Unmanned aerial vehicle cluster collaborative obstacle avoidance method based on distributed model predictive control

Abstract

The invention discloses an unmanned aerial vehicle cluster collaborative obstacle avoidance method based on distributed model predictive control, and belongs to the technical field of unmanned aerial vehicle cluster collaborative navigation. The method aims to solve the problem that the decision is easy to oscillate due to non-convex obstacle avoidance constraint, difficult solution and information asynchronization of the cluster in a dynamic environment. According to the scheme, each unmanned aerial vehicle constructs a local optimization problem containing a non-convex constraint and a cost function based on the unmanned aerial vehicle and neighbor information in each period; taking the optimal trajectory of the previous period as a reference, and converting constraint linearization and cost function second-order approximation into convex quadratic programming sub-problems; solving and outputting a control sequence within the time constraint; and executing the current control quantity and broadcasting a new predicted trajectory. The method is used for real-time collaborative obstacle avoidance of the unmanned aerial vehicle cluster in a communication limited environment.

Description

Technical Field

[0001] This invention relates to the field of unmanned aerial vehicle (UAV) swarm control and cooperative navigation technology. More specifically, this invention relates to a UAV swarm cooperative obstacle avoidance method based on distributed model predictive control. Background Technology

[0002] With the rapid development of drone technology, multi-drone systems are increasingly being used in areas such as regional patrols, logistics delivery, and collaborative detection. In these applications, drone swarms need to perform tasks efficiently and safely in dynamic, unknown, or complex environments. Real-time and reliable collaborative obstacle avoidance is a core technology for ensuring mission success and system safety. This requires the swarm to maintain its overall formation or cooperative objective while avoiding static obstacles, dynamic obstacles, and potential collisions between individual drones within the swarm. This places extremely high demands on the autonomy, real-time performance, and robustness of the control system.

[0003] Traditional solutions are mainly divided into two architectures: centralized and distributed. Centralized control methods aggregate the state information of all UAVs to a central processor for unified planning and decision-making. While theoretically capable of achieving a globally optimal solution, they suffer from high communication load, strong dependence on the central node, poor scalability, and the risk of system collapse if the central node fails. This makes them unsuitable for large-scale, highly dynamic cluster applications. Therefore, distributed control architecture has become the mainstream research approach in recent years. Among these, distributed model predictive control (MMCC) is considered a highly promising technology due to its ability to explicitly handle system constraints, make forward-looking decisions through prediction, and naturally align with the information structure of distributed systems.

[0004] However, applying distributed model predictive control theory to practical drone swarm cooperative obstacle avoidance still faces several core challenges that urgently need to be addressed. The primary challenge stems from the inherent non-convexity of the problem. To ensure absolute safety, obstacle avoidance constraints are typically expressed as maintaining a minimum Euclidean distance between the drone and the obstacle (or other drones), which mathematically constitutes a non-convex geometric set. Within the framework of rolling time-domain optimization, each drone needs to solve an optimization problem containing such non-convex constraints online. Although existing research has attempted to address this using techniques such as sequential convexification, current methods often introduce significant conservatism during the convexification process, leading to excessive compression of the feasible region or failure to tightly integrate with the feedback loop of distributed predictive control, thus affecting the optimality and smoothness of the final obstacle avoidance path.

[0005] Secondly, there is a profound contradiction between asynchronous distributed information and real-time computation. In real-world distributed systems, each UAV can only exchange limited predictive information (such as intended trajectories) through a communication network with limited bandwidth and potential delays and packet loss. This inconsistency and asynchronicity of information can easily lead to conflicting independent decisions made by each UAV based on local and outdated information, causing overall cluster decision oscillations or even obstacle avoidance failures. Furthermore, onboard computing resources are severely limited, requiring complex optimization solutions to be completed within millisecond-level time windows. Non-convex optimization problems are inherently time-consuming and yield uncertain results, making it difficult to meet the requirements of hard real-time control. Existing methods either oversimplify models and constraints in pursuit of real-time performance, sacrificing safety; or fail to meet computational time limits to ensure safety, leading to control interruptions. How to design a method that can accurately handle non-convex safety constraints, compensate for collaborative biases caused by distributed information inconsistencies, and ensure reliable real-time solutions under limited onboard computing power is a long-standing and unresolved technical bottleneck in this field, and the core problem that this invention aims to overcome. Summary of the Invention

[0006] One object of the present invention is to solve at least the above-mentioned problems and to provide at least the advantages that will be described later.

[0007] Another objective of this invention is to provide a collaborative obstacle avoidance method for UAV swarms based on distributed model predictive control. This method transforms the non-convex obstacle avoidance and collaborative problem into a convex quadratic programming subproblem in real time, and utilizes historical trajectory feedback and time constraint solution mechanisms to effectively compensate for collaborative deviations caused by asynchronous information while strictly ensuring safe flight distances. This enables UAV swarms to achieve highly reliable and real-time autonomous collaborative obstacle avoidance in complex environments.

[0008] To achieve these objectives and other advantages according to the present invention, a collaborative obstacle avoidance method for unmanned aerial vehicle (UAV) swarms based on distributed model predictive control is provided, wherein each UAV in the swarm executes independently in each control cycle: S1. Based on the local dynamics prediction model, the current state, the predicted trajectory of the neighboring UAV in the previous cycle, and the current environmental obstacle information, construct a local rolling time domain optimization problem that simultaneously includes a non-convex minimum safe distance constraint to prevent local collisions and a non-convex interactive cost function that quantifies and actively compensates for the group coordination deviation caused by the asynchronous distributed information. S2. Using the optimal predicted trajectory of the machine in the previous cycle as the reference trajectory, the non-convex minimum safe distance constraint and non-convex interaction cost function in step S1 are co-convexized to form a convex quadratic programming subproblem. S3. Solve the convex quadratic programming subproblem described in step S2 within the preset computation time constraint, and output a feasible control sequence. S4. Execute the instantaneous control quantity of the feasible control sequence output in step S3, and broadcast the local optimal predicted trajectory generated by the feasible control sequence through the local dynamics model to neighboring UAVs. Iterate in a loop to achieve continuous cooperative obstacle avoidance of the UAV swarm. In step S2, the co-convexification process for the non-convex minimum safe distance constraint and the non-convex interaction cost function includes: linearizing the non-convex minimum safe distance constraint point by point into a set of linear inequality constraints based on the optimal predicted trajectory of the previous cycle and the current location of obstacles in the environment; approximating the non-convex interaction cost function at the current trajectory prediction point to form a quadratic cost function; and combining the linear inequality constraints and the quadratic cost function with the dynamic model constraints of the local machine to form the convex quadratic programming subproblem.

