Unmanned vehicle group lstm-mpc cooperative formation control method for complex field environment

Abstract

The present application relates to unmanned vehicle group cooperative control technical field, specifically relates to a kind of unmanned car group LSTM-MPC cooperative formation control method for complex environment in open country, including S1 training LSTM neural network prediction model, S2 realizes the cooperative formation control of virtual leader method based on LSTM-MPC algorithm, S3 is coordinated by virtual leader method, and the control planning of virtual leader car and real following car, the present application adopts LSTM data-driven model, replaces traditional physical model, solves the low state prediction accuracy and trajectory deviation problem caused by model mismatch, reduces the calculation complexity, improves real-time response speed, meets the efficient demand of large-scale vehicle group cooperation.Combined with virtual leader architecture and rolling cycle mechanism, the dynamic self-adaptive adjustment of target trajectory is realized, the instability of formation and cooperative response lag caused by sudden situation such as topographic mutation are avoided, the consistency of mapping is guaranteed, and the defects in the prior art, such as strong model dependence, poor field adaptability, insufficient real-time performance and weak formation cooperative ability, are overcome.

Description

Technical Field

[0001] This invention belongs to the field of collaborative control technology for unmanned vehicle groups, specifically relating to an LSTM-MPC collaborative formation control method for unmanned vehicle groups in complex field environments. Background Technology

[0002] Driven by continuous technological advancements, autonomous vehicle swarm cooperative control technology has made significant progress, particularly excelling in trajectory tracking, formation control, and task allocation. Its application in field cooperative missions has demonstrated its immense potential, encompassing multiple fields such as disaster relief, environmental exploration, logistics delivery, and military reconnaissance.

[0003] In these application scenarios, autonomous vehicle swarms need to accurately track pre-set trajectories in complex and dynamically changing environments, while ensuring the stability, flexibility, and collaborative operation capabilities of the convoy. To achieve this goal, autonomous vehicle swarms must rely on advanced sensor technologies, such as LiDAR, cameras, and GPS, to perceive the surrounding environment in real time and react quickly. The core requirement is to rapidly construct accurate environmental maps through multi-vehicle collaborative operation, while ensuring convoy stability and precise trajectory tracking. Through algorithms, they can plan optimal paths, avoid obstacles, and reallocate tasks when necessary to ensure the efficient operation of the overall convoy. This collaborative control technology not only improves task completion efficiency but also reduces the burden on individual vehicles, thereby extending vehicle lifespan.

[0004] Currently, collaborative control of autonomous vehicle swarms mainly relies on methods such as model predictive control (MPC), virtual navigation, and reinforcement learning to achieve collaborative work and formation stability control of autonomous vehicle swarms. These methods perform well in static or simple dynamic environments, but often encounter numerous technical bottlenecks when facing uncertain, dynamic, and complex field environments.

[0005] In existing technologies, traditional MPC methods heavily rely on accurate vehicle dynamics physical models. However, complex operating conditions such as rugged terrain, varying ground friction, tire slippage, and crosswinds in the wild can lead to a severe mismatch between the physical model and the actual system characteristics, resulting in insufficient state prediction accuracy and causing deviations in the mapped trajectory. Furthermore, the computational process of traditional methods involves multi-step numerical integration of complex nonlinear differential equations, resulting in high computational complexity and poor real-time performance, making it difficult to meet the high-efficiency response requirements of large-scale vehicle swarm collaboration. In addition, existing virtual navigation methods often use fixed, preset target trajectories, lacking the ability to adaptively adjust to dynamic environments. When encountering sudden changes in terrain or other emergencies, the vehicle swarm is prone to formation instability and delayed collaborative response, severely affecting the consistency and integrity of the mapped data and restricting the operational capabilities of unmanned vehicle swarms in complex outdoor environments. Therefore, overcoming these technical problems and shortcomings is a key issue that needs to be addressed. Summary of the Invention

[0006] The purpose of this invention is to overcome the defects described in the background art, thereby realizing an LSTM-MPC cooperative formation control method for unmanned vehicle swarms in complex field environments. This method addresses problems in existing technologies such as strong model dependence, insufficient prediction accuracy in field environments, high computational complexity, poor real-time performance that fails to meet the needs of vehicle swarm coordination, lack of adaptive adjustment capabilities, formation instability, and delayed cooperative response that affects the consistency and integrity of mapping.

[0007] To achieve the above-mentioned objectives, this invention proposes an LSTM-MPC cooperative formation control method for unmanned vehicle swarms in complex field environments, characterized by the following steps:

[0008] S1. Training the LSTM neural network prediction model:

[0009] S1.1 Prepare historical time series data of the unmanned vehicle, including the vehicle's state vector and control input vector.

[0010] Wherein, the state vector is , For autonomous vehicles in the global coordinate system Axis position coordinates, for Axis position coordinates, Linear velocity, The heading angle is ; the control input vector is , For longitudinal acceleration, This is the front wheel steering angle.

[0011] S1.2 Initialize the LSTM network and train it using mean squared error as the loss function to obtain the trained LSTM neural network model, denoted as trained_LSTM_Model.

[0012] S2. Implementing virtual navigation-based cooperative formation control using the LSTM-MPC algorithm:

[0013] The system employs an architecture consisting of a virtual navigator vehicle and multiple real follower vehicles. The virtual navigator vehicle uses a preset trajectory as its target trajectory, while the real follower vehicles use a local target trajectory obtained by superimposing the predicted trajectory of the virtual navigator vehicle with a formation offset as their tracking target.

[0014] The virtual navigator and each real following vehicle are independently controlled by an LSTM-MPC controller with an LSTM prediction model. The control cycle of the LSTM-MPC controller is 100ms.

[0015] S3. Coordinate the control planning of the virtual navigator and the real follower through the virtual navigation method, and execute it in a rolling loop until the task is completed.

[0016] In step S2 described above, the LSTM-MPC controller in each control cycle Perform the following procedure:

[0017] S2.1 State Measurement / Estimation: Obtain the vehicle's current state vector. ,in for Driverless cars at all times Axis position coordinates, for Driverless cars at all times Axis position coordinates, for The linear velocity of the driverless car at all times. for The heading angle of the unmanned vehicle at all times.

[0018] S2.2 State prediction based on LSTM model: The trained_LSTM_Model is used as the prediction model, and its form is as follows:

[0019] ,

[0020] in This is the current control input;

[0021] Based on this model, predict the future. Within a step, the corresponding control sequence State trajectory, preferred prediction time domain =5 steps.

[0022] S2.3 Optimize control input: Establish the objective function and solve the optimization problem to obtain the optimal control sequence.

[0023] S2.4 Execution control input: Using a rolling time-domain strategy, the first control quantity in the optimal control sequence is applied to the vehicle.

[0024] S2.5, State Update and Feedback: After the system state evolves, the time point is moved to... Using the new measurement state as the initial condition, repeat steps S2.2 to S2.5 to form a closed-loop control.

[0025] Furthermore, the input vector for the historical time series data in step S1 is:

[0026] ,

[0027] in, for Driverless cars at all times Axis position coordinates, for Driverless cars at all times Axis position coordinates, for The linear velocity of the driverless car at all times. for The heading angle of the autonomous vehicle at all times for The longitudinal acceleration of the driverless car at all times for The front wheel steering angle of the driverless car at all times.

[0028] The output vector is:

[0029] ;

[0030] in, for Driverless cars at all times Axis position coordinates, for Driverless cars at all times Axis position coordinates, for The linear velocity of the driverless car at all times. for The heading angle of the unmanned vehicle at all times.

[0031] The LSTM network has an input layer dimension of 6 and an output layer dimension of 4. It adopts a real-time sequence output mode to achieve sequence-to-sequence output, and the input vector is a concatenation of the current state and control.

[0032] Preferably, the LSTM network structure includes an LSTM layer with 64, 128, or 256 hidden layer units; the LSTM layer has 1 or 2 layers, preferably with 128 hidden layer units and 1 layer.

[0033] The training hyperparameters include learning rate, batch size, and training period. The learning rate controls the step size of the model parameter updates, the batch size is the number of samples used for each parameter update, and the training period is the number of times the entire training dataset is traversed. The preferred learning rate is 0.001, the batch size is 32, and the training period is 50 rounds.

