Unmanned aerial vehicle formation path planning method, system and device based on sliding mode predictive control

Abstract

The application relates to the field of unmanned planes, and discloses an unmanned plane formation path planning method based on a sliding mode prediction control and electronic equipment, wherein the method comprises the following steps: setting a coordinate system, an unmanned plane kinematics model and a star-shaped communication topology structure; based on a sliding mode control and a model prediction control, designing a comprehensive control law, improving an algorithm, adopting a dynamic obstacle avoidance strategy based on the combination of an artificial potential field and motion control and the improved algorithm, planning an unmanned plane path, and dynamically updating; setting a formation control law according to the positions of a leader unmanned plane and each follower unmanned plane and a preset target relative position in the formation; in the dynamic obstacle avoidance strategy, fusing an obstacle avoidance force and a formation recovery force, and setting a final control law of each unmanned plane according to the formation control law weight and the obstacle avoidance weight. The method solves the contradiction between obstacle avoidance and formation stability, and realizes the smoothness of the motion trajectories of the unmanned planes.

Description

Technical Field

[0001] The embodiments of the present invention relate to the field of unmanned aerial vehicle (UAV) technology, and in particular to a method, system and device for UAV formation path planning based on sliding mode predictive control. Background Technology

[0002] In recent years, multi-UAV swarm systems have attracted significant attention from academia and industry due to their widespread applications in military reconnaissance, logistics transportation, and disaster relief. However, achieving autonomous obstacle avoidance and swarm control of UAVs in complex environments remains a major challenge.

[0003] The theoretical evolution of path planning algorithms has always been a core aspect of autonomous systems research. Heuristic search theory laid the mathematical foundation for Algorithm A, but the inherent curvature discontinuity of generated paths spurred the need for methodological improvements. Rapidly Expanding Random Trees (RRT) was the first to achieve feasible path search under nonholonomic constraints, but its probabilistic completeness is limited by the efficiency of random sampling. RRT and its dynamic variants improved path quality by 37% through asymptotic optimal strategies, but were limited by O(n log n) time complexity. Integrating vehicle dynamics into hybrid... The framework was experimentally verified to improve path smoothness in unknown semi-structured environments, and its engineering feasibility was further demonstrated through the deployment of mobile robots.

[0004] In the field of motion control, sliding mode control theory has established an anti-interference paradigm. Adaptive sliding mode predictive control (SMPC) achieves 92% tracking accuracy under wind disturbance through gain scheduling, but is limited by a decision delay of 160ms. The combination of parameter self-tuning architecture and deep reinforcement learning module has successfully compressed the dynamic response to the 50ms level, marking a paradigm shift towards intelligent control algorithms. Consensus protocol research reveals the persistent 0.15m-level position drift in multi-UAV formations, highlighting the unresolved stability challenges in distributed collaboration.

[0005] Breakthroughs in environmental perception have significantly improved system adaptability. Real-time obstacle avoidance theory pioneered the potential field method, solving local minima by harmonic potential fields, but at the cost of O(n²) computational complexity. The reciprocal velocity obstacle method achieves dynamic obstacle prediction, and integrates artificial potential fields to construct a VO-APF hybrid system, achieving an obstacle avoidance success rate of 98.6%, but with 22% path redundancy. The incremental Euclidean symbolic distance field (ESDF) mapping method achieves a 91% success rate for navigation in narrow spaces, but requires >2.5GHz of computing resources.

[0006] Advances in trajectory optimization are driving motion control toward higher-order continuity. Minimum jerk theory experiments have reduced mechanical vibration by 68%, and convex optimization methods have achieved 100% collision-free rates at dynamic intersections. The FASTER algorithm triples planning speed through safe corridor technology, but requires prior knowledge of obstacle motion. The "Teach-Repeat-Replan" framework enables the fusion of offline and online planning.

[0007] Energy optimization research exhibits multi-objective trade-offs. Roberge's Pareto optimal model extends range by 28% through energy-aware planning, but suffers a 12% accuracy loss due to the lack of modeling battery nonlinearity; Chen's LSTM-MPC architecture improves replanning efficiency by 40% through time-series prediction, but real-time obstacle avoidance in unstructured environments still needs improvement.

[0008] Current research bottlenecks in UAV path design focus on three dimensions: dynamic response latency (>200ms), computational resource requirements (>2.5GHz), and energy model fidelity (<30% endurance gain). These together constitute the key technical thresholds of this research. Improving these three dimensions is an urgent problem to be solved. Summary of the Invention

[0009] The purpose of this invention is to provide at least a method, system and device for UAV formation path planning based on sliding mode predictive control, which can at least solve the technical problems of the smoothness of UAV motion trajectory and low obstacle avoidance ability, at least achieve smooth UAV motion trajectory, resolve the contradiction between obstacle avoidance and formation stability, and improve path efficiency, formation maintenance and obstacle avoidance success rate.

[0010] In a first aspect, embodiments of this application provide a method for unmanned aerial vehicle (UAV) formation path planning based on sliding mode predictive control, including: Establish a kinematic model of a drone formation consisting of a leader and followers; Based on the kinematic model and basic formation control input, a comprehensive control law for the UAV is designed. Then, an obstacle avoidance control term generated by an artificial potential field is introduced on the basis of the comprehensive control law to obtain the obstacle avoidance control law for the UAV. An improved A-star algorithm is used to generate a global reference path for the UAV, and the integrated control law of the UAV is used to drive the UAV to track the global reference path. At the same time, the basic formation control input is corrected in real time based on the obstacle avoidance control law during flight. The formation recovery coefficient is introduced to determine the formation control law. Based on the formation control law, obstacle avoidance control law, and comprehensive control law, the final control law of each UAV in the UAV formation is obtained. By using the final control law to drive the UAV formation to fly along the reference path, obstacle avoidance and formation restoration can be achieved simultaneously during the flight of the UAVs.

[0011] Furthermore, the kinematic model includes: setting the control input of each UAV as the desired acceleration vector, the speed of the UAV being the integral result of the acceleration, and the position being the integral result of the speed.

[0012] Furthermore, the design of the integrated control law for the UAV based on the kinematic model and basic formation control input includes: A state-space model of UAV formation is established based on the kinematic model and basic formation control input of the UAV. Based on the state-space model, the state vector of the UAV is obtained and the state error is calculated. The weighted sum of the state errors is used as the sliding surface. The predicted state error is introduced as the sliding constraint to obtain the predicted state error sliding surface at the next prediction time. By introducing discontinuous control terms on the sliding surface to resist external disturbances, the sliding mode control law of the UAV is obtained. Predicting the future of drones based on model predictive control. The state sequence at time 1 and control input sequence The predicted state of the UAV at the next prediction moment is obtained. A cost function is established based on the deviation between the predicted state and the desired state of the UAV. The prediction state error sliding surface is introduced as a constraint term. By minimizing the cost function, the optimal control input sequence is obtained and used as the model predictive control law. By fusing the sliding mode control law and the model predictive control law, a comprehensive control law is obtained.

[0013] Furthermore, the basic formation control input of the follower is obtained from the position error and velocity error of the navigator and the follower; the basic formation control input of the navigator is the basic control input under the navigator's path tracking task.

[0014] Furthermore, based on the comprehensive control law, an obstacle avoidance control term generated by an artificial potential field is introduced to obtain the obstacle avoidance control law for the UAV, including: The total potential force is determined using the artificial potential field method; the total potential force includes the attractive force of the target point and the repulsive force of the obstacle. The repulsive force exerted by each obstacle on the drone is dynamically adjusted, and the total repulsive force exerted by all obstacles is obtained and used as an obstacle avoidance correction term. By introducing a weighted obstacle avoidance correction term based on the comprehensive control law, the obstacle avoidance control law for the UAV is obtained.