[0009] Preferably, the non-convex minimum safe distance constraint in step S1 includes a first type of collision avoidance constraint between the local drone and all neighboring drones, and a second type of collision avoidance constraint between the local drone and obstacles in the current environment. The first type of collision avoidance constraint requires that the square of the Euclidean distance between the local drone's predicted position at a future time and the predicted position of the corresponding neighboring drone obtained from the previous period at the same future time is not less than the square of a preset safe distance threshold between drones. The second type of collision avoidance constraint requires that the square of the distance between the local drone's predicted position at a future time and the position of the corresponding environmental obstacle is not less than the square of a preset safe distance threshold between a drone and an obstacle.

[0010] Preferably, the non-convex interaction cost function in step S1 is constructed in the following way: For each neighboring drone, calculate the difference between the predicted future trajectory planned by the drone in the current cycle and the predicted trajectory obtained by a neighbor from the previous cycle, and use it as the instantaneous trajectory deviation for the current cycle. The historical cooperative deviation accumulated for the neighboring UAV is obtained by multiplying the instantaneous trajectory deviations generated by the local machine for the neighboring UAV in the past several control cycles by a decay memory factor between 0 and 1 and then accumulating them. The non-convex interaction cost function is constructed based on the instantaneous trajectory deviation and the cumulative historical cooperative deviation. The non-convex interaction cost function is the sum of the norm squares of the instantaneous trajectory deviations of all neighboring UAVs in the current period plus the sum of the norm squares of the cumulative historical cooperative deviations of all neighboring UAVs.

[0011] Preferably, the implementation of the linear inequality constraint includes: A1. For each future moment in the prediction time domain, the prediction position of the corresponding moment in the optimal prediction trajectory of the previous cycle of the local machine is used as the reference point for linearization. A2. For the first type of collision avoidance constraint, calculate the function value of the squared Euclidean distance between the predicted position of the local drone at a certain future time and the predicted position of the corresponding neighboring drone obtained from the previous period at the same future time, and the gradient vector of the squared distance function at the reference point with respect to the local drone's predicted position variable; using the function value and the gradient vector, obtain the linear inequality with respect to the local drone's current predicted position variable through a first-order Taylor expansion. A3. For the second type of collision avoidance constraint, calculate the function value of the squared Euclidean distance between the predicted position of the machine at a certain future time and the position of the corresponding environmental obstacle at a reference point, and the gradient vector of the squared distance function at the reference point with respect to the predicted position variable of the machine; use the function value and the gradient vector to obtain the linear inequality with respect to the current predicted position variable of the machine through a first-order Taylor expansion. A4. Traverse all future moments, all neighboring drones, and all environmental obstacles within the prediction time domain, repeating steps A2 and A3 to finally generate a set of linear inequality constraints.

[0012] Preferably, the implementation of the quadratic cost function includes: B1. Use the optimal predicted trajectory of the previous cycle of the local machine as the reference trajectory for performing a second-order approximation on the non-convex interaction cost function; B2. At each future time prediction point of the reference trajectory, perform a second-order Taylor expansion on the non-convex interactive cost function; B3. Combine the results obtained from the second-order Taylor expansion at all future time points in step B2 to form a quadratic cost function for the predicted location variables of the local machine at each time point in the prediction time domain.

[0013] Preferably, when the optimal predicted trajectory of the machine in the previous cycle is unavailable in the first control cycle, it is generated by forward simulation based on the current state of the machine and the default control command through the machine dynamics prediction model.

[0014] Preferably, the convex quadratic programming subproblem in step S2 is a new optimization problem defined by using the quadratic cost function as the objective function and the set of linear inequality constraints and the state-space equation equality constraints obtained by discretizing the local dynamics prediction model as constraints.

[0015] Preferably, in step S3, the solution is performed within the preset computation time constraint using a numerical optimization solver based on the interior point method or the effective set method, and when the time constraint is exhausted, the optimal feasible solution obtained in the current iteration is output.

[0016] Preferably, the specific implementation of step S4 includes: C1. Extract the first control vector from the feasible control sequence output in step S3, use it as the immediate control command for the current control cycle, and send it to the flight control actuator of the machine for execution. C2. Input the feasible control sequence and the current state into the local dynamics prediction model for forward simulation calculation to obtain the predicted state of the local machine at each time in the future prediction time domain, and extract the position sequence from it to form the optimal prediction trajectory for this period. C3. The optimal predicted trajectory is encapsulated into a data packet according to a preset communication protocol and broadcast to all neighboring drones via a wireless communication network for their use in the next control cycle when performing collaborative optimization.

[0017] The present invention has at least the following beneficial effects: Firstly, this invention transforms the complex non-convex obstacle avoidance and cooperative optimization problem into a convex quadratic programming subproblem that can be solved in real time, fundamentally solving the irreconcilable contradiction between real-time performance and non-convex security in distributed predictive control, and realizing safe and cooperative autonomous obstacle avoidance of the cluster in a dynamic environment. Secondly, this invention further constructs a non-convex interactive cost function that includes a decay memory factor and historical bias accumulation, actively quantifies and compensates for group coordination errors caused by communication delays or information inconsistencies, and significantly improves the overall coordination robustness and obstacle avoidance consistency of the cluster under asynchronous information conditions. Thirdly, this invention also employs a collaborative convexification strategy based on the optimal trajectory of the previous cycle, combining first-order linearization and second-order approximation. This ingeniously transforms the geometric non-convex constraints and nonlinear collaborative objectives into a standard convex optimization problem, greatly reducing the complexity of online computation and providing a key guarantee for achieving reliable solutions on resource-constrained airborne platforms. Fourth, by introducing a strict time-constrained solution and optimal feasible solution output mechanism, this invention ensures that even with limited computing resources, each control cycle will necessarily obtain a control command that satisfies all safety constraints, thereby guaranteeing the hard real-time performance and decision reliability of the control system and avoiding system instability caused by solution failure.