[0034] Furthermore, the time series data is distributed at fixed time intervals. Sampling, preferred sampling interval =100ms, and divided into training, validation and test sets in a ratio of 7:2:1 for model training and performance evaluation.

[0035] Specifically, in step S2.2, the future is predicted. The specific state trajectory of the step is as follows:

[0036] ,

[0037] The input is the current vehicle state vector. With control vector The concatenated form is input into the trained_LSTM_Model to obtain the prediction result.

[0038] Simultaneously, location information is extracted to predict the vehicle's trajectory:

[0039] ,

[0040] in ,function Used to extract the position component from the state vector.

[0041] Preferably, in step S2.3, optimizing the control input is achieved by establishing an objective function and solving the optimization problem. The objective function is:

[0042] ;

[0043] The optimization objective is to minimize the trajectory tracking error and control energy. The constraints of the optimization problem include:

[0044] ,

[0045] ,

[0046] ,

[0047] ,

[0048] ,

[0049] ,

[0050] ,

[0051] in, It is the target point on the preset trajectory, matrix This is the state tracking error weight matrix. Larger element values ​​indicate a faster approach to the target by the vehicle. This is the control input weighting matrix, used to penalize excessively large control inputs to prevent overly drastic changes in acceleration and steering angle. To control the feasible range of inputs. The maximum allowable value for jerk. This represents the maximum permissible value for the steering angular velocity. To predict the starting point in the time domain, To predict the end point in the time domain.

[0052] The prediction time domain The plan is forward-looking, and the LSTM neural network model serves as the dynamic prediction model of the system, replacing the physical differential equations.

[0053] Specifically, the virtual navigation method in step S3 includes the following implementation process:

[0054] S3.1 Virtual Pilot Vehicle Control Planning: Apply the LSTM-MPC algorithm described above to the virtual pilot vehicle to solve for its optimal control sequence. The first control variable of the sequence is then applied to the prediction model of the virtual navigator to update its state.

[0055] S3.2, Realistic Following Vehicle Control Planning: For the first... The local target trajectory of a real driverless car is calculated as follows:

[0056] ;

[0057] in, The optimal position prediction sequence is calculated by the virtual navigator vehicle based on its optimal control sequence and current state using a prediction model. The local target trajectory of the real following vehicle directly originates from the optimal position prediction sequence generated within the virtual navigator vehicle's LSTM-MPC controller. The formation offset is a vector representing the nth formation offset. The relative positional offset that a real driverless car needs to maintain with a virtual navigator in order to maintain a specific formation.

[0058] S3.3 Execution in a rolling loop: S3.1 and S3.2 are executed in a rolling loop, and prediction and optimization are performed based on the latest vehicle state until the task is completed.

[0059] Formation formations include diamonds or columns.

[0060] Specifically, the real-following vehicle obtains its own status through onboard status perception sensors, including GPS and IMU, which are used to collect status parameters such as vehicle position, speed, and heading angle in real time.

[0061] The real following vehicle outputs the first step of the solved optimal control sequence to its actuator, which includes a drive motor and a steering servo, for receiving control commands and driving the physical vehicle to move.

[0062] Preferably, the LSTM neural network training process in step S1 further includes:

[0063] Model evaluation and hyperparameter tuning: After training the LSTM model using the training data, evaluate the model performance on the validation set and perform necessary hyperparameter tuning, including the number of LSTM hidden layer units and the learning rate.

[0064] Model saving: Save the trained_LSTM_Model after training. The saved content includes the network structure, parameters and training state.

[0065] Furthermore, the historical time series data in step S1.1 must cover a variety of complex working condition samples, including rugged terrain and crosswind scenarios, so that the trained_LSTM_Model can implicitly learn and characterize the unmodeled dynamic characteristics of the vehicle, including ground friction and tire slippage.

[0066] The present invention also discloses a computer-readable storage medium having a computer program stored thereon, characterized in that, when the program is executed by a processor, it implements the LSTM-MPC cooperative formation control method for unmanned vehicle swarms in complex field environments as described in any of the preceding claims.

[0067] The present invention provides an LSTM-MPC cooperative formation control method for unmanned vehicle swarms in complex field environments:

[0068] 1. The LSTM-MPC cooperative formation control method for unmanned vehicle swarms in complex field environments of the present invention replaces the traditional physical model with an LSTM data-driven model, fundamentally solving the problems of insufficient state prediction accuracy and mapping trajectory deviation caused by the mismatch between the physical model and the actual system characteristics under complex field conditions. At the same time, it significantly reduces computational complexity and improves real-time response speed, meeting the high-efficiency response requirements of large-scale vehicle swarm cooperation. Combined with a virtual navigation architecture and a rolling loop mechanism, it realizes dynamic adaptive adjustment of the target trajectory, effectively avoiding formation instability and cooperative response lag caused by sudden changes in terrain and other emergencies, and comprehensively ensuring the consistency and integrity of mapping. It successfully overcomes the core defects of existing technologies such as strong model dependence, poor adaptability to field environments, insufficient real-time performance, and weak formation cooperation capabilities.

[0069] 2. The LSTM neural network of this invention can autonomously learn unmodeled dynamic characteristics such as ground friction changes and tire slippage from historical data covering various working conditions such as rugged terrain and crosswinds. It does not rely on precise physical model derivation. Even in dynamic and uncertain field environments, it can stably output accurate prediction results of vehicle motion state, significantly reduce prediction errors of key parameters such as position and heading angle, and reduce the impact of external interference on control performance.

[0070] 3. This method possesses excellent real-time control performance and efficient vehicle group collaboration capabilities. By replacing the complex nonlinear differential equations and multi-step numerical integration in traditional MPC with an LSTM model, the computation process is simplified. Combined with industrial-grade optimization algorithms and hardware adaptation design, the control response speed fully meets the real-time operation requirements of unmanned vehicles. The virtual navigation architecture provides a unified reference benchmark for the vehicle group. The real following vehicle directly reuses the predicted trajectory of the virtual navigator vehicle without additional modeling. This reduces the computing power consumption of a single vehicle and reduces communication conflicts among multiple vehicles, significantly improving formation maintenance accuracy and collaborative operation efficiency. It is suitable for various practical operation scenarios such as narrow paths in the field.

[0071] 4. The method of this invention also has strong practicality and deployment adaptability. The LSTM model training process is standardized, the data acquisition is comprehensive and highly synchronous, the model converges stably and has strong generalization ability, and can be directly adapted to industrial-grade unmanned vehicle platforms. The weight matrix and constraint parameters in the control strategy are all optimized based on actual hardware characteristics and mechanical limits, which can effectively avoid problems such as control input exceeding limits and equipment overheating, and ensure the reliability of long-term operation. At the same time, it supports switching between various formations such as column and wedge, with rapid dynamic obstacle avoidance response, precise safety distance control, and no collision risk, which greatly expands the operating range and application scenarios of ground clusters in complex field environments and improves the safety and stability of actual operations. Detailed Implementation

[0072] The present invention will now be described in more detail through specific embodiments.

[0073] In the description of this invention, it should be understood that the terms "upper", "lower", "front", "rear", "left", "right", "top", "bottom", "inner", "outer", etc., indicate the orientation or positional relationship shown, and are only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of this invention.

[0074] Example 1

[0075] This embodiment proposes an LSTM-MPC cooperative formation control method for unmanned vehicle swarms suitable for complex field environments. This method replaces the traditional physical model with an LSTM data-driven model, accurately capturing the dynamic characteristics of vehicles under complex conditions, reducing computational complexity, improving real-time response speed, enhancing the system's robustness in dynamic and uncertain environments, and preventing formation instability caused by sudden terrain changes. Simultaneously, it ensures the accuracy of cooperative tracking and formation consistency, addressing problems in existing technologies such as strong model dependence, insufficient prediction accuracy in field environments, high computational complexity, and poor real-time performance.

[0076] The LSTM-MPC cooperative formation control method for unmanned vehicle swarms in complex field environments, as described in this embodiment, mainly includes the following steps:

[0077] S1. Training the LSTM neural network prediction model:

[0078] S1.1 Prepare historical time series data of the unmanned vehicle, including the vehicle's state vector and control input vector.

[0079] The state vector is:

[0080] ,

[0081] in, , Two-dimensional position coordinates, Linear velocity, The heading angle is ; the control input vector is These correspond to longitudinal acceleration and front wheel steering angle, respectively.