[0015] Furthermore, the step of generating the global reference path for the UAV using the improved A-Star algorithm includes: The three-dimensional workspace is divided into N equally spaced grid nodes, and the connection between different nodes is defined by the adjacency matrix. In the original Based on the algorithm's estimated cost function, a heuristic estimation of weight coefficients is introduced to obtain a new estimated cost function. Based on grid nodes and adjacency matrix, the initial planned path is output using the new estimated cost function. The initial planned path is smoothed using a cubic Bézier curve; Starting from the current state of the drone, the path is replanned periodically. After the path is successfully updated, the connection between the historical path and the newly planned path is retained.

[0016] Furthermore, a formation restoration coefficient is introduced to determine the formation control law. Based on the formation control law and the obstacle avoidance force control law, the basic control input is dynamically adjusted to obtain the final control law for each UAV in the UAV formation, including: Based on the preset relative positions of the target, followers, and navigator, the formation control law is determined by introducing a formation recovery coefficient; By weighted fusion of the obstacle avoidance control law and the formation control law, and combined with the comprehensive control law, the final control law for each drone in the drone formation is obtained.

[0017] Secondly, embodiments of this application provide a drone formation system based on sliding mode predictive control. The drone formation includes at least two drones, one of which acts as a navigator and the others as followers. Each drone operates according to the drone formation path planning method based on sliding mode predictive control described in this application, so as to achieve the desired state of the drone formation system.

[0018] Thirdly, embodiments of this application also provide an electronic device, including: at least one processor; and a memory communicatively connected to the at least one processor; wherein the memory stores instructions executable by the at least one processor, the instructions being executed by the at least one processor to enable the at least one processor to execute the above-described UAV formation path planning method based on sliding mode predictive control.

[0019] Compared with the prior art, the specific beneficial effects of the present invention are as follows: First, this application is based on the original Based on the algorithm, a heuristic estimation weight coefficient is introduced to obtain a new estimated cost function, which is more suitable for the smooth trajectory of UAV movement. After the path update is successful, the connection between the historical path and the newly planned path is retained, which can avoid sharp turns.

[0020] Second, this application combines the artificial potential field method to construct an attractive potential field and a repulsive potential field, defines the attractive and repulsive forces between obstacles and targets, and obtains the obstacle avoidance correction term generated by the artificial potential field by calculating the dynamic repulsive force of the UAV at different times in real time. Based on this, the obstacle avoidance control law of the UAV is designed to ensure that the UAV avoids obstacles in the real-time environment.

[0021] Third, this application defines the sliding surface as the weighted sum of state errors, which ensures that the state of the UAV formation system converges to the equilibrium point along the sliding surface under disturbance, and can converge quickly on the sliding surface; the sliding constraint ensures that the future predicted state gradually approaches the desired state; the introduction of discontinuous control terms can resist external disturbances and maintain stability on the sliding surface; Fourth, this application quantifies the deviation between the predicted state and the desired state through a cost function, and introduces sliding mode constraints into this cost function. This allows the model prediction optimization to not only reduce state tracking error and control cost in each prediction step, but also constrain the prediction error to converge along the sliding surface, thereby improving the robustness and convergence speed of the system. Furthermore, by minimizing the cost function, the model predictive control selects the optimal control input sequence, making the state of the UAV formation system as close as possible to the desired state. Fifth, this application integrates obstacle avoidance force with formation constraint force, enabling the UAV to automatically return to the preset formation shape after completing obstacle avoidance, thus resolving the contradiction between obstacle avoidance and formation stability, and improving path efficiency, formation maintenance and obstacle avoidance success rate. Attached Figure Description

[0022] One or more embodiments are illustrated by way of example with reference to the accompanying drawings, and these illustrative descriptions do not constitute a limitation on the embodiments.

[0023] Figure 1 This is a schematic diagram of the UAV coordinate system provided in one embodiment of this application; Figure 2 This is a schematic diagram of a drone formation provided in one embodiment of this application; Figure 3 This is a schematic diagram of the dynamic and static obstacle avoidance principle based on an artificial potential field provided in one embodiment of this application; Figure 4 This is a schematic diagram of the drone formation recovery process provided in one embodiment of this application; Figures 5-10 This is a schematic diagram illustrating the maneuverability and response characteristics of a UAV formation in dynamic obstacle avoidance during a dynamic obstacle avoidance simulation experiment, provided in one embodiment of this application; wherein: Figure 5 This is a schematic diagram illustrating the change in flight altitude over time. Figure 6 This is a schematic diagram showing the change of heading angular velocity over time; Figure 7 This is a schematic diagram illustrating the change of relative position error over time. Figure 8 This is a schematic diagram showing the change of vertical acceleration over time; Figure 9 This is a schematic diagram showing the change of acceleration over time in the XOY plane; Figure 10 This is a schematic diagram of the Lyapunov function changing over time; Figure 11 This is a schematic diagram of a three-dimensional flight path in a dynamic obstacle avoidance capability verification simulation experiment provided in another embodiment of this application; Figures 12-17 This is a schematic diagram illustrating the maneuverability and response characteristics of a UAV formation in dynamic obstacle avoidance in a simulation experiment scheme one provided by another embodiment of this application; wherein: Figure 12 This is a schematic diagram illustrating the change in drone flight altitude over time. Figure 13 This is a schematic diagram showing the change of acceleration over time in the XOY plane; Figure 14 This is a schematic diagram showing the change of vertical acceleration over time; Figure 15 This is a schematic diagram showing the change of heading angular velocity over time; Figure 16 This is a schematic diagram of the Lyapunov function changing over time; Figure 17 This is a schematic diagram illustrating the change of relative position error over time. Figures 18-20 This is a schematic diagram of the three-dimensional flight path of the comparative test scheme 1 of this application under sliding mode control from different viewing angles; wherein: Figure 18 It is a three-dimensional flight path main view diagram, used to show the overall trajectory of the drone formation flying along the planned path and avoiding obstacles; Figure 19 It is a three-dimensional flight path diagram from another perspective, used to show the lateral deviation during the formation obstacle avoidance process; Figure 20 It is a three-dimensional flight path diagram from another perspective, used to show the trajectory changes of the formation in the altitude direction and during spatial obstacle avoidance; Figures 21-26 This is a schematic diagram illustrating the maneuverability and response characteristics of the UAV formation under model predictive control in comparative test scheme two of this application; wherein: Figure 21 This is a schematic diagram of the Lyapunov function changing over time; Figure 22 This is a schematic diagram illustrating the change in flight altitude over time. Figure 23 This is a schematic diagram illustrating the change of relative position error over time. Figure 24 This is a schematic diagram showing the change of vertical acceleration over time; Figure 25 This is a schematic diagram showing the change of acceleration over time in the XOY plane; Figure 26 This is a schematic diagram showing the change of heading angular velocity over time; Figures 27-29 This is a schematic diagram of the three-dimensional flight path under model predictive control from different viewing angles in the second comparative test scheme of this application; wherein: Figure 27 It is a three-dimensional flight path main view diagram, used to show the overall trajectory of the drone formation flying along the planned path and avoiding obstacles; Figure 28 It is a three-dimensional flight path diagram from another perspective, used to show the lateral deviation during the formation obstacle avoidance process; Figure 29 It is a three-dimensional flight path diagram from another perspective, used to show the trajectory changes of the formation in the altitude direction and during spatial obstacle avoidance; Figures 30-35 This is a schematic diagram illustrating the maneuverability and response characteristics of the UAV formation under sliding mode predictive control in comparative experimental scheme three of this application; wherein: Figure 30 This is a schematic diagram of the Lyapunov function changing over time; Figure 31 This is a schematic diagram illustrating the change in flight altitude over time. Figure 32 This is a schematic diagram illustrating the change of relative position error over time. Figure 33 This is a schematic diagram showing the change of vertical acceleration over time; Figure 34 This is a schematic diagram showing the change of acceleration over time in the XOY plane; Figure 35 This is a schematic diagram showing the change of heading angular velocity over time; Figures 36-38 This is a schematic diagram of the three-dimensional flight path under sliding mode predictive control from different viewing angles in comparative experiment scheme three; where: Figure 36 It is a three-dimensional flight path main view diagram, used to show the overall trajectory of the drone formation flying along the planned path and avoiding obstacles; Figure 37 It is a three-dimensional flight path diagram from another perspective, used to show the lateral deviation during the formation obstacle avoidance process; Figure 38 It is a three-dimensional flight path diagram from another perspective, used to show the trajectory changes of the formation in the altitude direction and during spatial obstacle avoidance. Detailed Implementation

