstacle vehicle.

[0013] Preferably, in the design of the APF effective range for vehicles moving in the same direction, the furthest effective distance along the S-axis of the rearward triangular artificial potential field region is... and the farthest effective distance along the S-axis of the forward triangular artificial potential field region. The design is as follows:

[0014]

[0015] In the formula, The set S-axis safety distance; This is the proportional parameter for the dynamic speed adjustment term; and The speeds are for driverless vehicles and obstacle vehicles, respectively.

[0016] Preferably, in the APF design of the obstacle vehicle moving in the same direction, and in the APF design of the obstacle vehicle moving in the opposite direction, the furthest effective distance along the L-axis of each triangular artificial potential field region is... The design is as follows: Based on the center of the obstacle vehicle, an axial safety distance of L is expanded to both sides. .

[0017] Preferably, the specific method by which the obstacle APF is constructed by integrating the artificial potential field effects of obstacle vehicles moving in the same direction and in opposite directions on the unmanned vehicle is as follows:

[0018] Calculate the effective range of APF for vehicles moving in the same and opposite directions from the obstacle. Within, the obstacle APF value of each obstacle vehicle to the autonomous vehicle. :

[0019]

[0020] in, for k Obstacles j The APF value for autonomous vehicles; Indicates the amplitude of the artificial potential field; For vehicles with obstacles j Location, for k Obstacles j The distance between the center of the vehicle and the center of the driverless car;

[0021] Add up the obstacle APF values ​​of all vehicles with obstacles to obtain the obstacle APF value within the effective range.

[0022] Preferably, the objective function in step 3 includes a trajectory deviation term before and after optimization, an energy consumption term, an APF penalty term, and a destination deviation penalty term.

[0023] Preferably, the optimization objective function is:

[0024]

[0025] in, J To optimize the objective function; step represents the time frame contained within a time window in the MPC control;

[0026] The trajectory deviation term is the sum of multiples of the squared distances between the optimized trajectory and the expected trajectory within the time window. The closer the optimized trajectory is to the reference trajectory, the smaller the trajectory deviation term is. It consists of the state offset at each moment in the time window, where the state offset is the difference between the state values ​​of the predicted trajectory point and the expected trajectory point.

[0027] For energy consumption, the goal is to achieve the best optimization results while minimizing input energy consumption. for k Time-based control input;

[0028] The APF penalty term increases as the autonomous vehicle gets closer to the obstacle vehicle. This guides the autonomous vehicle to prioritize obstacle avoidance when the obstacle coincides with its trajectory, and to continue tracking the target trajectory after escaping the APF's influence. The total obstacle APF is calculated by integrating the artificial potential field effects of obstacle vehicles moving in the same and opposite directions on the unmanned vehicle. For adjustment factors;

[0029] As a penalty term for endpoint deviation, an additional independent design is made for the error of the last trajectory point of the predicted trajectory and the expected trajectory, increasing the penalty degree for the relative error at the end of the trajectory; This refers to the position of the last predicted trajectory point within the time window;

[0030] Q , R , F All are weight matrices.

[0031] Preferably, the optimization objective function further includes hard constraints, including the motion state equation of the unmanned vehicle, the acceptable range of the unmanned vehicle's position coordinates, the acceptable range of the control input, and the allowable deviation of the input error.

[0032] Beneficial effects:

[0033] (1) This invention takes into account the characteristics of vehicle obstacles in the road environment and designs the APF value according to the movement state of social vehicles to ensure that there is no collision with unmanned vehicles.

[0034] (2) The present invention fully considers the motion state of dynamic targets and performs real-time tracking based on their predicted trajectory information to ensure the real-time capture effect of dynamic targets.

[0035] (3) The present invention uses a linear unmanned vehicle kinematic model for model prediction function design, which improves the system's computing speed. Attached Figure Description

[0036] Figure 1 This is a schematic diagram of the kinematics model of an autonomous vehicle.