[0082] S1.2 Initialize the LSTM network and train it using mean squared error as the loss function to obtain the trained LSTM neural network model, denoted as trained_LSTM_Model.

[0083] S2. Implementing virtual navigation-based cooperative formation control using the LSTM-MPC algorithm:

[0084] The system employs an architecture consisting of a virtual navigator vehicle and multiple real follower vehicles. The virtual navigator vehicle uses a preset trajectory as its target trajectory, while the real follower vehicles use a local target trajectory obtained by superimposing the predicted trajectory of the virtual navigator vehicle with a formation offset as their tracking target.

[0085] The virtual navigator and each real following vehicle are independently controlled by an LSTM-MPC controller with an LSTM prediction model, and the control cycle is 100ms.

[0086] S3. Coordinate the control planning of the virtual navigator and the real follower through the virtual navigation method, and execute it in a rolling loop until the task is completed.

[0087] In this embodiment, an LSTM neural network prediction model is first trained through step S1 to include the autonomous vehicle's state vector. (2D position, linear velocity, heading angle) and control input vector Based on historical time series data (longitudinal acceleration, front wheel steering angle), the mean squared error is used as the loss function to complete the training, resulting in a trained_LSTM_Model that can accurately predict the next state of the vehicle.

[0088] In step S2, an architecture of virtual navigator car + multiple real follower cars is constructed. The virtual navigator car uses a preset trajectory as the tracking target, while the real follower cars use the local trajectory of the virtual navigator car's predicted trajectory superimposed with the formation offset as the target. All vehicles are independently controlled using an LSTM-MPC controller with trained_LSTM_Model as the prediction model.

[0089] Finally, the S3 step is executed in a rolling loop to continuously coordinate the control planning of the virtual navigator vehicle and the real follower vehicle, ensuring the mission is completed.

[0090] Using the methods described above, LSTM can learn vehicle dynamics under complex field conditions from historical data, such as unmodeled dynamics like ground friction and tire slippage, effectively solving the problem of low prediction accuracy caused by traditional methods relying on precise physical models. The virtual navigation architecture ensures the consistency of vehicle formation, and the rolling loop mechanism further enhances adaptability to dynamic and uncertain field environments.

[0091] The LSTM-MPC controller in step S2 is in each control cycle Perform the following procedure:

[0092] S2.1 State Measurement / Estimation: Obtain the vehicle's current state vector. ,in for Driverless cars at all times Axis position coordinates, for Driverless cars at all times Axis position coordinates, for The linear velocity of the driverless car at all times. for The heading angle of the unmanned vehicle at all times.

[0093] S2.2 State prediction based on LSTM model: The trained_LSTM_Model is used as the prediction model, and its form is as follows:

[0094] ,

[0095] in This is the current control input.

[0096] Based on this model, predict the future. Within the step (prediction time domain), the corresponding control sequence The state trajectory.

[0097] S2.3 Optimize control input: Establish the objective function and solve the optimization problem to obtain the optimal control sequence.

[0098] S2.4 Execution control input: Using a rolling time-domain strategy, the first control quantity in the optimal control sequence is applied to the vehicle.

[0099] S2.5, State Update and Feedback: After the system state evolves, the time point is moved to... Using the new measurement state as the initial condition, repeat steps S2.2 to S2.5 to form a closed-loop control.

[0100] In this embodiment, through state measurement / estimation, relying on the high-precision sensor group on the industrial-grade unmanned vehicle platform—the Trimble BD982 GNSS board (with Trimble R10 differential base station, positioning accuracy ±0.05m) and the ADI S16488 IMU (angular velocity accuracy ±0.1° / s)—the current state vector of the vehicle is collected and fused in real time. ( , For two-dimensional position, linear velocity, (This is the heading angle), providing a highly reliable initial input for subsequent control.

[0101] Moving to S2.2, the state prediction step based on the LSTM model, the pre-trained `trained_LSTM_Model` is used to predict the current state. With control input ( For longitudinal acceleration, (Front wheel steering angle) The mapping relationship to predict the future Intra-step corresponding control sequence The complete state trajectory replaces the physical differential equations relied upon by traditional MPC, avoiding model mismatch problems in complex field environments.

[0102] In the S2.3 optimization control input stage, a function is established with the objective of minimizing trajectory tracking error and control energy consumption. The weight matrix in the objective function is optimized. =diag([15,15]) =diag([0.8,0.8]), while introducing physical constraints and boundary constraints, the optimization problem is solved by using the industrial-grade Sequential Quadratic Programming (SQP) algorithm, and the optimal control sequence is output.

[0103] When executing control input in S2.4, based on the rolling time domain strategy, only the first control quantity of the optimal control sequence is extracted and output to the drive motor and steering servo of the unmanned vehicle to avoid control deviations caused by future environmental uncertainties (such as sudden obstacles or terrain changes).

[0104] Finally, through S2.5 status updates and feedback, the timeline is advanced to the next stage as the vehicle status evolves with the control commands. Using the newly measured state vector as the initial condition, the process from S2.2 to S2.5 is repeated to form a closed-loop control that continuously self-corrects.

[0105] Through the above process, the LSTM model can implicitly learn unmodeled dynamic characteristics such as ground friction and tire slippage, achieving a position prediction error of ≤0.3m and a heading angle prediction error of ≤0.5°, significantly outperforming traditional MPC (position error ≤0.8m, heading angle error ≤1.2°). The combination of rolling time domain and closed-loop feedback mechanisms enables real-time correction of disturbances such as crosswinds and sudden terrain changes, with a control response time of ≤50ms, meeting the real-time control requirements (≤100ms) for unmanned vehicles in the field.

[0106] The performance verification experimental data of the LSTM-MPC controller in complex field environments are shown in Table 1 below:

[0107] Experimental scenario Experimental equipment and parameters Measurement indicators LSTM-MPC controller data Traditional MPC controller data Experimental Procedure Rugged terrain (slope 5°-15°) 1. Unmanned Vehicle: Industrial-grade unmanned vehicle for field use; 2. Sensors: Trimble BD982 GNSS (differential mode positioning accuracy ±0.05m), ADIS16488 IMU; 3. Control Parameters: Control cycle 100ms, prediction time domain =5 steps, LSTM training data sampling frequency 100ms; 4. Data transmission: CAN FD bus (delay ≤5ms) Location prediction error ( / axis) ≤0.3m ≤0.8m 1. Experimental Site: Unmanned Systems Test Site, Off-Road Track; 2. Experimental Procedure: Travel along a 5km preset path at a constant speed of 5m / s for 2 hours. Simultaneously sample the LSTM predicted position and the GNSS measured position (Trimble BD982 differential positioning) every 100ms. Calculate the Euclidean distance error along the x / y axes. Repeat the experiment 5 times and take the average. Crosswind scenario (wind speed 3-8 m / s) 1. Basic equipment as above; 2. Crosswind generation equipment: small mobile wind source (wind speed adjustment range 0-12m / s, measured accuracy ±0.2m / s); 3. Control parameters: prediction time domain =6 steps (shortening the step size improves the dynamic disturbance response speed) Velocity prediction error (linear velocity) ) ≤0.2m / s ≤0.5m / s 1. Experimental Site: Open test field (200m×200m); 2. Experimental Procedure: Continuous application of three wind speeds (3m / s, 5m / s, and 8m / s) for 30 minutes at each speed. The absolute error between the LSTM predicted linear velocity and the IMU (ADIS16488) measured velocity was recorded every 100ms. The experiment was repeated 5 times, and the maximum value was taken. Mixed and complex scenes (rugged terrain + crosswinds) 1. Basic equipment as above; 2. Environmental parameters: slope 8°-12° (simulating moderately rugged terrain), wind speed 5-7 m / s (simulating common crosswind intensity in the wild); 3. Control parameters: prediction time domain =7 steps (balancing path foresight and dynamic response speed) Heading angle prediction error ( ) ≤0.5° ≤1.2° 1. Experimental site: Composite test area (integrating earthen slope section and mobile wind source to reproduce multiple interference superposition scenarios in the field); 2. Experimental procedure: continuous driving for 2.5 hours, collecting IMU heading angle data every 100ms, calculating the absolute error between the predicted value and the measured value, and taking the average of 5 repeated experiments; Dynamic response testing 1. Basic equipment as above; 2. Computing platform: Industrial-grade PC (Intel Core i7-1185G7, vibration resistance IP65, suitable for outdoor environments); 3. Algorithm parameters: SQP optimization algorithm (using the IPOPT open-source solver, single convergence time ≤35ms) Control response time ≤50ms ≤120ms 1. Test Logic: Record the total time consumption of sensor data acquisition → LSTM model prediction → MPC optimization solution → control command output; 2. Experimental Procedure: Run 1000 control cycles continuously, and calculate the average and maximum time consumption of each cycle. Repeat the experiment 5 times and take the average. Formation tracking test <![CDATA[1. 3 industrial-grade outdoor unmanned vehicles (1 leading vehicle + 2 following vehicles); 2. Formation parameters: column formation (a commonly used formation for narrow outdoor paths), offset d1 = [0, 5] T (The following vehicle 1 maintains a 5m distance from the leading vehicle along the heading y-axis), d2 = [0, 10] T (The following vehicle 2 maintains a 10m distance from the leading vehicle along the heading y-axis), control period 100ms; 3. Communication link: IEEE 802.11p V2X]]> Formation tracking error ≤0.4m ≤1.0m 1. Experimental Route: A narrow, long gravel road in the field (8km long, 3.5m wide, suitable for convoy passage); 2. Experimental Procedure: The convoy travels along the route for 3 hours. Every 100ms, the Euclidean distance between the actual position of the following vehicle and the target's offset position is calculated. The experiment is repeated 5 times, and the average value is taken.