[0024] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the various embodiments of this application will be described in detail below with reference to the accompanying drawings. However, those skilled in the art will understand that many technical details are presented in the various embodiments of this application to facilitate a better understanding of the application. However, the technical solutions claimed in this application can be implemented even without these technical details and various variations and modifications based on the following embodiments. The division of the various embodiments below is for ease of description and should not constitute any limitation on the specific implementation of this application. The various embodiments can be combined with and referenced by each other without contradiction.

[0025] To address the aforementioned technical problems of low trajectory smoothness and obstacle avoidance capability in UAV formation path planning, this invention proposes a UAV formation path planning method based on sliding mode predictive control. The implementation details of the UAV formation path planning method based on sliding mode predictive control in this embodiment are described below. The following content is only for ease of understanding and is not necessary for implementing this solution.

[0026] Example: This embodiment provides a UAV formation path planning method based on sliding mode predictive control, which can be applied to electronic devices with communication, computing, and data storage capabilities. See [link to relevant documentation]. Figures 1 to 12 The drone swarm consists of one leader and M followers, and the multiple drones in the swarm communicate using a star topology. The method includes the following steps: Step 1: Establish a kinematic model of the drone formation and obtain the basic formation control input based on the position and velocity errors of the leader and follower; To facilitate subsequent UAV formation path planning and control input design, a kinematic model of the UAV formation is first established to describe the state evolution of the UAVs and provide a state prediction basis for model predictive control and sliding mode control. This application uses the UAV's dynamic model as a foundation, neglecting the UAV's shape, and takes controlling the UAV's acceleration as the underlying control objective.

[0027] First, combined Figure 1 To describe the motion of a UAV in three-dimensional space, an inertial coordinate system is defined. ,in The origin is set at the initial position of the drone, which can be any point on the horizontal plane. The axis direction can be selected on the horizontal plane according to the approximate direction of the drone's designated mission. The axis is perpendicular to the horizontal plane and points upwards. The axis direction is selected using the right-hand rule.

[0028] Assuming the quadcopter drone maintains small pitch and roll angles during flight, and its total thrust is approximately equal to the weight of the quadcopter, its expression is as follows: ; in, , These represent the pitch angle and roll angle, respectively. Based on the above assumptions, the motion axes of the UAVs are decoupled. The motion state of each UAV in the inertial coordinate system can be represented by its position and velocity, where the... The location of the drone is ,speed for Specifically, speed For position The time derivative, i.e.: ; in, They represent the first A drone in , , velocity components in the direction, It is a time variable.

[0029] In one specific embodiment of this application, in a multi-UAV formation system, the UAVs in the system are equipped with autopilots, whose kinematic models describe the changes in position, velocity, and acceleration of the UAVs in the ground coordinate system, providing a basis for subsequent control design.

[0030] Definition of the first The control input for the drone is the desired acceleration vector. ,in These are drones , and Acceleration commands in direction. The drone adjusts its motion based on these acceleration commands to achieve formation control objectives.

[0031] Assume the first acceleration vector of the drone (i.e., control input) can be directly adjusted through control input, then the first The speed of drones and location The changes satisfy the following relationship: ; ; That is, at a certain moment, control input The acceleration of a drone is determined in actual drone formation control. Throttle commands are typically determined by the geometry of the drone's propellers and the operating speed of the motors, while speed is the integral of acceleration, and position is the integral of speed, thus forming the control input. The method of controlling the drone's position changes.

[0032] The above formulas (3)-(4) are the kinematic models of multi-UAV formations established using the acceleration vector as the control input of the UAV.

[0033] Next, we define the actual relative position error between UAVs, the leader-follower position error, and the leader-follower velocity error in formation control, as well as the asymptotic convergence conditions that these errors should satisfy when the system is stable: Set up drones And the adjacent drone The expected relative position is: ,in, , and drones and drones If the expected position difference is calculated along the X, Y, and Z axes, then the actual relative position error between the two is... for: ; in, Indicates the desired relative position (formation setting).

[0034] Actual relative position error Indicates drone and drones The offset between them is equal to the position difference between the two drones minus the expected relative position. .

[0035] To reduce errors, a relative position error term is added to the control input, allowing the drone to adjust its position relative to its neighbors, gradually approaching a preset formation. It should meet the following requirements: ; That is, when time t approaches infinity, the actual relative position error is zero.

[0036] By adjusting the drones respectively and drones control input To achieve the conditions of equation (6), ensure that the UAV formation maintains a stable relative positional relationship in three-dimensional space.

[0037] Network topology defines the connection method between nodes in an unmanned aerial vehicle (UAV) communication network. Common structural types include star, mesh, and ring topologies. In a specific embodiment of this application, the UAV communication network adopts a star communication topology. A star topology uses a central node as its core, with all other nodes connected to it. This structure offers low latency, simplicity, and ease of management. In this embodiment, the navigator in the UAV formation is the central node, and multiple followers are slave nodes that communicate with the central node.

[0038] Define the first in the drone formation One follower With the Navigator Positional error between for: ; In the formula, Indicates navigator The position vector, Indicates the first One follower The position vector, Represents the ideal relative displacement deviation, which refers to the vector of differences in ideal relative positions between the follower and the navigator.

[0039] In one specific embodiment of this application, multiple drones are arranged in a line, optionally combined with... Figure 2 The five drones in the picture are arranged in a line, with a distance of 2m between adjacent drones.

[0040] If the overall drone formation system is stable, then the positional error It should meet the following requirements: ; Similarly, define speed error for: ; in, Indicates navigator The velocity vector, Indicates follower The velocity vector.

[0041] If the drone formation system is stable, the speed error It should meet the following requirements: ; The aforementioned error equations and convergence conditions form the theoretical basis for subsequent control law design. Based on the position error and velocity error equations, the velocities of the navigator and follower are determined. and And the positions of navigators and followers and Ultimately, followers can be constructed. Basic control input .

[0042] Specifically, in complex environments, such as strong winds and obstacles, to ensure formation stability, the speed and position of the navigator and followers are used to obtain the first... One follower The control input is: ; In the formula, Indicates follower Control input; Indicates position control gain. This represents the speed control gain, used to adjust the convergence speed of position error and speed error, respectively. Representing the leader With followers The expected relative positions between them ensure that the relative positions of the followers within the formation remain constant. This control law ensures that the followers... Always Towards the Navigator The position is adjusted to match the speed of the navigator.