[0018] Other advantages, objectives and features of the present invention will become apparent in part from the following description, and in part from those skilled in the art through study and practice of the invention. Attached Figure Description

[0019] Figure 1 This is a flowchart illustrating the drone swarm cooperative obstacle avoidance method described in one of the technical solutions of the present invention. Detailed Implementation

[0020] The present invention will now be described in further detail with reference to the accompanying drawings, so that those skilled in the art can implement it based on the description.

[0021] It should be understood that terms such as “having,” “comprising,” and “including” as used herein do not exclude the presence or addition of one or more other elements or combinations thereof.

[0022] like Figure 1 As shown, this invention provides a collaborative obstacle avoidance method for UAV swarms based on distributed model predictive control, where each UAV in the swarm executes independently within each control cycle: S1. Based on the local dynamics prediction model, the current state, the predicted trajectory of the neighboring UAV in the previous cycle, and the current environmental obstacle information, construct a local rolling time domain optimization problem that simultaneously includes a non-convex minimum safe distance constraint to prevent local collisions and a non-convex interactive cost function that quantifies and actively compensates for the group coordination deviation caused by the asynchronous distributed information. S2. Using the optimal predicted trajectory of the machine in the previous cycle as the reference trajectory, the non-convex minimum safe distance constraint and non-convex interaction cost function in step S1 are co-convexized to form a convex quadratic programming subproblem. S3. Solve the convex quadratic programming subproblem described in step S2 within the preset computation time constraint, and output a feasible control sequence. S4. Execute the instantaneous control quantity of the feasible control sequence output in step S3, and broadcast the local optimal predicted trajectory generated by the feasible control sequence through the local dynamics model to neighboring UAVs. Iterate in a loop to achieve continuous cooperative obstacle avoidance of the UAV swarm. In step S2, the co-convexification process for the non-convex minimum safe distance constraint and the non-convex interaction cost function includes: linearizing the non-convex minimum safe distance constraint point by point into a set of linear inequality constraints based on the optimal predicted trajectory of the previous cycle and the current location of obstacles in the environment; approximating the non-convex interaction cost function at the current trajectory prediction point to form a quadratic cost function; and combining the linear inequality constraints and the quadratic cost function with the dynamic model constraints of the local machine to form the convex quadratic programming subproblem.

[0023] This invention provides a collaborative obstacle avoidance method for UAV swarms based on distributed model predictive control. It constructs a sequential convexity mechanism based on its own historical feedback and deeply embeds it into the closed-loop framework of distributed model predictive control to solve two major technical challenges: real-time solution of non-convex optimization and asynchronous distributed information coordination. Specifically, at the beginning of each control cycle, each UAV first collects three types of information: its current state obtained through sensors, the predicted trajectories calculated and broadcast by all neighboring UAVs in the previous cycle received through the communication network, and the current environmental obstacle information obtained through the onboard perception system. Based on this information, the UAV uses its own dynamic prediction model to construct a local rolling temporal optimization problem for several future time steps. This local rolling temporal optimization problem includes two types of non-convex components: first, a non-convex minimum safe distance constraint that ensures no collision between the UAV, neighboring UAVs, and obstacles (a geometrically non-convex set); second, a non-convex interactive cost function designed to quantify and proactively compensate for the group coordination deviation caused by communication delays, packet loss, etc., resulting in inconsistent neighbor information obtained by each UAV (i.e., asynchronous distributed information). The two types of non-convex components make it computationally very difficult and time-consuming to directly solve the local rolling time-domain optimization problem, which cannot meet the real-time requirements of UAV flight control. Furthermore, the asynchronous nature of information itself can lead to the failure of optimization results based on inaccurate information, resulting in decision conflicts or oscillations.

[0024] To address the aforementioned issues, this invention further employs a collaborative convexification process for two types of non-convex components. Specifically, it utilizes the optimal predicted trajectory from the previous cycle—the drone's own historical decision-making result—as a reference benchmark for linearizing and approximating the current non-convex problem. The specific operation consists of two parts: For the non-convex minimum safe distance constraint, using the corresponding points on the previous cycle's trajectory and the currently known obstacle positions as benchmarks, it linearizes point-by-point using mathematical methods (such as first-order Taylor expansion), thereby transforming the complex geometric collision avoidance requirements into a set of standard linear inequality constraints. For the non-convex interaction cost function, a second-order approximation is performed at the same historical trajectory reference points, transforming it into a quadratic function of the optimization variables. After processing, the original, difficult-to-solve non-convex component optimization problem is transformed into a mathematically formalized, mature, and efficient convex quadratic programming subproblem. This transformation process is distributed and independent; each drone relies only on its own historical information without requiring additional collaborative iterations, thus ensuring the algorithm's parallelism and real-time performance.

[0025] Next, the UAV sets a strict time limit (less than the control cycle length) for solving the obtained convex quadratic programming subproblem and calls an embedded, efficient convex optimization solver (such as an interior-point solver) for computation. Regardless of whether the solver converges to the theoretical optimum within the specified time, it will output a feasible control sequence found when time runs out. This sequence is a set of control commands that at least satisfies all linearized safety and dynamic constraints, ensuring timely and reliable output of control commands. The UAV then immediately executes the first, and most immediate, control variable in the feasible control sequence, completing the actual control of the current cycle. Simultaneously, based on the entire feasible control sequence and its own dynamic model, it calculates a predicted trajectory for a future period as its optimal predicted trajectory and broadcasts it to all neighboring UAVs via the wireless network. This completes one control cycle. When all UAVs synchronously complete this cycle and enter the next cycle, they will receive updated optimal predicted trajectories from each other and use this as new cooperative information input, repeating the above process to achieve continuous, online, and adaptive cooperative obstacle avoidance by the swarm.

[0026] The above technical solution transforms the distributed, non-convex cooperative obstacle avoidance optimization problem into a series of convex quadratic programming subproblems that can be solved quickly based on their own historical feedback. This fundamentally solves the problem of achieving safe collision avoidance and cooperative consistency in UAV swarms under the real-world conditions of limited onboard computing resources and communication delays. It significantly improves the real-time performance, reliability, and overall cooperative robustness of the swarm system in dynamic and complex environments.