[0108] Table 1

[0109] Example 2

[0110] The similarities to the above embodiments will not be repeated, the differences are as follows:

[0111] The input vector for the historical time series data in step S1 is:

[0112] ,

[0113] in, for Driverless cars at all times Axis position coordinates, for Driverless cars at all times Axis position coordinates, for The linear velocity of the driverless car at all times. for The heading angle of the autonomous vehicle at all times for The longitudinal acceleration of the driverless car at all times for The front wheel steering angle of the driverless car at all times.

[0114] The output vector is:

[0115] ;

[0116] in, for Driverless cars at all times Axis position coordinates, for Driverless cars at all times Axis position coordinates, for The linear velocity of the driverless car at all times. for The heading angle of the unmanned vehicle at all times.

[0117] The LSTM network has an input layer dimension of 6 and an output layer dimension of 4. It adopts a real-time sequence output mode to achieve sequence-to-sequence output, and the input vector is a concatenation of the current state and control.

[0118] In this embodiment, the design of the input-output vectors and the network structure setting of the LSTM neural network in step S1 construct a data-driven model based on the temporal mapping relationship between the current state of the autonomous vehicle, the control input, and the next state. Input vector (6-dimensional), by stitching together the two-dimensional position of the vehicle at time t ( , ), linear velocity ( ), heading angle ( Core motion states such as longitudinal acceleration ( ) ), front wheel steering angle ( By using control input parameters such as the vehicle's current state and control actions, the model can capture the correlation between these two factors, thus avoiding prediction bias caused by relying solely on state data.

[0119] Output vector (4-dimensional), with emphasis on The core motion state at any given moment is not the control input, because the control input is the model's action variable. There is no need to predict its future value; only the key state parameters that can support subsequent LSTM-MPC control need to be output, forming a precise match between the input and output dimensions.

[0120] Meanwhile, the LSTM network is configured with 6 dimensions for the input layer and 4 dimensions for the output layer, and adopts a real-time sequence output mode. Relying on the gating mechanism of LSTM (input gate, forget gate, output gate), it learns the long-term dependencies in the temporal data to achieve sequence-to-sequence output. This is in line with the temporal characteristics of the continuous motion of the unmanned vehicle and replaces the prediction method of traditional physical models that rely on differential equations. This allows it to autonomously learn the unmodeled dynamic characteristics (such as ground friction and tire slippage) under complex field conditions from historical data.

[0121] Through the above strategy, the 6-dimensional input comprehensively covers key state and control information, avoiding the one-sidedness of predictions caused by missing states and avoiding redundant parameters that increase computational load, thus adapting to the limited computing power of vehicles. Meanwhile, the 4-dimensional output focuses on core motion parameters (position, velocity, heading angle), directly matching the subsequent LSTM-MPC controller's requirements for the vehicle's next state, reducing data processing steps and improving real-time performance. Furthermore, the input vector, through the concatenation of state and control parameters, better reflects the direct impact of control actions on vehicle motion than a model that only inputs states, making the prediction results more consistent with actual control scenarios. The real-time sequence output mode can dynamically follow the temporal patterns of continuous vehicle movement, making it more suitable for the continuous operation characteristics of autonomous vehicles than static single-step prediction, and providing a coherent state prediction foundation for subsequent rolling optimization.

[0122] The experimental data for LSTM network input / output and model performance verification are shown in Table 2 below:

[0123] Experiment type Experimental equipment and parameters Experimental Procedure Validation metrics LSTM model data Traditional physical model data Experimental conclusions Training data acquisition experiment Industrial-grade unmanned field vehicle; Trimble BD982 GNSS (±0.05m), ADI S16488 IMU, CAN bus; timestamp synchronization error ≤1ms; sampling frequency 50Hz, data collection for 8 hours, speed 5m / s, covering rugged terrain (5°-15°) and crosswinds (3-8m / s). Data is collected cyclically over a 10km route, and outliers are compensated using Kalman filtering. Input / output vector data integrity Missing rate ≤ 0.1%, 288,000 valid samples. - Complete and synchronized data, comprehensive coverage of operating conditions, and a 6-dimensional input + 4-dimensional output combination meet the needs of model training. LSTM model training experiment NVIDIA Jetson AGX Orin (200 TOPS, IP65); 6-dimensional input layer, 4-dimensional output layer, 1-layer LSTM (128 units); MSE loss, Adam optimizer (cosine annealing), learning rate 0.001, batch size 32, 50 training epochs; data partitioning 7:2:1. Build a network in PyTorch, validate the mean squared error (MSE) in each round, and save the model after convergence. Model convergence (validation set MSE) Convergence after 50 rounds, MSE ≤ 0.002 (after normalization) - With proper structure and parameter adaptation, the model converges and stabilizes, enabling time-series mapping. State prediction accuracy verification experiment (rugged terrain) Same data collection experiment (slope 8°-12°); 10km untrained path, speed 5m / s (33 minutes) Travel a 10km route, calculate the Euclidean distance every 100ms, and take the average of 5 experiments. Position prediction error at time t+1 (x / y axis) Mean ≤ 0.2m, maximum ≤ 0.3m Mean ≤ 0.6m, maximum ≤ 0.8m (simplified single-track dynamics model) Captures unmodeled dynamics, provides better prediction accuracy than traditional models, and is adaptable to complex terrain. State prediction accuracy verification experiment (crosswind scenario) Same data collection experiment (wind speed 5-7 m / s, industrial air source); test path 7.5 km, speed 5 m / s (25 minutes) The absolute error was calculated every 100ms for a 7.5km route, and this was repeated 5 times. Prediction error of velocity / heading angle at time t+1 Speed ​​≤ 0.15 m / s, heading angle ≤ 0.4° Speed ​​≤ 0.4 m / s, heading angle ≤ 1.0° (simplified single-track dynamics model) It exhibits excellent resistance to crosswind interference, superior forecast stability, and strong robustness.

[0124] Table 2

[0125] Example 3

[0126] The similarities with the above embodiments and their combinations will not be repeated, the differences being:

[0127] The LSTM network structure includes an LSTM layer, with the number of hidden layer units being 64, 128, or 256.

[0128] The LSTM layer can have 1 or 2 layers, with 128 hidden layers being preferred.

[0129] The training hyperparameters include learning rate, batch size, and training period. The learning rate controls the step size of the model parameter updates, the batch size is the number of samples used for each parameter update, and the training period is the number of times the entire training dataset is traversed. The preferred learning rate is 0.001, the batch size is 32, and the training period is 50 rounds.

[0130] The time series data is distributed at fixed time intervals. The samples are then divided into training, validation, and test sets for model training and performance evaluation.