[0043] For the first The basic formation control input for each follower describes the follower's position and velocity tracking of the leader. To standardize subsequent control law expressions, this basic formation control input will be denoted as... The initial term; that is, for the follower, the term obtained in step 1. As the basic control input in the subsequent integrated control law design, it participates in the fusion calculation of state space modeling, sliding mode control, model predictive control and obstacle avoidance control.

[0044] Step 2: Based on the kinematic model and basic formation control inputs, design the integrated control law for the UAV; This step designs the UAV controller based on the aforementioned kinematic model, and constructs control laws to achieve UAV formation tracking, stability maintenance, and obstacle avoidance functions. The control input... To unify variables, different control strategies (such as formation control, sliding mode control, model predictive control, obstacle avoidance control, etc.) are calculated in different stages, and finally, the actual control input of the UAV is obtained through fusion, i.e., the integrated control law. Among them, the basic formation control input obtained in step 1 Constitute a unified control variable The initial source of this is the control law, and all subsequent control laws are modified, optimized, or integrated based on it.

[0045] Optionally, step 2 includes the following sub-steps: Step 2.1: Kinematic model and basic formation control input based on UAV The state-space model of the UAV formation is obtained; wherein, the basic formation control input For the follower, this corresponds to the control input obtained in step 1 based on the position and speed errors of the navigator and follower. For the navigator, This represents the basic control input for its path tracing task; The state-space representation of the kinematic model of a drone can be described by the following state equations, thus establishing the state-space model of a drone formation: ; in, including location and speed ; A represents the UAV formation state matrix, and B represents the UAV formation control matrix, which are defined in this application as: .

[0046] Step 2.2: Obtain the UAV's state vector based on the state-space model. Calculate the state error, use the weighted sum of the state errors as the sliding surface, introduce the predicted state error as the sliding constraint, and obtain the predicted state error sliding surface at the next prediction time. Sliding mode control is used to make the UAV formation state converge to the equilibrium point along the sliding mode surface under disturbance.

[0047] Setting up the drone formation The state error of each drone is Its definition is: ; in, Let be the state vector at time t. Let be the desired state vector at time t.

[0048] The weighted sum of state errors is used as the sliding surface. By designing the sliding surface This allows the drone formation state to converge rapidly to the sliding mode surface within a finite time, at time t. Sliding surface of a drone for: ; in, This represents the sliding mode gain, which determines the convergence speed of the drone formation. This represents the estimated state error of the i-th UAV.

[0049] By introducing the prediction state error As a sliding mode constraint, the predicted future state gradually approaches the desired state. For the prediction time... Define the predicted state error sliding surface as:

[0050] in, for The prediction state error sliding surface at time t is used to reflect the dynamic behavior of the prediction error on the sliding surface.

[0051] Step 2.3: Introduce discontinuous control terms into the sliding surface to resist external disturbances, and obtain the sliding mode control law of the UAV; Specifically, by introducing discontinuous control terms To resist external disturbances. Thus, the sliding mode control law of the drone can be obtained. That is, sliding mode control input:

[0052] in, To control the gain, the sliding mode control strength is determined; It is a saturation function. This is the saturation limit.

[0053] The function of the sliding mode control law is to drive the UAV formation state to the sliding surface. It maintains stability on the sliding surface, enhancing system robustness, and participates in subsequent fusion as a compensation term for control input.

[0054] Step 2.4: Establish a cost function based on the deviation between the predicted state and the desired state of the UAV, and introduce sliding mode constraints to constrain the prediction error sliding surface in each prediction step. By minimizing the cost function, the optimal control input sequence is obtained and used as the model predictive control law. The core of Model Predictive Control (MPC) lies in calculating future control sequences based on predictive models, thereby optimizing the response of UAV formations.

[0055] The discrete-time state equation of a drone in a drone swarm is: ; in, for Time of the first A state vector of an unmanned aerial vehicle (UAV) control system. for Time of the first The control input of a drone control system and These are the state matrix and control matrix of the drone formation, respectively. This represents the external disturbance vector.

[0056] Based on the prediction model of equation (18), the future of the drone can be predicted through recursion. The state sequence at time 1 and control input sequence :

[0057] Based on state sequences and control input sequence Equation (18) is recursively expanded into equation (19), thus explicitly representing the future 19th equation. The relationship between the state vector of each prediction step and the current state, control input sequence, and disturbance accumulation term provides a basis for constructing the cost function in the prediction time domain and solving the optimal control sequence. Equation (18) can then be expressed as: ; in, Indicates the future The cumulative effect of the time-matter disturbance term; State matrix of The exponentiation is used to describe the recursive progression of the system from the current state to the next state under conditions of no control input. The natural evolutionary relationship at each predicted step; This represents the cumulative impact of control inputs on future states within the prediction time domain.

[0058] Define a cost function This is used to quantify the deviation between the predicted state and the desired state, and a sliding surface for the predicted state error is introduced. As a constraint, the model prediction optimization not only reduces state tracking error and control cost in each prediction step, but also constrains the prediction error to converge along the sliding surface, thereby improving the robustness and convergence speed of the system. ; in, This is the state error weight matrix, used to adjust the importance of position error and velocity error in the optimization objective; The input weight matrix is ​​used to constrain the control input amplitude and prevent the control quantity from being too large. These are the sliding mode constraint weighting coefficients, used to balance the influence of sliding surface errors on the cost function; for The expected state vector at time t; For the corresponding prediction time The sliding surface error.

[0059] By minimizing the cost function Model predictive control (MPC) selects the optimal control input sequence so that the UAV formation state approximates the desired state as closely as possible, i.e.: ; in, and Control the upper and lower limits of the input separately; Based on the model predictive control characteristics, control input constraints need to be set. ,in, and To control the upper and lower limits of the input, the optimal control input sequence is used as the model predictive control input, i.e., the model predictive control law.

[0060] Step 2.5: Combine sliding mode control law and model predictive control law to design a comprehensive control law; The integrated control law is used to make the control input of the UAV control system It can minimize prediction errors while maintaining the robustness of drone formations.

[0061] By fusing the sliding mode control law with the model predictive control law, the fused control input, i.e., the integrated control law, is obtained: ; In the formula, The model predicts the control law by minimizing the cost function. For sliding mode control, This refers to the intermediate control input form after the fusion of sliding mode control and model predictive control, which is the fused control input.

[0062] Step 2.6: Based on the comprehensive control law, introduce the obstacle avoidance control term generated by the artificial potential field to obtain the obstacle avoidance control law of the UAV; Dynamic obstacle avoidance is a critical issue in UAV path planning, especially in dynamic environments where real-time response is essential to avoid moving obstacles while maintaining global path optimality. This application employs a dynamic obstacle avoidance strategy combining artificial potential fields and motion control. A schematic diagram of UAV obstacle avoidance based on this dynamic strategy is shown below. Figure 3 As shown.

[0063] The artificial potential field method includes constructing attractive and repulsive potential fields, defining the forces between obstacles and targets, and guiding the trajectory of the drone.

[0064] like Figure 3 As shown, the drone is at any location Total potential force Defined as: ; In the formula, Indicates the first The attraction of a target point draws the drone closer to the target; This represents the total repulsive force of an obstacle, used to avoid collisions.

[0065] Target point attraction The expression is: ; In the formula, It is the attraction coefficient, and , Indicates the location of the target point.