[0027] In one technical solution, the non-convex minimum safe distance constraint in step S1 includes a first type of collision avoidance constraint between the local drone and all neighboring drones, and a second type of collision avoidance constraint between the local drone and obstacles in the current environment. The first type of collision avoidance constraint requires that the square of the Euclidean distance between the local drone's predicted position at a certain future time and the predicted position of the corresponding neighboring drone obtained from the previous period at the same future time is not less than the square of a preset safe distance threshold between drones. The second type of collision avoidance constraint requires that the square of the distance between the local drone's predicted position at a certain future time and the position of the corresponding environmental obstacle is not less than the square of a preset safe distance threshold between a drone and an obstacle.

[0028] This invention further specifies and precisely constructs a non-convex minimum safe distance constraint to prevent collisions with the local drone. This constraint is a lower bound requirement on the squared Euclidean distance between the unknown future prediction of the local drone and external entities (neighboring drones and environmental obstacles). The squared distance defines a non-convex feasible region, leading to increased complexity in solving the local rolling time-domain optimization problem. Simultaneously, addressing the challenge of asynchronous distributed information, the constraint on neighboring drones (the first type of collision avoidance constraint) cleverly sets the comparison object as the predicted position of the corresponding neighboring drone obtained from the previous cycle. This acknowledges and models the reality that information in a distributed system inevitably has a periodic delay, rather than idealized instantaneous synchronization. By constructing a hard safety constraint based on this delayed information, each drone's local safety decision is established on a foundation of consistent and predictable information, even if not the latest, thus providing a logical starting point for ensuring safety in an asynchronous environment.

[0029] According to the above technical solution, the unknown prediction of UAV i at time t (current control period) for future time t+k is represented as p. i (t+k|t)∈R n , where n=2 or 3, represents the two-dimensional or three-dimensional spatial position coordinates, and its physical dimension is length [L].

[0030] Type 1 collision avoidance constraint (with neighboring drones): ; , ; Type II collision avoidance constraints (with environmental obstacles): ; , ; in, The predicted position of the neighboring UAV j at time t+k is received from the communication network, calculated and broadcast by the neighboring UAV j in the previous control period t-1, and has the dimension [L]. Q i (t) is the set of neighboring drones that have a communication connection with drone i during period t; d safe,1 The preset minimum safe distance threshold between drones is defined in units of [L]. N is the total number of prediction steps in the time domain, a positive integer; Let be the Euclidean norm of the vector, with dimensions [L]. 2 ; p o (t) represents the location of the environmental obstacle o as sensed by the airborne sensor or obtained from the map during period t, with dimensions [L]. W i (t) represents the set of environmental obstacles that need to be considered by UAV i with period t; d safe,2 d is the preset minimum safe distance threshold between the drone and environmental obstacles. safe,2 ≥d safe,1 Its dimension is [L]; β>0 represents the weighting coefficient of the historical deviation compensation term, which is dimensionless and ranges from 0.1 to 2.

[0031] The aforementioned technical solution quantifies the collaborative error caused by asynchronous information into an optimizable objective by constructing a non-convex interactive cost function that includes instantaneous deviation penalties and historical deviation compensation. This enables each UAV to not only avoid instantaneous collisions but also proactively correct group motion deviations caused by inconsistencies in historical information. This significantly enhances the inherent coordination and consistency convergence capabilities of UAV swarms in environments with limited communication or latency, fundamentally alleviating the oscillation problem easily caused by distributed decision-making, and providing key algorithmic support for stable and robust collaborative obstacle avoidance in complex environments.

[0032] In actual implementation, UAV i reads the data packets broadcast by its neighboring UAV j in the previous period t-1 from its communication buffer, and parses them to extract the predicted trajectory information, that is, the position prediction sequence of each neighboring UAV j for the next N time moments. Meanwhile, the airborne perception system (such as lidar, visual sensors) or the global mission planning module provides the position information p of all relevant obstacles o at the current time t. o (t). The UAV i loads the system's preset security parameters, including d, from its local memory. safe,1 d safe,2 And the predicted time domain length N.

[0033] The constraint generation loop is a multi-layered nested automated process. The outer loop iterates through each future time k (from 1 to N) in the prediction time domain. For each fixed future time k, the inner loop executes two parallel sub-loops. The first sub-loop targets the current set of neighboring drones Q. i For each neighboring drone j in (t): the algorithm extracts the local position variable to be optimized at that moment. And retrieve the predicted position of neighboring drone j at the same moment from the cache. Then, the square of the Euclidean norm of the difference between the two is calculated. Based on the requirements of the first type of collision avoidance constraint, an inequality condition is generated, whereby the calculated result must be greater than or equal to d. safe,1 The second sub-loop targets the currently perceived set of obstacles W. i For each obstacle o in (t): use the same native predicted location variable relative to obstacle position p o (t) Calculate the squared distance and generate an inequality based on the second type of collision avoidance constraint, requiring the result to be greater than or equal to d. safe,2 This process will ultimately output a value containing |Q. i (t)|×N+|W i A constraint set of (t)|×N inequalities. Each inequality represents a safety rule that must be satisfied at a specific future time. Geometrically, all these inequalities represent a space carved out by multiple repulsion spheres, where the center of each sphere is the known location of a neighbor or obstacle, and the radius is the corresponding safety distance. It is the non-convex property of this set that makes the optimization problem containing it difficult to solve directly, thus requiring convexification.

[0034] The aforementioned technical solution lays a rigorous and computable mathematical foundation for the entire cooperative obstacle avoidance method by precisely transforming the abstract requirement of preventing local collisions into a specific set of Euclidean distance square inequalities concerning the predicted position variables of the local drones. This provides a clear and unique operational object for subsequent point-by-point linearization and convexity processing, ensuring that complex spatial safety geometric constraints can be accurately and unambiguously incorporated into the optimization framework. Thus, at the algorithm design level, it provides the most fundamental and formally verifiable safety constraint model for real-time and reliable collision avoidance of UAV swarms.