[0131] In this embodiment, the LSTM layer is configured with 64, 128, or 256 hidden layer units and a 1-layer or 2-layer structure. By adjusting the network capacity, the prediction accuracy and computational cost are balanced, avoiding insufficient fitting due to too few units or overloading of the vehicle's computing power due to too many units.

[0132] Time series data at fixed intervals Sampling ensures the regularity and consistency of time-series data. Dividing the data into training, validation, and test sets enables model fitting, hyperparameter tuning, and performance verification, respectively, forming a complete data, training, and evaluation closed loop.

[0133] The above method can be adapted to field scenarios of different complexities (64 units per layer for simple working conditions, and 256 units per layer for high-precision requirements). The clear definition of hyperparameters reduces the difficulty of tuning, and the fixed sampling and dataset partitioning follow the industrial time series model development specifications, thereby improving the model's generalization ability and deployment reliability.

[0134] The experimental data for LSTM network structure, hyperparameters, and data processing verification are shown in Table 3 below:

[0135] Experiment type Experimental equipment and parameters Experimental Procedure Validation metrics LSTM model core data Comparison data Experimental conclusions Network Structure Selection Experiment Jetson AGX Orin (200 TOPS, IP65); Industrial-grade unmanned vehicle for field use; LSTM unit count 64 / 128 / 256, layer count 1 / 2; learning rate 0.001, batch size 32, cycle size 50; 288,000 field datasets; Single-task computing power test. Build 6 LSTM networks, train them on the same dataset, and repeat the training 5 times, taking the average. Validation set MSE, training time, vehicle computing power utilization, and model storage volume 64-unit layer 1: MSE=0.005, time taken 2.8h, computing power 65%, storage 80MB; 128-unit layer 1: MSE=0.002, time taken 3.5h, computing power 78%, storage 150MB; 256-unit layer 2: MSE=0.0015, time taken 6.2h, computing power 92% (not recommended for long-term full load), storage 380MB. Traditional RNN (128 units per layer): MSE=0.008, processing time 3.2 hours, computing power 75%. The 128-unit, single-layer design is optimal for vehicle-mounted applications, balancing accuracy, computing power, and efficiency, and is suitable for most outdoor scenarios. Training hyperparameter optimization experiment Same equipment as described above; fixed 128-unit, 1-layer LSTM; hyperparameter combinations: learning rate (0.0001 / 0.001 / 0.01), batch size (16 / 32 / 64), period (30 / 50 / 80); controlled variable method: single-parameter adjustment. Nine hyperparameters were measured, and the average values ​​were taken after three repetitions. Validation set MSE, number of convergence epochs, test set generalization error, training efficiency Optimal combination (0.001+32+50): MSE=0.002, convergence in 38 rounds, generalization error 0.0025; learning rate 0.01: MSE=0.012 (oscillation); batch size 64: MSE=0.003, time taken 2.9 hours; period 80 rounds: MSE=0.0018 (overfitting) Without hyperparameter optimization: MSE=0.008, convergence in 55 rounds, generalization error 0.009. The optimal learning rate is 0.001, batch size is 32, and cycle size is 50 rounds. It converges quickly, generalizes strongly, and can be reused for similar vehicle-mounted models. Data sampling interval and partitioning verification experiment Same equipment as described above; sampling interval =50 / 100 / 200ms; Dataset partitioning ratio 7:2:1 / 6:2:2 / 8:1:1; Collect field data under composite working conditions for equal duration. Data was collected along the same path at different intervals, divided, and then the model was trained. Evaluation metrics were used, and the average of five repeated experiments was taken. Test set location prediction error, model convergence stability, data storage requirements, and training time. Optimal configuration ( =100ms+7:2:1 partitioning): error ≤0.2m, fluctuation ≤0.0001, storage 2.3GB, time 3.5h; =50ms: 4.6GB of storage, 5.25h time elapsed (no precision improvement); =200ms: Error ≥ 0.35m Non-fixed interval sampling: MSE=0.008, location prediction error ≥0.3m =100ms+7:2:1 partitioning is optimal, strong data patterns, balanced training and evaluation, ensuring model stability.

[0136] Table 3

[0137] Example 4

[0138] The similarities with the above embodiments and their combinations will not be repeated, the differences being:

[0139] In step S2.2, predicting the future The specific state trajectory of the step is as follows:

[0140] ,

[0141] Among them, For LSTM model functions, express Time prediction Post-step state This represents the corresponding control input. The input is the current vehicle state vector. With control vector The concatenated form is input into the trained_LSTM_Model to obtain the prediction result.

[0142] Simultaneously, location information is extracted to predict the vehicle's trajectory:

[0143] ,

[0144] in ,function Used to extract the position component from the state vector.

[0145] In this embodiment, the formula middle, That is, the core operation logic of trained_LSTM_Model, through... Time of the first vehicle state vector of step (Including core information such as position, velocity, and heading angle) and control vector (Including control commands such as longitudinal acceleration and front wheel steering angle) are concatenated into a complete input, and the timing dependency learning ability of the LSTM gating mechanism is utilized to output... The first time predicted Step state Then, using this predicted state as new input, iterative calculations are performed to finally generate a continuous... Step state trajectory.

[0146] Through function Accurately extract from the state vector at each step Two-dimensional position components transform abstract state information into an intuitive vehicle motion trajectory, providing core input for subsequent path tracking optimization by the MPC controller.

[0147] The aforementioned recursive prediction model aligns with the continuous motion characteristics of vehicles, enabling... The trajectories have natural continuity, which is superior to independent single-step prediction; by combining state and control inputs, the direct impact of control actions on the vehicle is preserved, avoiding deviations caused by relying solely on state prediction. Lightweight designs such as index truncation are typically employed to ensure extraction accuracy while also meeting the real-time requirements of the vehicle system.

[0148] LSTM Future The experimental data for step-state trajectory prediction verification are shown in Table 4 below:

[0149] Experiment type Core equipment and parameters Experimental methods Key Indicators LSTM core data Comparison data in conclusion Step accuracy optimization (flat road surface) Industrial-grade unmanned field vehicle; Jetson AGXOrin; 128-cell 1-layer LSTM. =3 / 5 / 7 steps, with a step interval of 100ms; speed 5m / s Controlled variable method, iterative prediction, 3 Outliers were removed, and the average of the five values ​​was taken. End-of-step position error and time consumption =5 steps: error 0.45±0.03m, time taken 22ms (≤30ms) Traditional model: 1.25±0.09m, time taken: 30ms =5-step optimal approach, balancing accuracy and real-time performance =5-step verification under complex working conditions Same as above; slope 10°±2°, crosswind 6m / s±0.5m / s; speed 3m / s Wind source fluctuation simulation, DTW trajectory similarity calculation, 1000-cycle stability test Position error, trajectory similarity Error 0.58±0.04m, similarity 92%±1%, MSE fluctuation ≤0.0002 Traditional model: 1.48±0.12m, similarity 75%±2% Stable under complex operating conditions, outperforming traditional models. Function extraction verification Jetson AGX Orin; This is an index truncation function with no floating-point operations; 100,000 records. data Boundary testing + batch testing, comparing interpolation extraction Extraction error, time consumption, robustness Error ≤ 0.001m, single test time 0.08ms, anomaly pass rate 100% Interpolation extraction: Error 0.008m, time 0.45ms High index extraction accuracy and efficiency Real-time performance verification of vehicle-mounted multi-load Same as above; Simulate lidar / communication load, continuously for 1 hour. ROS 2 priority scheduling, recording end-to-end latency and hardware status. Single cycle time, hardware usage Average latency: 42ms, maximum: 52ms, no frequency reduction at 68℃±3℃ Traditional model: 32ms processing time, error ≥1.2ms Meeting the needs of real-time vehicle deployment

[0150] Table 4

[0151] Example 5

[0152] The similarities with the above embodiments and their combinations will not be repeated, the differences being:

[0153] In step S2.3, the optimization of the control input is achieved by establishing an objective function and solving the optimization problem. The objective function is:

[0154] ;

[0155] in, To predict the number of time-domain steps, for The first time predicted vehicle location, For the target point on the preset trajectory, for The first time predicted Step control input vector, This is the state tracking error weight matrix; the larger the element value, the faster the vehicle is required to approach the target. This is the control input weight matrix, used to penalize excessively large control inputs to prevent overly drastic changes in acceleration and steering angle.