[0037] Figure 2 This is a schematic diagram of an unmanned vehicle avoiding obstacles while moving in the same direction.

[0038] Figure 3 This is a schematic diagram of an unmanned vehicle avoiding obstacles in the case of reverse motion.

[0039] Figure 4 This is a schematic diagram of the APF area of ​​an unmanned vehicle under the condition of moving in the same direction.

[0040] Figure 5 This is a schematic diagram of the APF area of ​​an unmanned vehicle in the case of reverse motion. Detailed Implementation

[0041] The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0042] This invention provides a method for encircling and capturing multiple unmanned vehicle targets based on MPC-APF control, the detailed implementation of which is as follows:

[0043] Step 1: The changes of various parameters of the autonomous vehicle in the global coordinate system during its movement are as follows: Figure 1 As shown.

[0044] The autonomous vehicle is mathematically modeled, and the single-vehicle kinematic model with the rear axle center as the vehicle center is as follows:

[0045]

[0046] This model is a nonlinear model. The symbols for the three equations are provided for ease of writing in the following text. To simplify the computation, the model is linearized. The state variables are selected as... , These represent the x-coordinate, y-coordinate, and yaw angle of the unmanned vehicle; the selected control variable is... Let and represent the linear velocity and angular velocity of the autonomous vehicle, respectively. For any reference point on the reference trajectory, denoted by r, the above equation can be rewritten as:

[0047]

[0048] in, , Expand the above equation using a Taylor series at the reference point, and ignore higher-order terms:

[0049]

[0050] right and Find the Jacobian matrix, we have:

[0051]

[0052]

[0053] The change in state error Represented as:

[0054]

[0055]

[0056] The above equation shows that the state error quantity can form a linear state space.

[0057] The state error equation is discretized using forward Euler method, resulting in...

[0058]

[0059] Therefore, the state error of the autonomous vehicle at the current time and the next time can be obtained after discretization. and input error The linear equation:

[0060]

[0061] In the formula, T is the sampling step size, and I is the identity matrix with the same dimension as matrix A. The above formula is the motion state equation of the unmanned vehicle. It is worth noting that the derivation of the above motion state equation uses xy coordinates for simplicity, but this invention is designed in the Frenet coordinate system; therefore, the subsequent parts will use ls coordinates. The Frenet coordinate system "straightens" the road with the original road centerline as a reference, decomposing the vehicle's motion into the tangent and normal directions of the road. Assuming the current road is a standard road with a constant width and equal vertical distances from the centerline on both sides, the origin of the coordinate system is taken as the starting point of the left edge of the road. The road coordinates in the Frenet coordinate system are designed according to the following requirements. :

[0062] Lateral offset ( ): The vertical distance of this point from the left edge of the road is always a non-negative value;

[0063] Longitudinal distance ( ): The distance traveled along the center line of the road, which is always a non-negative value.

[0064] The Frenet coordinate system decomposes space into two orthogonal directions. and This means that these directions match classic control modes (throttle and steering). Within this coordinate system, the original winding shape of the road can be ignored, simulating the actual control process of an autonomous vehicle and intuitively exploring waypoints. The Frenet coordinate system is also known as... l-s Coordinate system.

[0065] Step 2: In the encirclement and control phase, the reference trajectory of each unmanned vehicle is the trajectory after the predicted trajectory deviation of the target. Due to the presence of dynamic obstacles in the surrounding area, the trajectory may overlap with the obstacles or exceed the edge lines on both sides of the road. At this time, obstacle avoidance constraints need to be added to the control function so that the optimized input parameters can ensure the safety of the actual running trajectory.