[0035] In one of the technical solutions, the non-convex interaction cost function in step S1 is constructed in the following way: For each neighboring drone, calculate the difference between the predicted future trajectory planned by the drone in the current cycle and the predicted trajectory obtained by a neighbor from the previous cycle, and use it as the instantaneous trajectory deviation for the current cycle. The historical cooperative deviation accumulated for the neighboring UAV is obtained by multiplying the instantaneous trajectory deviations generated by the local machine for the neighboring UAV in the past several control cycles by a decay memory factor between 0 and 1 and then accumulating them. The non-convex interaction cost function is constructed based on the instantaneous trajectory deviation and the cumulative historical cooperative deviation. The non-convex interaction cost function is the sum of the norm squares of the instantaneous trajectory deviations of all neighboring UAVs in the current period plus the sum of the norm squares of the cumulative historical cooperative deviations of all neighboring UAVs.

[0036] This invention further specifies a non-convex interactive cost function that quantifies and actively compensates for group coordination deviations caused by asynchronous distributed information. In real distributed systems, each UAV can only receive the predicted trajectory of its neighboring UAVs from the previous cycle through a communication network with inherent delays. This information asynchrony results in outdated reference information (the intentions of neighboring UAVs) used by each UAV to plan its own trajectory. If UAVs optimize solely based on instantaneous trajectory differences (e.g., only penalizing the deviation between the current predicted position and that of neighboring UAVs), they are highly susceptible to decision deadlock or oscillations due to inconsistent reference information, failing to achieve globally consistent coordinated movement. The interactive cost function incorporating historical memory provided by this invention not only penalizes the instantaneous trajectory deviation calculated in the current cycle but also uses a decaying memory factor to weight and accumulate deviations generated over multiple past cycles, forming a historical coordination deviation accumulation. This memorizes past coordination errors caused by information inconsistency and actively applies a compensating force in the current optimization, guiding the UAV's trajectory towards a direction that eliminates these historical accumulated deviations. This enables the UAV's decision-making not only to focus on current collision avoidance but also to proactively correct historical coordination errors and promote convergence of group movement trends, thereby effectively addressing the challenges posed by information asynchrony.

[0037] Specifically, the predicted position sequence of UAV i at time t for the next N steps can be represented as follows: , where p i (t+k|t)∈R n The dimension is length [L]. Its predicted trajectory for the previous cycle, received from neighboring UAV j, is... .

[0038] Instantaneous trajectory deviation calculation: For a neighboring drone j and a prediction step k, its instantaneous trajectory deviation vector is: ; Calculation of historical cumulative coordination deviation: For neighboring drone j, its historical cumulative coordination deviation E i,j (t) is calculated as follows: ; Construction of non-convex interaction cost function: Based on the above quantities of all neighboring drones, a non-convex interaction cost function is constructed. : ; in, Let J be the predicted position of neighboring UAV j at time t+k obtained from the previous period t-1, with the dimension [L]. e i,j(t+k|t) represents the difference in expected birth time position between the local drone and its neighboring drone j at time t+k in the current period t, with the dimension [L]. M is the memory window length, which is a preset positive integer representing how many past control cycles of deviation are considered; τ is the historical cycle offset index, where τ=0 represents the previous cycle t-1, τ=1 represents the cycle before that t-2, and so on. This represents the instantaneous trajectory deviation vector between UAV i and its neighboring UAV j, calculated over a historical period t-τ, stored locally on UAV i. The representative value at the corresponding moment can be regarded as a memory of the direction of historical deviation for the sake of simplification, and its dimension is [L]. α is the decay memory factor, 0 < α < 1. The closer its value is to 1, the longer the historical memory; the closer it is to 0, the more attention is paid to recent bias. E i,j (t) is the weighted vector sum of historical deviations, with dimensions [L].

[0039] In one of the technical solutions, the implementation of the linear inequality constraint includes: A1. For each future moment in the prediction time domain, the prediction position of the corresponding moment in the optimal prediction trajectory of the previous cycle of the local machine is used as the reference point for linearization. A2. For the first type of collision avoidance constraint, calculate the function value of the squared Euclidean distance between the predicted position of the local drone at a certain future time and the predicted position of the corresponding neighboring drone obtained from the previous period at the same future time, and the gradient vector of the squared distance function at the reference point with respect to the local drone's predicted position variable; using the function value and the gradient vector, obtain the linear inequality with respect to the local drone's current predicted position variable through a first-order Taylor expansion. A3. For the second type of collision avoidance constraint, calculate the function value of the squared Euclidean distance between the predicted position of the machine at a certain future time and the position of the corresponding environmental obstacle at a reference point, and the gradient vector of the squared distance function at the reference point with respect to the predicted position variable of the machine; use the function value and the gradient vector to obtain the linear inequality with respect to the current predicted position variable of the machine through a first-order Taylor expansion. A4. Traverse all future moments, all neighboring drones, and all environmental obstacles within the prediction time domain, repeating steps A2 and A3 to finally generate a set of linear inequality constraints.

[0040] This invention further realizes the linearization of non-convex minimum safety distance constraints. By using the optimal predicted trajectory of the previous cycle as a reference point, the geometrically non-convex constraints are approximated as linear inequalities through a first-order Taylor expansion, thereby transforming the non-convex feasible region, which is difficult to solve in real time, into a convex polyhedral description. This solves two problems faced by distributed model predictive control in UAV swarm cooperative obstacle avoidance: first, non-convex safety constraints (such as minimum distance constraints) directly lead to a non-convex optimization problem, making it impossible to guarantee a reliable real-time solution under limited onboard computing resources; second, oversimplification or conservative treatment of such constraints will sacrifice path optimality or safety. By performing point-by-point linearization based on its own historical trajectory (the optimal prediction of the previous cycle), a set of compact and feasible linear constraints can be dynamically generated in each control cycle, maintaining the geometric meaning of the safety constraints while transforming the problem into a convex quadratic programming form that can be solved quickly.

[0041] Specifically, the unknown prediction of UAV i at time t (current control period) for future time t+k is represented as p. i (t+k|t)∈R n (n=2 or 3). Let... This represents the reference position of the local optimal predicted trajectory obtained from the previous period t-1 at the corresponding time t+k. For the first type of collision avoidance constraint, its non-convex form is: , To predict the location of neighboring drone j obtained from the previous period, d safe,1 >0 represents the safe distance threshold between drones. (At the reference point) Performing a first-order Taylor expansion at , we obtain the linear inequality: ; Similarly, for the second type of collision avoidance constraint, the non-convex form Linearized to: ; Where, d safe,2 ≥d safe,1 The above linearization process applies to each neighbor j∈Q in the prediction time domain k=1,…,N. i (t) and each obstacle o∈W i (t) is executed, ultimately forming a set of linear inequality constraints.