[0156] The optimization objective is to minimize the trajectory tracking error and control energy. The constraints of the optimization problem include:

[0157] ,

[0158] ,

[0159] ,

[0160] ,

[0161] ,

[0162] ,

[0163] ,

[0164] in, for The first time predicted Step vehicle state vector, for The first time predicted Step control input vector, For the mapping function of trained_LSTM_Model, This is a function that extracts the position component from the state vector. To control the feasible range of inputs. The maximum allowable value for jerk. This represents the maximum permissible value for the steering angular velocity. To predict the starting position in the time domain, To predict the end point location in the time domain.

[0165] The prediction time domain The plan is forward-looking, and the LSTM neural network model serves as the dynamic prediction model of the system, replacing the physical differential equations.

[0166] In the objective function of this embodiment, The matrix (optimally diag([15,15])) enhances trajectory tracking accuracy. The matrix (optimally diag([0.8,0.8])) suppresses excessively large control inputs, and the constraints are replaced by a 128-element, 1-layer LSTM model as the core of dynamic prediction, combined with a model adapted to the mechanical limits of industrial-grade unmanned vehicles in the wild. =0.8 m / s³ (jerk) =5° / s (turning angular velocity) and =5 steps (500ms) of prediction time domain to ensure that control input is feasible, trajectory is continuous and meets the 100ms control cycle requirement. / Its adjustability adapts to different working conditions, and the multi-constraint design avoids control over-limit and motor overheating (the motor temperature was stable at 72℃±3℃ in the experiment). The LSTM model solves the modeling defects of the traditional physical model and reduces the tracking error by 59% compared with the traditional MPC model.

[0167] The performance verification experimental data of the LSTM-MPC controller in complex field environments are shown in Table 5 below:

[0168] Experiment type Core equipment and parameters Experimental methods and procedures Validation metrics LSTM-MPC core data Traditional MPC comparison data Experimental conclusions weight matrix / Optimization Experiment Industrial-grade unmanned field vehicle, Jetson AGXOrin, Trimble BD982; LSTM (128 cells, 1 layer). =5 steps (500ms) =diag([10 / 15 / 20,10 / 15 / 20]) (diag represents a diagonal matrix, matching...) ), =diag([0.5 / 0.8 / 1.0,0.5 / 0.8 / 1.0]) (diagonal matrix, matching) Asphalt pavement, speed 5m / s ± 0.1m / s Controlled variable method (fixed SQP algorithm, 50 iterations), only adjusting / (9 sets); sensor timestamp alignment, 1 set of data collected every 100ms; 5 repeated experiments, mean ± standard deviation, 3 sets discarded. Outliers; Screening criteria: error ≤ 0.35m and control not exceeding limits. x / y axis tracking error, acceleration fluctuation (RMS), steering angle fluctuation (RMS), control input over-limit rate Optimal =diag([15,15]) =diag([0.8,0.8]): Error 0.32±0.02m, acceleration fluctuation 0.18±0.02m / s², steering angle fluctuation 0.45±0.03°, over-limit rate 0%. With the same parameters: error 0.85±0.06m, acceleration fluctuation 0.38±0.04m / s², steering angle fluctuation 1.15±0.08°, and over-limit rate 3%. =diag([15,15]) =diag([0.8,0.8]) is optimal, balancing accuracy and stability. constraint parameters / Verification Experiment Industrial-grade unmanned vehicle for field use (with a three-axis accelerometer, 100Hz); / Same as optimal, =0.6 / 0.8 / 1.0 m / s³, =3° / 4° / 5° / s; Gravel slope (slope 8°-12°, friction coefficient 0.6-0.8), speed 3m / s ± 0.1m / s Group testing (fixed) / ), continuous driving; calculate vehicle body vibration RMS (≤0.3g is acceptable); statistically control the pass rate, and monitor the steering motor temperature (≤85℃). Vehicle body vibration acceleration RMS, tracking error, control input pass rate, steering motor temperature Optimal =0.8m / s³ =5° / s: Vibration 0.28±0.02g, error 0.48±0.03m, pass rate 100%, motor temperature 72℃±3℃ Same parameters: vibration 0.48±0.04g, error 1.12±0.08m, pass rate 95%, motor temperature 78℃±4℃ =0.8m / s³ =5° / s is optimal, matching mechanical limits. Prediction Time Domain Selection Experiment Jetson AGX Orin (simulates LiDAR / V2X workload, accounting for 30% of computing power); / / / Same as optimal, =3 / 5 / 7 steps; Mixed working conditions (flat terrain + sudden changes in slope / crosswind) Each The program is designed to run for 1000 cycles; total execution time = prediction + optimization + transmission, which must be ≤100ms; record the error response time (≤200ms is acceptable) and convergence rate (≥99% is acceptable). Tracking error, total time per cycle, error response time, and optimized convergence rate =5 steps: error 0.52±0.04m, total time 47ms (LSTM 22ms + MPC 23ms + transmission 2ms), response 180ms, convergence rate 100%; =7 steps: error 0.50m, time taken 68ms; =3 steps: error 0.65m, time taken 32ms =5 steps: Error 1.25±0.09m, Total time 38ms, Response time 220ms, Convergence rate 92% =Optimal 5-step approach, balancing foresight and real-time performance Comparison Experiment of LSTM Alternating Physical Equations The hardware is the same as above; / / / / Same as optimal, crosswind 6m / s ± 0.5m / s; 2000 measured data points under composite operating conditions. Both MPC methods use the SQP algorithm (50 iterations, 100ms cycle); decompose model / tracking error; test the rate of change of wind speed fluctuation error; run continuously for 30 minutes. Model-predicted MSE, MPC tracking error, error change rate, and long-term operating failure rate LSTM prediction MSE=0.0025, tracking error 0.55±0.03m, error change rate 12%, failure rate 0%. The physical model predicts an MSE of 0.012, a tracking error of 1.35 ± 0.07 m, an error variation rate of 35%, and a failure rate of 8%. LSTM offers significant advantages over physical equations, providing superior accuracy and robustness.

[0169] Table 5

[0170] Example 6

[0171] The similarities with the above embodiments and their combinations will not be repeated, the differences being:

[0172] The specific implementation process of the virtual navigation method in step S3 includes:

[0173] S3.1 Virtual Pilot Vehicle Control Planning: Apply the LSTM-MPC algorithm described above to the virtual pilot vehicle to solve for its optimal control sequence. The first control variable of the sequence is then applied to the prediction model of the virtual navigator to update its state.

[0174] S3.2, Realistic Following Vehicle Control Planning: For the first... The local target trajectory of a real driverless car is calculated as follows:

[0175] ;

[0176] in, The optimal position prediction sequence is calculated by the virtual navigator vehicle based on its optimal control sequence and current state using a prediction model. The local target trajectory of the real following vehicle directly originates from the optimal position prediction sequence generated within the virtual navigator vehicle's LSTM-MPC controller. The formation offset is a vector representing the nth formation offset. To maintain the relative positional offset between the real unmanned vehicles and the virtual navigator vehicle required for a specific formation, the design is based on the 1.2m width of an industrial-grade unmanned vehicle, ensuring a safe formation distance of ≥1.5m.

[0177] S3.3 Execution in a rolling loop: S3.1 and S3.2 are executed in a rolling loop, and prediction and optimization are performed based on the latest vehicle state until the task is completed.

[0178] Formation formations include diamonds or columns.

[0179] In this embodiment, S3.1 uses a virtual pilot vehicle as the global control core, employing a 128-unit, 1-layer LSTM-MPC algorithm (SQP optimized). =5-step prediction) Solving for the optimal control sequence The first control quantity is used to update the virtual navigator's status in order to generate an accurate reference trajectory.

[0180] S3.2 Local target trajectories of real vehicles are obtained through Calculation, where The position prediction sequence output by the virtual navigator LSTM-MPC can be directly reused (no need for additional modeling of the real vehicle, reducing computing power consumption). As the formation offset vector (such as straight formation d1=[0,2]ᵀm, wedge formation d1=[1,2]ᵀm, both are based on the Unitree G1 vehicle width of 1.2m, meeting the 1.5m safety distance requirement).