[0066] This paper uses the artificial potential field method to design obstacle avoidance constraints in MPC control, which is divided into two parts:

[0067] (1) Road boundary line APF

[0068] Since vehicles can only travel within the boundary lines, artificial potential and repulsive fields are designed on both sides of the road to constrain the autonomous vehicles away from the boundary lines. The magnitude of the repulsive field on the left and right sides of the road's s-axis is designed using the following formula:

[0069]

[0070] in, A road The APF intensity parameter determines the magnitude of the artificial potential field and is generally determined through empirical methods or simulation parameter tuning. The APF decay rate parameter determines how quickly the artificial potential field changes with the distance from the unmanned vehicle to the boundary line, and is generally set according to the desired repulsion distance threshold. l and l roadi These are the current L-axis coordinates of the vehicle and the boundary lines on both sides of the road. l Axis coordinate values. i These are the serial numbers of the boundary lines on both sides of the road. i The value can be 1 or 2.

[0071] (2) Obstacle APF Design

[0072] Design the Action-Friendly Field (APF) between the autonomous vehicle and other obstacle vehicles. Since vehicles behind the autonomous vehicle do not affect its motion, only the impact of vehicles in front of the autonomous vehicle at the current moment is considered. For vehicles traveling in the same direction as the autonomous vehicle, consider overtaking from the left or right and returning to the original lane after overtaking. Because the two vehicles move in the same direction, the following distance can be set to a small value. Overtaking from the left or right is considered only when approaching the vehicle; however, when returning to the original lane, a rapid turn could easily lead to a side collision with the overtaken vehicle, so a slow turn is needed based on the speed difference between the two vehicles. Figure 2 As shown.

[0073] For vehicles traveling in the opposite direction to the autonomous vehicle, a head-on collision is possible. It's necessary to anticipate the speed difference between the two vehicles and avoid them from the left or right. After avoiding the collision, the two vehicles will have created enough distance that there's no need to consider collision issues when returning to the lane. Figure 3 As shown. Therefore, when designing the potential field force, a larger threshold should be reserved for the safety distance in the tangential direction of the road, while a smaller safety distance can be designed in the direction perpendicular to the road to facilitate the autonomous vehicle's turning and lane changing operations.

[0074] To guide autonomous vehicles to overtake from the left and right when encountering obstacles, and to avoid prolonged lingering in front of or behind other vehicles or getting trapped in local minima, this paper draws on a method commonly used in autonomous driving research: designing artificial potential fields for social vehicles. A triangular artificial potential field region is designed with the obstacle center as the dividing point. For social vehicles moving in the same direction as the autonomous vehicle, a design is created as follows: Figure 4 The artificial potential field region is shown.

[0075] The scope of effect can be expressed as

[0076]

[0077] in, Ll To expand a fixed distance to both sides of the L-axis based on the position of the obstacle. l_safe , L sl and L sr These represent the maximum effective distances of the potential fields at the front and rear ends of the obstacle, respectively. The effective range is dynamically adjusted based on the velocities (vectors) of the autonomous vehicle and the obstacle: at the rear of the obstacle, the effective range is shortened by subtracting the velocities (in the same direction) of the two obstacles and then summing this difference with the longitudinal safety distance s_safe; at the front of the obstacle, the effective range is extended by summing the velocities (in the same direction) of the two obstacles and then summing this difference with the longitudinal safety distance s_safe, thus reserving sufficient buffer space for the autonomous vehicle's safe return to its lane. A s The proportional parameter representing the speed difference is defined by the following design formula.

[0078]

[0079] For social vehicles moving in the opposite direction to driverless cars, the design should be as follows: Figure 5 The artificial potential field region is shown.

[0080] The scope of effect can be expressed as

[0081]

[0082] L l The design is the same as above. L sl This represents the furthest effective distance in front of the obstacle. When the autonomous vehicle is behind the obstacle, the difference between their speeds (in opposite directions) is summed with the longitudinal safety distance s_safe to provide sufficient buffer space for head-on collision avoidance. A s The proportional parameter representing the speed difference is defined by the following design formula.