[0042] In the specific workflow, UAV i executes the following sequentially in each control cycle t: First, it loads the optimal predicted trajectory stored locally in the previous cycle, and then extracts the reference positions for each future time t+k. Next, for each future time k, iterate through the current set of neighboring drones Q. i (t) and the set of obstacles W i(t), calculate the linear inequality coefficients corresponding to each collision avoidance constraint according to the above formula; then, integrate all the generated linear inequalities in sequence into a linear constraint system. This linear system, together with the dynamic model equality constraints, constitutes the constraint conditions of the convex quadratic programming subproblem, which is used by the subsequent optimization solver. The above technical solution efficiently transforms non-convex geometric safety constraints into linear inequalities through a first-order Taylor expansion based on historical trajectory reference points, significantly reducing the solution complexity of the optimization problem and making reliable solutions possible within a finite computation time. At the same time, the linearization process relies on its own optimal prediction in the previous cycle, maintaining a reasonable approximation of the constraints to the real safety boundary, avoiding the loss of maneuverability due to excessive conservatism, thus maintaining the accuracy and robustness of cooperative obstacle avoidance while ensuring hard real-time control.

[0043] In one of the technical solutions, the implementation of the quadratic cost function includes: B1. Use the optimal predicted trajectory of the previous cycle of the local machine as the reference trajectory for performing a second-order approximation on the non-convex interaction cost function; B2. At each future time prediction point of the reference trajectory, perform a second-order Taylor expansion on the non-convex interactive cost function; B3. Combine the results obtained from the second-order Taylor expansion at all future time points in step B2 to form a quadratic cost function for the predicted location variables of the local machine at each time point in the prediction time domain.

[0044] This invention further achieves the convexification of the non-convex interaction cost function. By using the optimal predicted trajectory of the previous cycle as the reference trajectory for the second-order approximation, the original nonlinear interaction cost function is transformed into a standard quadratic form through point-by-point second-order Taylor expansion. This solves the optimization problem caused by the non-convexity of the interaction cost function in distributed cooperative obstacle avoidance: the non-convex objective function may cause the optimization problem to have multiple local extrema, and it cannot be guaranteed that the solver will converge to a feasible solution in a finite time, seriously threatening the real-time performance and decision reliability of control. By performing a second-order approximation based on its own historical trajectory, the complex cooperative deviation penalty objective can be transformed into a strictly convex quadratic function, thereby ensuring that the transformed subproblem is a convex quadratic programming problem with a unique global optimum, and can be solved reliably and quickly using an efficient numerical solver.

[0045] Specifically, let the predicted position sequence of UAV i at time t be represented as: ∈R nN , where p i (t+k|t)∈R n (n=2 or 3) are positional variables, let This represents the local optimal predicted trajectory obtained from the previous period t-1, used as the reference trajectory. Non-convex interaction cost function. It's about P i A function of (t). At the reference trajectory point Performing a second-order Taylor expansion at this point yields its quadratic approximation: ; in, , is the deviation vector of the predicted trajectory relative to the meal card trajectory; , where is the gradient vector of the function at the reference point; , where is the Hessian matrix of the function at the reference point.

[0046] Due to the nonconvex interaction cost function The Hessian matrix H is composed of the sum of squares of norms. i It is positive semi-definite, thus guaranteeing that the approximated quadratic form function is convex. (Ignoring the constant term) Then, the aforementioned P is formed. i The quadratic cost function of (t). Finally, using g i and H i Construct a quadratic cost function This function will serve as the objective function for the convex quadratic programming subproblem. This invention transforms the non-convex interaction cost function into a strictly convex quadratic function by applying a second-order approximation based on historical trajectories. This ensures that the distributed optimization subproblem is a convex quadratic programming problem with a unique global optimum and a mature, fast solution algorithm. This significantly improves the computational efficiency and reliability of online optimization, enabling stable and efficient solving of the cooperative obstacle avoidance problem under limited onboard computing resources and strict time constraints. It effectively supports real-time, robust cooperative decision-making by UAV swarms in asynchronous information environments.

[0047] In one technical solution, when the optimal predicted trajectory of the previous cycle is unavailable in the first control cycle, it is generated by forward simulation based on the current state of the machine and the default control command through the machine's dynamic prediction model. By generating an initial reference trajectory based on the current state of the machine and the default control command when the optimal predicted trajectory of the previous cycle is unavailable (such as in the first control cycle), the cooperative convexity processing can be reliably performed during the system startup phase. This effectively solves the initialization problem caused by the lack of historical information in distributed predictive control and ensures the immediate startup and continuous operation of the closed-loop cooperative obstacle avoidance process.

[0048] In one technical solution, the convex quadratic programming subproblem in step S2 is a new optimization problem defined by using the quadratic cost function as the objective function and the set of linear inequality constraints and the state-space equation equality constraints obtained by discretizing the local dynamics prediction model as constraints. Let the predicted position sequence of UAV i at each time point in the prediction time domain of the control period t be: The corresponding control input sequence is: ; k=0,…,N-1; k=1, …,N; Where m is the control input dimension; N is the prediction time-domain step number; x i (t+k|t) represents the state variables, typically including position, velocity, etc. A d and B d The discretized state-space model matrix; C represents the output matrix (extraction position).

[0049] This invention standardizes and integrates convexized safety constraints, cooperative objectives, and UAV dynamics models, clearly defining a convex quadratic programming subproblem with a clear structure and rigorous mathematical form. This lays a directly calculable foundation for subsequent real-time solutions. This definition ensures the convexity of the optimization problem, enabling reliable solutions using efficient numerical optimization algorithms. It effectively solves the problems of difficulty and time consumption caused by complex non-convex constraints and dynamic coupling, and is a key link in enabling the entire distributed cooperative obstacle avoidance method to achieve real-time and reliable operation under limited airborne computing power.