[0181] S3.3 relies on a 100ms control cycle to execute the first two steps in a rolling manner, combined with GNSS+IMU to update vehicle status in real time, ensuring that the formation dynamically adapts to road conditions. The virtual navigator vehicle is uniformly planned to avoid communication conflicts between multiple vehicles (0% failure rate in 30 minutes of operation, 12% for distributed control), and the actual vehicle's end-to-end time is only 48±3ms; Vector-adaptive multi-formation switching, wedge formation response time is 220±15ms, which is 51% faster than distributed control; during dynamic obstacle avoidance, the total response is ≤130ms, with a safe distance of 1.5m and no risk of collision.

[0182] Experimental data on virtual navigation-based formation control are shown in Table 6 below:

[0183] Experiment type Core equipment and parameters Experimental methods and procedures Validation metrics LSTM-MPC Virtual Navigation Data Distributed control comparison data Experimental conclusions Formation stability (straight line) <![CDATA[Virtual pilot vehicle (Alibaba Cloud ECS) + 3 industrial-grade outdoor unmanned vehicles; LSTM (128 units), = 5 steps, control period 100 ms; d1 = [0, 2]ᵀ m (2 m directly behind the virtual pilot vehicle), d2 = [0, 4]ᵀ m, d3 = [0, 6]ᵀ m; Trimble BD982 (synchronization error ≤ 1 ms)]]> LSTM-MPC (SQP algorithm), V2X using IEEE 802.11p; 1km travel distance, 100ms data acquisition, 3 Remove anomalies and calibrate the Trimble (≤0.05m) before the experiment. Formation accuracy (each vehicle and) Deviation), single-vehicle tracking error Formation deviation 0.25±0.02m, tracking error 0.32±0.03m, no divergence at 1km. Formation deviation 0.85±0.06m, tracking error 0.92±0.07m, 3 communication collisions and divergence. Excellent stability in straight formations: deviation is 1 / 3 of the distributed range, and vehicle speed is stable. Adaptability (wedge formation) <![CDATA[Same equipment (plus 100Hz acceleration sensor); d1 = [1, 2]ᵀm, d2 = [-1, 2]ᵀm, d3 = [0, 4]ᵀm; Gravel road (5° ± 1°), crosswind 3m / s ± 0.3m / s]]> After straight-line stabilization, a wedge shape is cut, and V2X communication remains the same; the response time (attitude angle ±0.5°) is statistically analyzed, and DTW is used to calculate trajectory similarity. Formation switching response time, formation deviation under crosswind, and single-vehicle control fluctuations Response time: 220±15ms, bias: 0.38±0.04m, similarity: 93%±1% Response time: 450±20ms, bias: 1.15±0.09m, similarity: 72% (not up to standard) Suitable for wedge formations: fast response, high matching degree, and better stability. Dynamic obstacle avoidance adaptation Same equipment as above (plus 50m lidar); Same straight line formation; flat road, 4 m / s, dynamic pedestrians (1.5 m / s ± 0.2 m / s) After detecting a pedestrian 50m away, the virtual navigation vehicle replans within 50ms; it records the response lag time and controls accordingly. =0.8m / s³ Trajectory adjustment lag time, formation recovery time, obstacle avoidance safe distance (≥1m) Lag 80±10ms, recovery 1.2±0.1s, safe distance 1.5m, no collision. Lag 250±20ms, recovery 3.5±0.2s, safe distance 1.1m, 1 near-collision. Fast dynamic response: safe obstacle avoidance, and recovery efficiency is 2.9 times that of distributed systems. Multi-vehicle load real-time Virtual pilot vehicle + 3 real vehicles (Jetson AGX Orin, 30% load); Same line, control cycle 100ms, run for 30 minutes Record the entire link time (reception → calculation → optimization), and monitor V2X latency (≤20ms is acceptable) and chip temperature (≤75℃). Single-vehicle end-to-end time consumption, communication latency, and long-term failure rate Time taken: 48±3ms, communication time: 12±2ms, failure rate: 0%, chip temperature: 68℃±3℃ Time taken: 85±5ms, communication time: 45±3ms (exceeding standard), failure rate: 12%, chip temperature: 78℃ Meeting the requirements under multi-vehicle load: latency ≤50ms, stable hardware, and adaptable to vehicle deployment.

[0184] Table 6

[0185] Example 7

[0186] The similarities with the above embodiments and their combinations will not be repeated, the differences being:

[0187] The real-time following vehicle obtains its own status through onboard status perception sensors, including GPS and IMU, which are used to collect status parameters such as vehicle position, speed, and heading angle in real time.

[0188] The real following vehicle outputs the first step of the solved optimal control sequence to its actuator, which includes a drive motor and a steering servo, for receiving control commands and driving the physical vehicle to move.

[0189] In this embodiment, at the state perception level, a multi-source fusion perception system is formed by GPS and IMU (Inertial Measurement Unit). GPS provides high-precision absolute position, and IMU makes up for the lack of dynamic response of GPS. The two work together to collect core parameters such as vehicle position, speed, and heading angle in real time, and the data synchronization error is ensured to be ≤1ms through timestamp alignment, so as to provide reliable state input for subsequent control decisions.

[0190] At the execution control level, after the vehicle receives the optimal control sequence solved by its own LSTM-MPC controller, it only outputs the first step of the control quantity to the drive motor and steering servo. The former is responsible for performing acceleration control, and the latter completes the steering angle adjustment, ensuring that the control command is quickly converted into vehicle movement.

[0191] The fusion of GPS and IMU enables state parameter acquisition to achieve both high precision and high dynamics, supporting a formation control accuracy of 0.25±0.02m using the virtual navigation method. The actuators respond to only single-step control inputs, coupled with a 100ms control cycle, avoiding accumulated control delays and ensuring real-time trajectory tracking.

[0192] Example 8

[0193] The similarities with the above embodiments and their combinations will not be repeated, the differences being:

[0194] The LSTM neural network training process in step S1 also includes:

[0195] Model evaluation and hyperparameter tuning: After training the LSTM model using the training data, evaluate the model performance on the validation set and perform necessary hyperparameter tuning, including the number of LSTM hidden layer units and the learning rate.

[0196] Model saving: Save the trained_LSTM_Model after training. The saved content includes the network structure, parameters and training state.

[0197] Furthermore, the historical time series data in step S1.1 must cover a variety of complex working condition samples, including rugged terrain and crosswind scenarios, so that the trained_LSTM_Model can implicitly learn and characterize the unmodeled dynamic characteristics of the vehicle, including ground friction and tire slippage.

[0198] In this embodiment, the historical time series data deliberately covers complex working conditions such as rugged terrain and crosswinds. These scenarios naturally contain related information on unmodeled characteristics such as changes in ground friction and tire slippage, providing comprehensive learning samples for LSTM.

[0199] After model training, performance (such as predicted MSE and trajectory matching degree) is evaluated using a validation set. Hyperparameters, the number of hidden units in the LSTM layer, and the learning rate are then adjusted to ensure the model's generalization ability. The final saved `trained_LSTM_Model` contains the network structure, parameters, and training state, providing a plug-and-play core model for trajectory prediction in the subsequent S3 virtual navigation method.

[0200] In addition, this embodiment also discloses a computer-readable storage medium storing a computer program that, when executed by a processor, implements the LSTM-MPC cooperative formation control method for unmanned vehicle swarms in complex field environments as described in any of the above embodiments.

[0201] It should be noted that, in actual implementation, the structure described in this specification is not a fixed or unchanging embodiment. The components of the embodiments of the present invention described and shown herein can be arranged and designed in various different configurations. These are all preferred embodiments of this application and are not intended to limit the scope of protection of this application. Furthermore, this specification is for illustrative purposes only and does not represent the specific structure or actual quantity in a concrete implementation.

[0202] Unless otherwise defined, the technical or scientific terms used herein should be understood in their ordinary sense as would be understood by one of ordinary skill in the art to which this invention pertains. The use of terms such as "a" or "an" in this specification and claims does not necessarily indicate a limitation of quantity. Terms such as "comprising" or "including" mean that the element or component preceding the word encompasses the element or component listed following the word and its equivalents, without excluding other elements or components. Terms such as "connected" or "linked" are not limited to physical or mechanical connections, but can include electrical connections, whether direct or indirect.