[0066] No. The repulsive force of the obstacle The expression is as follows: ; In the formula, Denotes the repulsion coefficient, and ; Indicates the distance from the drone to the center of the obstacle. This indicates the range of the repulsive force; beyond this range, the repulsive force is zero. Indicates the center location of the obstacle.

[0067] Since the position of a dynamic obstacle changes over time, its position is defined as... Its speed is defined as Then the drone is in Dynamic repulsive force at any moment It needs to be calculated in real time using the following formula: (26); Dynamically updated repulsive forces ensure that drones can avoid obstacles in real-time environments.

[0068] Assuming all obstacles move at a constant speed, the motion prediction of the obstacles can be achieved through the following methods: at a constant speed The future positions of the moving obstacles are predicted as follows: (27); in, This indicates the length of the obstacle avoidance detection time window. express Predicted obstacle location at any given time; Employing multi-objective programming to address multiple obstacles Using the same rules, calculate the total repulsive force by superposition: (28); in, Indicates the first The total repulsive force experienced by the drone at its current location; Indicates the j-th obstacle to the j-th obstacle. The repulsive force generated by the drone; This represents the total number of obstacles.

[0069] By introducing an obstacle avoidance correction term generated by an artificial potential field based on the fused control input, an obstacle avoidance control law for the UAV is formed. That is, obstacle avoidance control input: (29); in, This is a weighting factor used to balance path tracking and obstacle avoidance requirements. This represents the obstacle avoidance correction term, which originates from the total potential field force and is used for obstacle avoidance adjustments.

[0070] Step 3: Generate the global reference path of the UAV using the improved A* algorithm, and utilize the integrated control law of the UAV. The drone is driven to track this global reference path, while its obstacle avoidance control law is applied during flight. Real-time correction of basic formation control inputs; improve The algorithm is used to generate a global reference path for the UAV, which is then input into the subsequent controller as the desired trajectory. The control law designed in step 2 is used to drive the UAV to track the reference path and to make real-time corrections to the control input during flight by combining a dynamic obstacle avoidance strategy (i.e., obstacle avoidance control law).

[0071] The algorithm is a path planning method based on heuristic estimation, the core of which lies in minimizing the estimated cost function. To achieve fast search of the target node, the original estimated cost function is defined as follows: (30); in, From the starting point to the current node The cumulative actual cost, For the current node Heuristic cost estimation to the target node.

[0072] The original output path of the algorithm is usually a connection of discrete nodes, which is difficult to meet the smoothness requirements of UAV motion. Therefore, this application addresses the original... The algorithm was improved, resulting in an improved version. Algorithm, and utilize improvements The algorithm plans the global reference path for the drone; specifically including: Step 3.1: Divide the 3D workspace into N equidistant mesh nodes, denoted as The connection between two nodes is determined by the adjacency matrix. definition.

[0073] For any two nodes and ,like Then its connection weight for: (31); like If the number is 0, it means that the nodes are not reachable.

[0074] Step 3.2: Introduce heuristic estimation weight coefficients based on the original estimated cost function to obtain a new estimated cost function, and use the new estimated cost function to output the initial planned path; The new estimated cost function is: (32); in, It is a heuristic estimation of weight coefficients, used to adjust the global optimality and computational efficiency of the balance search.

[0075] Specifically, N grid nodes are equivalent to The state in the algorithm, the adjacency matrix corresponds to the state transition rules, that is, which adjacent nodes can be reached from the current node, and finally the next optimal node is selected through a new cost function.

[0076] Step 3.3: Smooth the initial planned path using a cubic Bézier curve; Assume the path node is For each path segment The definition of a cubic Bézier curve is: (33); In the formula, control points and By dynamically calculating the path direction and node spacing, the path curve is ensured to meet the physical motion constraints of the UAV. Control points, defined by the Bézier curve, are the points where the UAV's projected location intersects with the control points. These control points constrain the shape of the Bézier curve, ensuring the path meets the requirements for the continuity and smoothness of the UAV's motion.

[0077] The smoothness of the path curve is evaluated using the second derivative: (34); in, Indicates path curvature. and These are the first and second derivatives of the path, respectively.

[0078] In dynamic environments, obstacles or targets may change in real time, requiring periodic replanning of the path, including the following steps: S1. Starting from the current state of the drone, re-execute the improvement. The algorithm obtains the updated planned path; S2. After the route update is successful, retain the connection between the historical route and the newly planned route to avoid drastic changes.

[0079] improve The algorithm flow is as follows: A1. Initialize the node set and adjacency matrix ; A2. Let the starting point be s and the target point be t. Initialize the value to the cumulative actual cost from the starting point to the target point. From the starting point to the current node The cumulative actual cost Minimize the estimated cost function Equal to node Heuristic cost estimation to target node t , ; A3. Add the starting point to the open list. ,use An algorithm to obtain the set of nodes with the minimum cost; A4. Reconstruct the drone path and smooth the path using a Bezier curve.

[0080] Step A3 includes: A31, From the Open List The node with the lowest substitution cost ; A32, Calculation All neighboring nodes and ,like Update, will join in ; A33, will from Move to closed list ; A34. Repeat steps A31-A33. When the minimum cost node set is obtained, the set of nodes with the minimum cost is obtained.

[0081] Step 4: Introduce the formation restoration coefficient to determine the formation control law. Based on the formation control law and obstacle avoidance control law, dynamically adjust the basic control input to obtain the final control law for each UAV in the UAV formation. Along the drone During the planned flight path, obstacle avoidance control and formation control are integrated to dynamically adjust the control input, thereby ensuring path tracking while achieving obstacle avoidance and formation recovery.

[0082] Specifically, step 4 may include: Step 4.1: Based on the preset relative position of the target, the positions of the followers and the navigator, the formation control law is determined by introducing the formation recovery coefficient; By introducing a formation recovery coefficient, a formation control law is determined to provide recovery force when the drones deviate from the preset formation, thus maintaining the formation of the drone formation.

[0083] like Figure 4 As shown, the diagram illustrates the recovery process when a drone formation fails to maintain its formation during obstacle avoidance, as well as the formation maintenance process. The dashed lines in the diagram represent the preset target relative positions of the drones.

[0084] Formation control law as follows: (35); in, The relative positions of the targets in the formation are preset. and These represent the positions of follower and navigator, respectively. This is the formation recovery coefficient.

[0085] Step 4.2: Weigh and fuse the obstacle avoidance control law and the formation control law, and combine them with the comprehensive control law to design the final control law for each UAV in the UAV formation; By integrating obstacle avoidance force and formation recovery force on the basis of dynamic obstacle avoidance strategy, it can be ensured that the drone automatically returns to the preset formation shape after completing obstacle avoidance.

[0086] Combining the above formation control, sliding mode control, model predictive control, and obstacle avoidance control, the final control input of the UAV is obtained. as follows It can be represented as: (36); in, This represents the obstacle avoidance control law. This indicates the priority of restoring formation and obstacle avoidance.

[0087] The stability of UAV formations is analyzed using Lyapunov functions.

[0088] Selecting Lyapunov candidate functions A quadratic function for the sliding surface: (37); In formula (37), It is a sliding surface, defined as: (38); in, For drone formation state error, These are the sliding surface gain parameters. Lyapunov candidate functions. It is a non-negative function (i.e.) ), representing the energy of the sliding surface. If Decreasing over time (i.e.) If the drone formation state converges to the sliding surface, then the drone formation state will converge to the sliding surface.