[0083]

[0084] The APF value of obstacles within this effective range is designed as shown in the following formula:

[0085]

[0086] in, A o Indicates the amplitude of the artificial potential field. This represents the distance between the center of the obstacle and the center of the vehicle. Using this method to design an artificial potential field can guide the autonomous vehicle to move to the left or right of other vehicles, better aligning with the dynamic characteristics of autonomous vehicles accelerating, decelerating, and overtaking.

[0087] Typically, the artificial potential field also includes the gravitational effect of the target point on the control target. This part can be achieved by designing the trajectory tracking effect in the MPC optimization function. However, to simplify the design process, the gravitational field effect is not set here.

[0088] Step 3: Optimize the trajectory from k to k+step at time k. Then, at time k+j, the desired trajectory point information and control input parameters of the trajectory to be tracked are expressed as follows: and The superscript 'i' represents the sequence number of the autonomous vehicle, and the subscripts 'k' and 'j' represent the time. The parameters represent the autonomous vehicle... i Expectation of trajectory points l axis, s Axis, orientation (the angle between the tangent and the l-axis, counterclockwise is positive), linear velocity, and rotation angle per unit time. Autonomous vehicle. i The actual trajectory and control input parameters are respectively expressed as: and .

[0089] The reference trajectory and reference input information at each time point are shown in the following formula. Since the desired trajectory only contains coordinate information, the trajectory orientation, velocity, and rotation angle information are obtained through forward interpolation:

[0090] (a)

[0091] (b)

[0092]

[0093] in, and Let J and Y represent the coordinates of the desired trajectory point to be tracked at time j. and Let represent the offsets of the i-th autonomous vehicle relative to the desired trajectory point, respectively, describing the desired formation; summing these two values ​​yields... and Let represent the coordinates of the desired trajectory point to be tracked by the i-th autonomous vehicle at time j. Formula (a) represents the formation, and formula (b) represents the desired angle calculated based on the desired formation.

[0094] The optimization function is designed independently for each vehicle. This description is specific to each autonomous vehicle, therefore the superscript in the above expression is omitted. i Using the state offset and control offset as the state and input parameters of the linear model, the following linear state equation can be obtained based on the kinematic model of the autonomous vehicle:

[0095]

[0096]

[0097] T is the unit prediction time step, and matrices A and B are respectively represented as follows:

[0098]

[0099] Combining the above formula, the initial state of this planning is used in an iterative manner. And optimize the difference between the input and the expected input. The state offset at time k+1 - k+step is represented as follows:

[0100]

[0101]

[0102]

[0103]

[0104]

[0105] This yields the expected trajectory offset within the predicted time range. Combining the APF penalty term, the following MPC optimization control function is designed:

[0106]

[0107] Where Q, R, and F are all weight matrices. The optimization function consists of four parts:

[0108] The first part is the bias term, which is the sum of multiples of the squared distances between the optimized trajectory and the reference trajectory points within time k—k+step-1. The closer the optimized trajectory is to the reference trajectory, the smaller this term is. Matrix Q can be designed as a non-zero diagonal matrix; the value of each column is equal to the influence of the optimization effect of the corresponding trajectory point on the optimization function.

[0109] The second part is the energy consumption item, which aims to achieve the optimization effect while using the minimum input energy consumption;

[0110] The third and fourth parts represent the APF (Automatic Passive Function) penalties for obstacles and road boundaries. The closer the autonomous vehicle is to an obstacle or road boundary, the larger the penalty, guiding the vehicle to avoid obstacles and move away from road boundaries. When an obstacle coincides with the trajectory, obstacle avoidance is prioritized, and the vehicle continues to track the target trajectory after escaping the APF effect.

[0111] The fifth part is the endpoint deviation penalty term, which is an additional independent design for the error of the last trajectory point of the predicted trajectory and the reference trajectory. F is used as the weight matrix to increase the penalty degree of the relative error at the end of the trajectory.