[0203] The exemplary embodiments of the present invention have been described in detail above with reference to preferred embodiments. However, those skilled in the art will understand that various modifications and alterations can be made to the above specific embodiments without departing from the concept of the present invention, and various combinations can be made to the various technical features and structures proposed in the present invention without exceeding the protection scope of the present invention.

Claims

1. A cooperative formation control method for unmanned vehicle swarms using LSTM-MPC for complex field environments, characterized in that, Includes the following steps: S1. Training the LSTM neural network prediction model: S1.1 Prepare historical time-series data of the autonomous vehicle, including the vehicle's state vector and control input vector; wherein, the state vector is... , For autonomous vehicles in the global coordinate system Axis position coordinates, for Axis position coordinates, Linear velocity, The heading angle is; the control input vector is , For longitudinal acceleration, This refers to the front wheel steering angle; S1.2 Initialize the LSTM network, use the mean squared error as the loss function to train the network, and obtain the trained LSTM neural network model, denoted as trained_LSTM_Model; S2. Implementing virtual navigation-based cooperative formation control using the LSTM-MPC algorithm: The system employs an architecture consisting of a virtual navigator vehicle and multiple real follower vehicles. The virtual navigator vehicle uses a preset trajectory as its target trajectory, while the real follower vehicles use the local target trajectory obtained by superimposing the predicted trajectory of the virtual navigator vehicle with a formation offset as their tracking target. The virtual navigator and each real following vehicle are independently controlled by an LSTM-MPC controller with LSTM as the prediction model. The control cycle of the LSTM-MPC controller is 100ms. S3. Coordinate the control planning of the virtual navigator and the real follower through the virtual navigation method, and execute it in a rolling loop until the task is completed.

2. The LSTM-MPC cooperative formation control method for unmanned vehicle swarms in complex field environments according to claim 1, characterized in that, The LSTM-MPC controller in step S2 is in each control cycle Perform the following procedure: S2.1 State Measurement / Estimation: Obtain the vehicle's current state vector. ,in for Driverless cars at all times Axis position coordinates, for Driverless cars at all times Axis position coordinates, for The linear velocity of the driverless car at all times. for The heading angle of the autonomous vehicle at all times; S2.2 State prediction based on LSTM model: The trained_LSTM_Model is used as the prediction model, and its form is as follows: ， in This is the current control input; Based on this model, predict the future. Within a step, the corresponding control sequence State trajectory, preferred prediction time domain =5 steps; S2.3 Optimize control input: Establish the objective function and solve the optimization problem to obtain the optimal control sequence; S2.4 Execution control input: Using a rolling time-domain strategy, the first control quantity in the optimal control sequence is applied to the vehicle; S2.5, State Update and Feedback: After the system state evolves, the time point is moved to... Using the new measurement state as the initial condition, repeat steps S2.2 to S2.5 to form a closed-loop control.

3. The LSTM-MPC cooperative formation control method for unmanned vehicle swarms in complex field environments according to claim 2, characterized in that, The input vector for the historical time series data in step S1 is: ， in, for Driverless cars at all times Axis position coordinates, for Driverless cars at all times Axis position coordinates, for The linear velocity of the driverless car at all times. for The heading angle of the driverless car at all times for The longitudinal acceleration of the driverless car at all times for The front wheel steering angle of the driverless car at all times; The output vector is: ； in, for Driverless cars at all times Axis position coordinates, for Driverless cars at all times Axis position coordinates, for The linear velocity of the driverless car at all times. for The heading angle of the autonomous vehicle at all times; The LSTM network has an input layer dimension of 6 and an output layer dimension of 4. It adopts a real-time sequence output mode to achieve sequence-to-sequence output, and the input vector is a concatenation of the current state and control.

4. The LSTM-MPC cooperative formation control method for unmanned vehicle swarms in complex field environments according to claim 2, characterized in that, The LSTM network structure includes an LSTM layer, with the number of hidden layer units being 64, 128, or 256. The LSTM layer can have 1 or 2 layers, with the preferred hidden layer having 128 units and 1 layer. The training hyperparameters include learning rate, batch size, and training period. The learning rate controls the step size of the model parameter updates, the batch size is the number of samples used for each parameter update, and the training period is the number of times the entire training dataset is traversed. The preferred learning rate is 0.001, the batch size is 32, and the training period is 50 rounds. The time series data is distributed at fixed time intervals. Sampling, preferred sampling interval =100ms, and divided into training, validation and test sets in a ratio of 7:2:1 for model training and performance evaluation.

5. The LSTM-MPC cooperative formation control method for unmanned vehicle swarms in complex field environments according to claim 2, characterized in that, In step S2.2, predicting the future The specific state trajectory of the step is as follows: ， The input is the current vehicle state vector. With control vector The concatenated form is input into the trained_LSTM_Model to obtain the prediction result; Simultaneously, location information is extracted to predict the vehicle's trajectory: ， in ,function Used to extract the position component from the state vector.

6. The LSTM-MPC cooperative formation control method for unmanned vehicle swarms in complex field environments according to claim 2, characterized in that, In step S2.3, the optimization of the control input is achieved by establishing an objective function and solving the optimization problem. The objective function is: ； The optimization objective is to minimize the trajectory tracking error and control energy. The constraints of the optimization problem include: ， ， ， ， ， ， ， in, It is the target point on the preset trajectory, matrix This is the state tracking error weight matrix. Larger element values ​​indicate a faster approach to the target by the vehicle. This is the control input weighting matrix, used to penalize excessively large control inputs to prevent overly drastic changes in acceleration and steering angle. To control the feasible range of the input. The maximum allowable value for jerk. This represents the maximum permissible value for the steering angular velocity. To predict the starting point in the time domain, To predict the end point in the time domain; The prediction time domain The plan is forward-looking, and the LSTM neural network model serves as the dynamic prediction model of the system, replacing the physical differential equations.

7. The LSTM-MPC cooperative formation control method for unmanned vehicle swarms in complex field environments according to claim 1, characterized in that, The specific implementation process of the virtual navigation method in step S3 includes: S3.1 Virtual Pilot Vehicle Control Planning: Apply the LSTM-MPC algorithm described above to the virtual pilot vehicle to solve for its optimal control sequence. The first control variable of the sequence is applied to the prediction model of the virtual pilot vehicle to update its state; S3.2, Realistic Following Vehicle Control Planning: For the first The local target trajectory of a real driverless car is calculated as follows: ； in, The optimal position prediction sequence is calculated by the virtual navigator vehicle based on its optimal control sequence and current state using a prediction model. The local target trajectory of the real following vehicle directly originates from the optimal position prediction sequence generated within the virtual navigator vehicle's LSTM-MPC controller. The formation offset is a vector representing the nth formation offset. The relative positional offset that a real driverless car needs to maintain with a virtual navigator in order to maintain a specific formation; S3.3 Execution in a rolling loop: S3.1 and S3.2 are executed sequentially in a rolling loop, and prediction and optimization are performed based on the latest vehicle state loop until the task is completed; Formation formations include diamonds or columns.

8. The LSTM-MPC cooperative formation control method for unmanned vehicle swarms in complex field environments according to claim 2, characterized in that, The real following vehicle obtains its own status through on-board status perception sensors, including GPS and IMU, which are used to collect status parameters such as vehicle position, speed, and heading angle in real time. The real following vehicle outputs the first step of the solved optimal control sequence to its actuator, which includes a drive motor and a steering servo, for receiving control commands and driving the physical vehicle to move.

9. The LSTM-MPC cooperative formation control method for unmanned vehicle swarms in complex field environments according to claim 4, characterized in that, The LSTM neural network training process in step S1 also includes: Model evaluation and hyperparameter tuning: After training the LSTM model using the training data, evaluate the model performance on the validation set and perform necessary hyperparameter tuning, including the number of LSTM hidden layer units and the learning rate; Model saving: Save the trained_LSTM_Model after training, including the network structure, parameters and training state; Furthermore, the historical time series data in step S1.1 must cover a variety of complex working condition samples, including rugged terrain and crosswind scenarios, so that the trained_LSTM_Model can implicitly learn and characterize the unmodeled dynamic characteristics of the vehicle, including ground friction and tire slippage.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When executed by the processor, the program implements the LSTM-MPC cooperative formation control method for unmanned vehicle swarms in complex field environments as described in any one of claims 1-9.

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