[0050] In one technical solution, step S3 involves solving the problem within a preset computation time constraint using a numerical optimization solver based on the interior-point method or the effective set method. When the time constraint is exhausted, the optimal feasible solution obtained in the current iteration is output. By setting a solution time constraint and employing an efficient optimization algorithm, a feasible control sequence can be output even if complete convergence is not achieved within each control cycle, thus ensuring the hard real-time performance and decision reliability of the control system under limited onboard computing power.

[0051] In one of the technical solutions, the specific implementation of step S4 includes: C1. Extract the first control vector from the feasible control sequence output in step S3, use it as the immediate control command for the current control cycle, and send it to the flight control actuator of the machine for execution. C2. Input the feasible control sequence and the current state into the local dynamics prediction model for forward simulation calculation to obtain the predicted state of the local machine at each time in the future prediction time domain, and extract the position sequence from it to form the optimal prediction trajectory for this period. C3. The optimal predicted trajectory is encapsulated into a data packet according to a preset communication protocol and broadcast to all neighboring drones via a wireless communication network for their use in the next control cycle when performing collaborative optimization.

[0052] Let the feasible control input sequence output in step S3 be: Extract real-time control quantities It is sent to the flight control actuator based on the current state x. i (t) and the entire control sequence U i (t), through the local dynamics model F d (·,·) Perform forward simulation: k=0,1,…,N-1. Extract the position sequence from it. This constitutes the optimal predicted trajectory for this period. P i (t) Encapsulated according to a preset communication protocol, the signal is broadcast to all neighboring UAVs via a wireless network. The above technical solution ensures real-time control and closed-loop feedback by executing the first control variable of the optimized solution immediately; simultaneously, it generates and broadcasts a predicted trajectory using the entire control sequence, providing collaborative information to neighboring UAVs. This allows the entire cluster to optimize for the next cycle based on each other's latest intentions, thereby achieving closed-loop feedback and continuous collaboration in distributed predictive control, effectively improving the collaboration and robustness of the cluster's obstacle avoidance.

[0053] To verify the effectiveness of the method of this invention, a test was conducted in a three-dimensional simulation environment. A square airspace of 10m × 10m × 5m was set up, with three static cubic obstacles randomly distributed within it. Five UAVs (UAV1-UAV5) were deployed, with their initial positions randomly distributed on one side of the airspace, and their target point being a designated location on the other side of the airspace. The UAVs shared predicted trajectories through a communication network. The communication topology was fully connected, but a fixed communication delay of one control cycle was artificially introduced to simulate asynchronous information. The minimum safe distance d between the UAVs was determined. safe,1 The minimum safe distance d between the drone and the obstacle is set to 1.0m. safe,2The time interval is set to 1.2m. The control cycle is 100ms, and the prediction time domain N=10. Each UAV is equipped with the algorithm provided by this invention and independently executes the UAV swarm cooperative obstacle avoidance method based on distributed model predictive control within each control cycle (t=0, 0.1s, 0.2s…). The time budget for solving the convex quadratic programming subproblem is 80ms. Two comparison groups are set up, using centralized MPC (Comparison 1) and simplified distributed MPC (Comparison 2). Centralized MPC uses a central processor to collect the states of all UAVs, solves the global optimization problem, and then distributes instructions. Theoretically, it has the best performance, but the communication load is large. Simplified distributed MPC adopts a similar framework to this invention, but omits the interaction cost function of historical memory (i.e., β=0) and uses a more conservative fixed convex approximation for non-convex constraints. Under the same initial conditions and random obstacle scenarios, 50 Monte Carlo simulations were performed, and the statistical performance indicators are shown in Table 1.

[0054] Table 1 Simulation Performance Indicators As shown in Table 1, in terms of trajectory coordination, when traversing obstacle courses, the five UAVs of this invention exhibited smooth and coordinated mutual avoidance, with the overall formation dynamically changing but without conflict. In contrast, the UAVs in Comparison 2 showed significant hesitation and reverse adjustments, resulting in unnecessary circling of some UAV trajectories. Regarding decision oscillation suppression, the control command sequence of this invention is smooth and continuous, and the introduced historical memory mechanism effectively compensates for the asynchronous information caused by communication delays. Even with increased delays, it maintains a high success rate (94%), significantly suppressing cluster decision oscillations and achieving smooth and consistent group movement. In contrast, when facing conflicts, Comparison 2, lacking historical deviation compensation, exhibited high-frequency positive and negative switching of its control quantities over multiple cycles, demonstrating decision oscillations. In terms of real-time performance, this invention achieves a solution time of less than 78ms in all control cycles, meeting the 80ms time limit requirement. Furthermore, it obtains high-precision solutions within 50ms in 95% of the cycles. Strict convexification processing and a warm-start strategy ensure that a feasible solution can be obtained within a predetermined time in each control cycle under limited onboard computing resources, meeting the hard real-time requirements of the UAV flight control system and demonstrating the efficient solvability of the convexified problem. In terms of safety, the obstacle avoidance success rate of this invention (98%) is significantly higher than that of the simplified distributed method (82%) and approaches the theoretically globally optimal centralized method (100%). The number of devices and processing scale described herein are for simplification of the invention. Applications, modifications, and variations of the UAV swarm cooperative obstacle avoidance method based on distributed model predictive control of this invention will be readily apparent to those skilled in the art.

[0055] Although embodiments of the present invention have been disclosed above, they are not limited to the applications listed in the specification and embodiments. They can be applied to various fields suitable for the present invention. For those skilled in the art, other modifications can be easily made. Therefore, without departing from the general concept defined by the claims and their equivalents, the present invention is not limited to the specific details and illustrations shown and described herein.