[0089] Differentiate formula (38): (39); Therefore, based on the definitions of the sliding surface in formulas (39) and (38), we can obtain: (40); (41); in, This represents the first-order rate of change of the state error; if the position error component is further expanded, it corresponds to the velocity error, and if the velocity error component is expanded, it corresponds to the acceleration error. Error state equation of drone formation Discrete-time state equations The error acceleration can be obtained : (42) The formula of the comprehensive control law Substituting into the above equation, we get: (43); Substitute equation (43) into equation (41) We can obtain: (44); To prove It is necessary to ensure that the sliding mode control term can resist disturbance terms. Other uncertainties necessitate the addition of Lyapunov functions. Sufficient conditions: (45); Select an appropriate control gain This makes the sliding mode gain Large enough to ensure control The amplitude exceeds the maximum amplitude of the disturbance. .

[0090] Ultimately, this resulted in: (46).

[0091] Another embodiment of this application provides a UAV formation system based on sliding mode predictive control, including at least two UAVs, one of which acts as a navigator and the other as followers. Each UAV plans a path according to the UAV formation path planning method based on sliding mode predictive control described above and runs along a smooth flight path.

[0092] Simulation Case: The method of this application is used to conduct simulations to compare the performance of four different control strategies in static and dynamic obstacle avoidance tasks, so as to verify the advantages and disadvantages of each control strategy under various environmental conditions.

[0093] (1) The main purpose of the experiment is: 1. Test the effectiveness of the control strategy: improve it through comparison. The combined effect of the algorithm with different control methods (sliding mode control, model predictive control, sliding mode predictive control) was evaluated, and their obstacle avoidance efficiency and effectiveness in static and dynamic obstacle environments were assessed.

[0094] 2. Comparison of the overall performance of different control strategies: The experiment reveals the advantages and limitations of each strategy in handling static and dynamic obstacle avoidance tasks through quantitative analysis of indicators such as total path length, path smoothness and number of collisions.

[0095] The simulation depicted a formation flight mission involving five drones (one leader and four followers). The initial position, velocity, and target position of each drone were pre-defined. Multiple static obstacles were introduced during the flight, distributed with random three-dimensional coordinates. The performance of the improved algorithm was verified by comparing different path planning algorithms. The experiment employed four control strategies, as shown in Table 1. Table 1 Four Control Strategies (2) Experimental environment and parameter settings: This experiment utilizes a MATLAB / Simulink simulation platform to evaluate the obstacle avoidance performance of UAV formations using four designed control strategies. The experimental environment and parameter settings aim to simulate real flight missions and ensure the comparability of performance indicators and the reliability of experimental results. The following provides a detailed description of the experimental environment and related parameters, including the simulation platform and tools, the experimental scenario and obstacle settings, and the control-related parameters.

[0096] Simulation platforms and tools The experiment used MATLAB / Simulink as the simulation tool, leveraging its powerful mathematical modeling and simulation capabilities to construct a multi-UAV formation model. All control algorithms (including improvements) were implemented. The algorithms, sliding mode control, model predictive control, and sliding mode predictive control (SMDC) were all implemented in MATLAB function modules and integrated with the UAV kinematic model. Real-time feedback and path planning functions of the control strategy were implemented using the Simulink simulation environment.

[0097] ② Experimental scenario and obstacle setup: The experimental scenarios included two types of environments: static obstacle scenarios and dynamic obstacle scenarios. In the static obstacle scenarios, the positions and sizes of the obstacles were fixed, simulating obstacle avoidance tasks involving stationary objects; while in the dynamic obstacle scenarios, the obstacles moved randomly along preset trajectories, simulating obstacle avoidance tasks in dynamic environments. Five obstacles were set in the static scenarios and three obstacles were set in the dynamic scenarios to ensure the complexity and challenge of the obstacle avoidance tasks.

[0098] 1) Static obstacle scenario: All obstacles have a radius of 1.6 meters and are fixed in position, simulating fixed obstacles in the real environment (such as buildings, ground obstacles, etc.). The coordinates of the static obstacles are: [7, 3, 2], [4, 6, 7], [12, 12, 8], [16, 15, 14], [21, 17, 15].

[0099] 2) Dynamic obstacle scenario: The movement trajectory of the obstacle is based on a speed of 0.5m / s and moves along a set straight line to simulate obstacle avoidance tasks in a dynamic environment (such as flocks of birds, other aircraft, etc.).

[0100] Control the relevant parameter settings: In this embodiment, the control input is the three-dimensional acceleration of each UAV, expressed as:

[0101] In particular, since the focus of simulation is not on predicting multi-step effects but on verifying the feasibility of simple control laws, both the leader and the follower combine formulas. - Formula (23) MPC control method, adopting quasi-optimal control, that is, combining the linearity and small disturbance characteristics of the experimental system, select Therefore, the designed MPC control law is as follows: (47); Among them, the weight matrix of the state error The weight matrix that controls the input , This represents the state error.

[0102] In the implementation of the other control strategies (such as Equations (17), (22), (35) and (36)), the key control parameters have been debugged and optimized. The specific parameters are set according to different control strategies, as shown in Table 2.

[0103] Table 2 Different control strategies and parameters The parameters in Table 2 were obtained from the optimal performance state of the model after multiple repeated experiments. The control parameters in Table 1... Substituting the parameters into formula (36), we obtain the final result. The final acceleration input of the drone : (50); In the experiment, the initial position of the Navigator drone was (0, 0, 0). The target location is (20, 20, 20). The sampling frequency of the simulated environment is 100 Hz.

[0104] (3) Experimental results: Dynamic obstacle avoidance capability verification: To verify the effectiveness of the four proposed control strategies in dynamic environments, this experiment simulates the dynamic obstacle avoidance requirements of real-world flight scenarios by introducing moving obstacles. Following the improved... The algorithm, which combines path planning, dynamic obstacle avoidance using artificial potential fields, and sliding mode predictive control, calculates the maneuverability and related response curves of the UAV during obstacle avoidance tasks, as shown in the figure. Figures 5-10 As shown, this demonstrates the maneuverability and response characteristics of a UAV formation in dynamic obstacle avoidance, validating the dynamic obstacle avoidance function of the proposed control algorithm. In the experiment, the obstacle moves along a predetermined path, and each UAV in the formation adjusts its trajectory based on real-time perception information to avoid collision.

[0105] The three-dimensional flight path of a drone formation under the influence of dynamic obstacles, such as Figure 11 As shown in the experiment, as the obstacle moved, the formation members successfully avoided it by adjusting their flight trajectory in real time. The path adjustment was smooth and continuous, demonstrating the adaptability and stability of the control algorithm in dynamic environments. The path colors and markings in the figure clearly show the relative positions of the UAV and the obstacle, verifying the effectiveness and efficiency of the algorithm in dynamic obstacle avoidance.

[0106] Record the drone based on the Reich collision model's definition of collision: (51) In the formula, Indicates drone and obstacles At any moment Euclidean distance, This represents the Euclidean distance between vectors.

[0107] The average rate of change of path curvature of each UAV in obstacle avoidance task is calculated according to formula (34) to record the smoothness of the path. The results in Table 3 are summarized.

[0108] Table 3 Results of Dynamic Obstacle Avoidance Drone Formation Indicators comprehensive Figure 5Table 3 shows that when dynamic obstacles enter the formation flight path, the formation members quickly adjust their paths to effectively avoid the obstacles and maintain formation stability. The flight trajectory is smooth and continuous, without drastic directional changes, proving that the algorithm can smoothly control the UAV attitude and avoid unnecessary maneuvers. Furthermore, the formation's response to dynamic obstacles demonstrates high timeliness. When obstacles change their direction or speed, the formation adjusts promptly to ensure safe distances and formation stability during flight. This result indicates that the proposed algorithm has strong adaptability and efficiency in dynamic obstacle avoidance scenarios.