[0112] The above is one cycle of MPC control. After obtaining the optimized system input, it is converted into actual input parameter values. In order to ensure that the input can be quickly responded to and changed when the environment changes, each cycle only takes the optimization result of the first step and inputs it into the unmanned vehicle control, waiting for the next moment to start the cycle again.

[0113] The complete optimization function and hard constraints are shown below:

[0114]

[0115]

[0116] The four constraints represent the linear state equation of the autonomous vehicle, the acceptable range of the vehicle's position coordinates, the acceptable range of the control input, and the allowable deviation range of the input error. Since the obstacle's position changes over time, its potential field influence on the autonomous vehicle also changes over time, requiring recalculation of the potential force influence on the autonomous vehicle at each prediction time.

[0117] The initial solution for MPC control can use all zeros as the system input, or a warm-start method can be used, which takes the unused predicted input values ​​from time steps k+1 to k+step-1 calculated in the previous time step. As the initial solution for the next time step, the control input for the next time step is warm-started based on historical data, thereby accelerating the convergence rate of the optimization variables and improving the optimization effect.

[0118] Using the above process, the design of a multi-vehicle target capture algorithm can be realized.

[0119] The specific embodiments described above only illustrate the design principles of the present invention. The shapes and names of the components in this description may differ and are not limited. Therefore, those skilled in the art can modify or make equivalent substitutions to the technical solutions described in the foregoing embodiments; and these modifications and substitutions do not depart from the inventive spirit and technical solutions of the present invention, and should all fall within the protection scope of the present invention.

Claims

1. A method for encircling and capturing multiple unmanned vehicle targets based on MPC-APF control, characterized in that: Step 1: Using the single-vehicle model centered on the rear axle as the kinematic model, construct the motion state equation of the unmanned vehicle; Step 2: Establish the artificial potential field (APF) within the environment, including the road boundary line APF and the obstacle APF; The obstacle APF is constructed by integrating the artificial potential field effect of obstacle vehicles moving in the same direction and in opposite directions on the unmanned vehicle; The effective range of the APF (Advanced Potential Field) for vehicles moving in the same direction is defined as follows: Taking the center of the obstacle vehicle as the dividing point, design a forward triangular artificial potential field region and a backward triangular artificial potential field region. The furthest effective distance between the front and rear ends of these two artificial potential field regions along the S-axis in the Frenet coordinate system is defined, with the S-axis as the safety distance. Based on this, the speed is dynamically adjusted according to the speed of the driverless vehicle and the obstacle vehicle; The effective range of the APF for vehicles moving in the opposite direction is defined as follows: with the center of the obstacle vehicle as the dividing point, a forward rectangular artificial potential field region and a backward triangular artificial potential field region are designed; forward... The maximum effective distance along the S-axis of the rectangular artificial potential field region is a set value. ; The furthest effective distance along the S-axis of the backward triangular artificial potential field region is the safe distance along the S-axis. Based on this, the speed is dynamically adjusted according to the speed of the driverless vehicle and the obstacle vehicle; Step 3: Transform the target capture problem into a dynamic trajectory tracking problem. Add an APF penalty term based on artificial potential field design to the optimization objective function. Based on the motion state equation of the unmanned vehicle, use model predictive control (MPC) to track and control the dynamic target trajectory. In the design of the APF effective range for vehicles moving in the same direction from obstacles, the furthest effective distance along the S-axis of the rearward triangular artificial potential field region is... and the farthest effective distance along the S-axis of the forward triangular artificial potential field region. The design is as follows: In the formula, The set S-axis safety distance; This is the proportional parameter for the dynamic speed adjustment term; and The speeds are for driverless vehicles and obstacle vehicles, respectively.