Claims

1. A collaborative obstacle avoidance method for UAV swarms based on distributed model predictive control, characterized in that, Each drone in the cluster executes independently within each control cycle: S1. Based on the local dynamics prediction model, the current state, the predicted trajectory of the neighboring UAV in the previous cycle, and the current environmental obstacle information, construct a local rolling time domain optimization problem that simultaneously includes a non-convex minimum safe distance constraint to prevent local collisions and a non-convex interactive cost function that quantifies and actively compensates for the group coordination deviation caused by the asynchronous distributed information. S2. Using the optimal predicted trajectory of the machine in the previous cycle as the reference trajectory, the non-convex minimum safe distance constraint and non-convex interaction cost function in step S1 are co-convexized to form a convex quadratic programming subproblem. S3. Solve the convex quadratic programming subproblem described in step S2 within the preset computation time constraint, and output a feasible control sequence. S4. Execute the instantaneous control quantity of the feasible control sequence output in step S3, and broadcast the local optimal predicted trajectory generated by the feasible control sequence through the local dynamics model to neighboring UAVs. Iterate in a loop to achieve continuous cooperative obstacle avoidance of the UAV swarm. In step S2, the co-convexification process for the non-convex minimum safe distance constraint and the non-convex interaction cost function includes: linearizing the non-convex minimum safe distance constraint point by point into a set of linear inequality constraints based on the optimal predicted trajectory of the previous cycle and the current location of obstacles in the environment; approximating the non-convex interaction cost function at the current trajectory prediction point to form a quadratic cost function; and combining the linear inequality constraints and the quadratic cost function with the dynamic model constraints of the local machine to form the convex quadratic programming subproblem.

2. The UAV swarm cooperative obstacle avoidance method based on distributed model predictive control as described in claim 1, characterized in that, The non-convex minimum safe distance constraint mentioned in step S1 includes a first type of collision avoidance constraint between the local drone and all neighboring drones, and a second type of collision avoidance constraint between the local drone and obstacles in the current environment. The first type of collision avoidance constraint requires that the square of the Euclidean distance between the local drone's predicted position at a certain future time and the predicted position of the corresponding neighboring drone obtained from the previous period at the same future time is not less than the square of the preset safe distance threshold between drones. The second type of collision avoidance constraint requires that the square of the distance between the predicted position of the drone at a certain future moment and the position of the corresponding environmental obstacle is not less than the square of a preset safe distance threshold between the drone and the obstacle.

3. The UAV swarm cooperative obstacle avoidance method based on distributed model predictive control as described in claim 2, characterized in that, The non-convex interaction cost function in step S1 is constructed in the following way: For each neighboring drone, calculate the difference between the predicted future trajectory planned by the drone in the current cycle and the predicted trajectory obtained by a neighbor from the previous cycle, and use it as the instantaneous trajectory deviation for the current cycle. The historical cooperative deviation accumulated for the neighboring UAV is obtained by multiplying the instantaneous trajectory deviations generated by the local machine for the neighboring UAV in the past several control cycles by a decay memory factor between 0 and 1 and then accumulating them. The non-convex interaction cost function is constructed based on the instantaneous trajectory deviation and the cumulative historical cooperative deviation. The non-convex interaction cost function is the sum of the norm squares of the instantaneous trajectory deviations of all neighboring UAVs in the current period plus the sum of the norm squares of the cumulative historical cooperative deviations of all neighboring UAVs.

4. The UAV swarm cooperative obstacle avoidance method based on distributed model predictive control as described in claim 3, characterized in that, The implementation of the linear inequality constraints includes: A1. For each future moment in the prediction time domain, the prediction position of the corresponding moment in the optimal prediction trajectory of the previous cycle of the local machine is used as the reference point for linearization. A2. For the first type of collision avoidance constraint, calculate the function value of the squared Euclidean distance between the predicted position of the local drone at a certain future time and the predicted position of the corresponding neighboring drone obtained from the previous period at the same future time, and the gradient vector of the squared distance function at the reference point with respect to the local drone's predicted position variable; using the function value and the gradient vector, obtain the linear inequality with respect to the local drone's current predicted position variable through a first-order Taylor expansion. A3. For the second type of collision avoidance constraint, calculate the function value of the squared Euclidean distance between the predicted position of the machine at a certain future time and the position of the corresponding environmental obstacle at a reference point, and the gradient vector of the squared distance function at the reference point with respect to the predicted position variable of the machine; use the function value and the gradient vector to obtain the linear inequality with respect to the current predicted position variable of the machine through a first-order Taylor expansion. A4. Traverse all future moments, all neighboring drones, and all environmental obstacles within the prediction time domain, repeating steps A2 and A3 to finally generate a set of linear inequality constraints.

5. The UAV swarm cooperative obstacle avoidance method based on distributed model predictive control as described in claim 4, characterized in that, The implementation of the quadratic cost function includes: B1. Use the optimal predicted trajectory of the previous cycle of the local machine as the reference trajectory for performing a second-order approximation on the non-convex interaction cost function; B2. At each future time prediction point of the reference trajectory, perform a second-order Taylor expansion on the non-convex interactive cost function; B3. Combine the results obtained from the second-order Taylor expansion at all future time points in step B2 to form a quadratic cost function for the predicted location variables of the local machine at each time point in the prediction time domain.

6. The UAV swarm cooperative obstacle avoidance method based on distributed model predictive control as described in claim 4 or 5, characterized in that, When the optimal predicted trajectory of the machine in the previous cycle is unavailable in the first control cycle, it is generated by forward simulation based on the current state of the machine and the default control command through the machine dynamics prediction model.

7. The UAV swarm cooperative obstacle avoidance method based on distributed model predictive control as described in claim 6, characterized in that, The convex quadratic programming subproblem in step S2 is a new optimization problem defined by using the quadratic cost function as the objective function and the set of linear inequality constraints and the state-space equation equality constraints obtained by discretizing the local dynamics prediction model as constraints.

8. The UAV swarm cooperative obstacle avoidance method based on distributed model predictive control as described in claim 7, characterized in that, In step S3, the solution is performed within the preset computation time constraint using a numerical optimization solver based on the interior point method or the effective set method, and when the time constraint is exhausted, the optimal feasible solution obtained in the current iteration is output.

9. The UAV swarm cooperative obstacle avoidance method based on distributed model predictive control as described in claim 8, characterized in that, The specific implementation of step S4 includes: C1. Extract the first control vector from the feasible control sequence output in step S3, use it as the immediate control command for the current control cycle, and send it to the flight control actuator of the machine for execution. C2. Input the feasible control sequence and the current state into the local dynamics prediction model for forward simulation calculation to obtain the predicted state of the local machine at each time in the future prediction time domain, and extract the position sequence from it to form the optimal prediction trajectory for this period. C3. The optimal predicted trajectory is encapsulated into a data packet according to a preset communication protocol and broadcast to all neighboring drones via a wireless communication network for their use in the next control cycle when performing collaborative optimization.

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