[0109] Comparative test To verify the obstacle avoidance performance of different control strategies in UAV formations, this simulation case designed multiple sets of comparative experiments to compare the performance of different control algorithms in path planning, obstacle avoidance efficiency, and safety under the condition of an ideal path length of 34.64 m.

[0110] (1) Comparative test scheme 1: Improved Algorithm + Static obstacle avoidance using artificial potential field + sliding mode control: In this experimental scheme, an algorithm based on sliding mode control was used to control the UAV formation to perform dynamic obstacle avoidance. Relevant indicators were measured to compare the model performance. Similarly, relevant performance indicators were generated as shown in Table 4.

[0111] Table 4 Sliding Mode Control Unmanned Aerial Vehicle Formation Indicators As shown in Table 4, the actual path length of the UAV formation significantly exceeds the ideal path, indicating that sliding mode control exhibits path extension during obstacle avoidance. During obstacle avoidance, UAV 3 (the navigator) collided with obstacles twice, demonstrating that sliding mode control cannot guarantee the safety of the UAV formation in obstacle avoidance. The calculated average curvature change rate of 0.019423 indicates that the path generated by sliding mode control is relatively smooth.

[0112] According to the formula - as well as - (29) The control logic constructs the path planning strategy for UAV formation and generates model prediction results of UAV formation maneuvers and related response curves, such as Figures 12-17 As shown. The maneuver path and response curves of the UAV formation under sliding mode control (SMC) are as follows. Figures 18-20 As shown.

[0113] As shown in the figure, sliding mode control exhibits strong real-time response capabilities and can adjust paths more quickly. However, it suffers from excessive oscillations and instabilities in the kinematic control of the UAV itself during obstacle avoidance. The increased path length and collisions with some UAVs during obstacle avoidance indicate that sliding mode control still has certain limitations in complex obstacle environments, particularly in terms of accuracy and efficiency in avoiding complex obstacles. Lyapunov function analysis shows that the system state gradually approaches a steady state during simulation, indicating that the system is asymptotically stable, effectively achieving the desired trajectory without deviating from the target state. In conclusion, sliding mode control has high robustness in dynamic obstacle avoidance and path planning, but in extreme cases, it can still lead to some path lengthiness and occasional collision risks.

[0114] Based on the generated relevant performance index table 4, Figures 12-20 It can be seen that although sliding mode control has strong real-time response capabilities and can quickly adjust the path with a smooth overall path, it cannot avoid collisions during obstacle avoidance. Furthermore, the significant increase in the total path length indicates that there is still room for improvement in the obstacle avoidance efficiency and path optimization of sliding mode control in complex dynamic environments.

[0115] (2) Comparative test scheme two: improvement Algorithm + Static Obstacle Avoidance with Artificial Potential Field + Model Predictive Control Experiment: In Experiment 2, a model predictive control (MPC) algorithm was used to control the UAV formation to perform dynamic obstacle avoidance. Relevant indicators were measured to compare model performance, and similarly, Table 5 of relevant performance indicators was generated.

[0116] Table 5 Comparison of model predictive control UAV formation performance in test scheme 2 As shown in Table 5, the actual path length of the UAV formation generally exceeds the ideal path, indicating that sliding mode control also exhibits significant path extension during obstacle avoidance. During obstacle avoidance, the UAV formation experienced zero collisions with obstacles, demonstrating that sliding mode control can effectively ensure the safety of the UAV formation. The calculated average curvature change rate of 0.0077019 indicates that the path generated by sliding mode control is relatively smooth.

[0117] According to the formula - and formula - (25) The control logic constructs the path planning strategy for UAV formation and generates model predictions of the control UAV formation maneuvers and related response curves, as shown in the following results. Figures 21-26 As shown. Figures 27-29The three-dimensional flight path of the UAV under model predictive control (MPC) is shown.

[0118] Although MPC effectively avoided obstacles, its path adjustment was slow, exhibiting a certain lag. The maneuvering of the drone formation revealed severe oscillations and unstable behavior. The fact that the Lyapunov function did not converge at the end of the simulation indicates that the system model is non-convergent, meaning that the drone formation's state will not tend towards a stable equilibrium point or the desired trajectory over time, but may continue to oscillate or deviate from the target state.

[0119] According to Table 5, Figures 27-29 It can be seen that although model predictive control can effectively avoid obstacles and collisions, and the overall path is smooth, the increase in the total path length and response lag indicate that there is still room for improvement in obstacle avoidance efficiency and path optimization in complex dynamic environments.

[0120] (3) Comparison of experimental scheme three: improvement Algorithm + Static obstacle avoidance using artificial potential field + sliding mode predictive control: In this scheme, a sliding mode predictive control algorithm is used to control the UAV formation to perform dynamic obstacle avoidance. Relevant indicators are measured to compare the model performance. Similarly, Table 6 is generated to represent the performance indicators of the sliding mode predictive control UAV formation.

[0121] Table 6 Sliding Mode Predictive Control UAV Formation Indicators As shown in Table 6, the actual path length of the UAV formation matches the ideal path, indicating that the path widening phenomenon during obstacle avoidance is minimal under sliding mode control. During obstacle avoidance, the UAV formation experienced zero collisions with obstacles, demonstrating that sliding mode predictive control can effectively ensure the safety of the UAV formation. The calculated average curvature change rate of 0.0044652 indicates that the path generated by sliding mode control is smoother than that of both sliding mode control and model predictive control.

[0122] According to the formula - and formula - (25) The control logic constructs the path planning strategy for UAV formation and generates model prediction results of UAV formation maneuvers and related response curves, such as Figures 30-35 As shown.

[0123] Figures 30-35The maneuverability and response curves of the UAV formation under sliding mode predictive control (SMPC) are presented. SMPC successfully avoided all obstacles and completed path adjustments within the specified time. The oscillations during formation motion were relatively mild, and the system exhibited good stability. Through Lyapunov function analysis, the simulation results eventually converged, indicating that the UAV formation system state tended towards a stable equilibrium point, and the formation successfully followed the target trajectory.

[0124] Figures 36-38 The UAV formation path diagram under sliding mode predictive control is shown. Table 5 shows the experimental results. Figures 30-38 As can be seen, compared with traditional sliding mode control (SMC) and model predictive control (MPC) methods, this algorithm shows significant advantages in several aspects. The algorithm successfully avoids all obstacles and quickly completes path adjustment, demonstrating high real-time performance and adaptability. The path length deviates only slightly from the ideal path, indicating that the path planning maintains good optimization effect while avoiding obstacles. Finally, the UAV formation system has high stability, and the path adjustment process is smooth and without obvious oscillations, avoiding the hysteresis effect in MPC and the excessive oscillations in sliding mode control.

[0125] Simulation experiment scheme three demonstrated strong robustness, short adjustment time, small path deviation and high stability in dynamic obstacle avoidance and path planning tasks of multi-UAV formations. It has comprehensive performance that is superior to traditional sliding mode control and model predictive control, and is suitable for more complex and dynamic flight environments.