2. The multi-unmanned vehicle target capture method based on MPC-APF control as described in claim 1, characterized in that, In the design of the APF effective range of the vehicle moving in the same direction, the furthest effective distance along the S-axis of the rearward triangular artificial potential field region is... Designed with an S-axis safety distance Based on this, dynamic adjustments are made according to the speed difference between the autonomous vehicle and the obstacle vehicle; the maximum effective distance along the S-axis of the forward triangular artificial potential field region. Designed with an S-axis safety distance Based on this, dynamic adjustments are made according to the sum of the speeds of the autonomous vehicle and the obstacle vehicles to reserve buffer space for the safe return of the autonomous vehicle to the road. In the design of the APF effective range of the reverse-moving obstacle vehicle, the furthest effective distance along the S-axis of the rearward triangular artificial potential field region is... Designed with an S-axis safety distance Based on this, dynamic adjustments are made according to the speed difference between the driverless vehicle and the obstacle vehicle.

3. The multi-unmanned vehicle target encirclement method based on MPC-APF control as described in claim 1, characterized in that, In the design of the APF effective range for the obstacle vehicle moving in the same direction, and in the design of the APF effective range for the obstacle vehicle moving in the opposite direction, the furthest effective distance along the L-axis of each triangular artificial potential field region is... The design is as follows: Based on the center of the obstacle vehicle, an axial safety distance of L is expanded to both sides. .

4. The multi-unmanned vehicle target capture method based on MPC-APF control as described in claim 1, characterized in that, The specific method by which the obstacle APF is constructed by integrating the artificial potential field effect of obstacle vehicles moving in the same direction and in opposite directions on the unmanned vehicle is as follows: Calculate the effective range of APF for vehicles moving in the same and opposite directions from the obstacle. Within, the obstacle APF value of each obstacle vehicle to the autonomous vehicle. : in, for k Obstacles j The APF value for autonomous vehicles; Indicates the amplitude of the artificial potential field; For vehicles with obstacles j Location, for k Obstacles j The distance between the center of the vehicle and the center of the driverless car; Add up the obstacle APF values ​​of all vehicles with obstacles to obtain the obstacle APF value within the effective range.

5. The multi-unmanned vehicle target capture method based on MPC-APF control as described in claim 1, characterized in that, The objective function described in step 3 includes the trajectory deviation term before and after optimization, the energy consumption term, the APF penalty term, and the endpoint deviation penalty term.

6. The multi-unmanned vehicle target encirclement method based on MPC-APF control as described in claim 5, characterized in that, The specific optimization objective function is as follows: in, J To optimize the objective function; step represents the time frame contained within a time window in the MPC control; The trajectory deviation term is the sum of multiples of the squared distances between the optimized trajectory and the expected trajectory within the time window. The closer the optimized trajectory is to the reference trajectory, the smaller the trajectory deviation term is. It consists of the state offset at each moment in the time window, where the state offset is the difference between the state values ​​of the predicted trajectory point and the expected trajectory point. For energy consumption, the goal is to achieve the best optimization results while minimizing input energy consumption. for k Time-based control input; The APF penalty term increases as the autonomous vehicle gets closer to the obstacle vehicle. This guides the autonomous vehicle to prioritize obstacle avoidance when the obstacle coincides with its trajectory, and to continue tracking the target trajectory after escaping the APF's influence. The total obstacle APF is calculated by integrating the artificial potential field effects of obstacle vehicles moving in the same and opposite directions on the unmanned vehicle. For adjustment factors; As a penalty term for endpoint deviation, an additional independent design is made for the error of the last trajectory point of the predicted trajectory and the expected trajectory, increasing the penalty degree for the relative error at the end of the trajectory; This is the state offset of the last predicted trajectory point in the time window; Q , R , F All are weight matrices.

7. The multi-unmanned vehicle target capture method based on MPC-APF control as described in claim 5 or 6, characterized in that, The optimization objective function further includes hard constraints, including the motion state equation of the unmanned vehicle, the acceptable range of the unmanned vehicle's position coordinates, the acceptable range of control inputs, and the allowable deviation of input error.

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