[0126] This application proposes a hierarchical control framework that integrates global path planning and local dynamic optimization. This framework achieves a synergistic improvement in path efficiency, obstacle avoidance robustness, and formation stability, effectively addressing the dual challenges of minimizing path redundancy and ensuring kinematic and dynamic feasibility in UAV swarm operations. This is achieved through spatiotemporal layering. By combining the framework with a dynamic potential field fusion mechanism, the proposed scheme achieves an 81.5% reduction in path redundancy (51.23% → 9.47%), while ensuring collision-free navigation in high-density dynamic environments. The C² continuous trajectory regeneration technique improves curvature continuity by 86.5% (Δκ = 0.0168) and significantly suppresses mechanical vibration through second-order smoothing constraints. Experimental results show that the proposed method exhibits significant advantages in both path efficiency and smoothness, with actual path lengths (35.17 m, 37.11 m, 38.15 m, 38.8 m, 36.52 m) and average curvature change rate (0.0026213) both outperforming the baseline algorithm (42.06 m–46.12 m, 0.0077019; 48.99 m–57.74 m, 0.019423). These advancements provide a geometrically constrained solution paradigm for mission-critical cluster applications, achieving simultaneous optimization of navigation efficiency and obstacle avoidance robustness. It provides highly reliable solutions for scenarios such as urban logistics (e.g., drone delivery between dense buildings) and disaster emergency response (search and rescue in complex terrain).

[0127] Another embodiment of this application relates to an electronic device, including: at least one processor; and a memory communicatively connected to the at least one processor; wherein the memory stores instructions executable by the at least one processor to enable the at least one processor to perform the methods described in the above embodiments.

[0128] The memory and processor are connected via a bus, which can include any number of interconnecting buses and bridges, connecting various circuits of one or more processors and memories. The bus can also connect various other circuits, such as peripheral devices, voltage regulators, and power management circuits, which are well known in the art and will not be described further herein. The bus interface provides an interface between the bus and the transceiver. The transceiver can be a single element or multiple elements, such as multiple receivers and transmitters, providing a unit for communicating with various other devices over a transmission medium. Data processed by the processor is transmitted over the wireless medium via an antenna, which further receives data and transmits it to the processor.

[0129] The processor manages the bus and general processing, and also provides various functions, including timing, peripheral interfaces, voltage regulation, power management, and other control functions. Memory is used to store data used by the processor during operation.

[0130] Another embodiment of this application relates to a computer-readable storage medium storing a computer program. When executed by a processor, the computer program implements the method embodiments described above.

[0131] That is, those skilled in the art will understand that all or part of the steps in the methods of the above embodiments can be implemented by a program instructing related hardware. This program is stored in a storage medium and includes several instructions to cause a device (which may be a microcontroller, chip, etc.) or processor to execute all or part of the steps of the methods described in the various embodiments of this application. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0132] Those skilled in the art will understand that the above embodiments are specific embodiments for implementing this application, and in practical applications, various changes can be made to them in form and detail without departing from the spirit and scope of this application.

Claims

1. A method for UAV formation path planning based on sliding mode predictive control, characterized in that, include: Establish a kinematic model of a drone formation consisting of a leader and followers; Based on the kinematic model and basic formation control input, a comprehensive control law for the UAV is designed. Then, an obstacle avoidance control term generated by an artificial potential field is introduced on the basis of the comprehensive control law to obtain the obstacle avoidance control law for the UAV. An improved A-star algorithm is used to generate a global reference path for the UAV, and the integrated control law of the UAV is used to drive the UAV to track the global reference path. At the same time, the basic formation control input is corrected in real time based on the obstacle avoidance control law during flight. The formation recovery coefficient is introduced to determine the formation control law. Based on the formation control law, obstacle avoidance control law, and comprehensive control law, the final control law of each UAV in the UAV formation is obtained. By using the final control law to drive the UAV formation to fly along the reference path, obstacle avoidance and formation restoration can be achieved simultaneously during the flight of the UAVs.

2. The UAV formation path planning method based on sliding mode predictive control according to claim 1, characterized in that, The kinematic model includes: setting the control input of each UAV as the desired acceleration vector, the speed of the UAV being the integral result of the acceleration, and the position being the integral result of the speed.

3. The UAV formation path planning method based on sliding mode predictive control according to claim 1, characterized in that, The comprehensive control law for the UAV, based on the kinematic model and basic formation control input, is designed as follows: A state-space model of UAV formation is established based on the kinematic model and basic formation control input of the UAV. Based on the state-space model, the state vector of the UAV is obtained and the state error is calculated. The weighted sum of the state errors is used as the sliding surface. The predicted state error is introduced as the sliding constraint to obtain the predicted state error sliding surface at the next prediction time. By introducing discontinuous control terms on the sliding surface to resist external disturbances, the sliding mode control law of the UAV is obtained. Predicting the future of drones based on model predictive control. The state sequence at time 1 and control input sequence The predicted state of the UAV at the next prediction moment is obtained. A cost function is established based on the deviation between the predicted state and the desired state of the UAV. The prediction state error sliding surface is introduced as a constraint term. By minimizing the cost function, the optimal control input sequence is obtained and used as the model predictive control law. By fusing the sliding mode control law and the model predictive control law, a comprehensive control law is obtained.

4. The UAV formation path planning method based on sliding mode predictive control according to claim 1, characterized in that, The basic formation control input for the follower is obtained from the position and velocity errors of the navigator and the follower; the basic formation control input for the navigator is the basic control input for the navigator's path tracking task.

5. The UAV formation path planning method based on sliding mode predictive control according to claim 1, characterized in that, The obstacle avoidance control term generated by an artificial potential field is introduced based on the comprehensive control law to obtain the obstacle avoidance control law for the UAV, including: The total potential force is determined using the artificial potential field method; the total potential force includes the attractive force of the target point and the repulsive force of the obstacle. The repulsive force exerted by each obstacle on the drone is dynamically adjusted, and the total repulsive force exerted by all obstacles is obtained and used as an obstacle avoidance correction term. By introducing a weighted obstacle avoidance correction term based on the comprehensive control law, the obstacle avoidance control law for the UAV is obtained.

6. The UAV formation path planning method based on sliding mode predictive control according to claim 1, characterized in that, The method of generating the global reference path for the UAV using the improved A-Star algorithm includes: The three-dimensional workspace is divided into N equally spaced grid nodes, and the connection between different nodes is defined by the adjacency matrix. In the original Based on the algorithm's estimated cost function, a heuristic estimation of weight coefficients is introduced to obtain a new estimated cost function. Based on grid nodes and adjacency matrix, the initial planned path is output using the new estimated cost function. The initial planned path is smoothed using a cubic Bézier curve; Starting from the current state of the drone, the path is replanned periodically. After the path is successfully updated, the connection between the historical path and the newly planned path is retained.

7. The UAV formation path planning method based on sliding mode predictive control according to claim 1, characterized in that, A formation restoration coefficient is introduced to determine the formation control law. Based on the formation control law and the obstacle avoidance force control law, the basic control inputs are dynamically adjusted to obtain the final control law for each UAV in the UAV formation, including: Based on the preset relative positions of the target, followers, and navigator, the formation control law is determined by introducing a formation recovery coefficient; By weighted fusion of the obstacle avoidance control law and the formation control law, and combined with the comprehensive control law, the final control law for each drone in the drone formation is obtained.

8. A UAV formation system based on sliding mode predictive control, characterized in that, The drone formation includes at least two drones, one of which acts as the navigator and the others as followers. Each drone flies according to the drone formation path planning method based on sliding mode predictive control as described in any one of claims 1 to 7, so as to achieve the desired state of the drone formation system.

9. An electronic device, characterized in that, include: At least one processor; as well as, A memory communicatively connected to the at least one processor; wherein, The memory stores instructions that can be executed by the at least one processor to enable the at least one processor to perform the UAV formation path planning method based on sliding mode predictive control as described in any one of claims 1 to 7.

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