Unmanned aerial vehicle two-stage robust trajectory optimization method, device and medium for complex low-altitude wind disturbance
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- TONGJI UNIV
- Filing Date
- 2026-03-31
- Publication Date
- 2026-07-10
Smart Images
Figure CN122360458A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of unmanned aerial vehicle (UAV) technology, and in particular to a two-stage robust trajectory optimization method, apparatus, and medium for UAVs facing complex low-altitude wind disturbances. Background Technology
[0002] I. Existing Technology When drones perform tasks such as logistics delivery, environmental monitoring and emergency rescue in low-altitude environments, their flight path planning always faces severe challenges caused by complex wind disturbances.
[0003] Currently, while mainstream optimization methods each have their own focus, they all have significant limitations. Deterministic trajectory optimization methods plan under known or assumed wind field models, failing to incorporate the randomness of wind disturbances. This makes them highly susceptible to trajectory deviations, obstacle avoidance failures, and even collision risks due to wind field deviations during actual flight, resulting in insufficient safety. To improve robustness, single-stage robust optimization methods construct bounded uncertainty sets to ensure constraints are met in the worst-case scenario. While providing strict safety guarantees, these methods presuppose all possible wind conditions, forcing the optimization results to have excessively large safety margins. This leads to lengthy trajectories, high energy consumption, and excessive conservatism, potentially even resulting in no solution in complex environments. Probabilistic or chance-constrained planning methods attempt to reduce conservatism by allowing constraints to be violated with a certain probability. However, the reliability of their probabilistic guarantees heavily relies on simplified assumptions about the distribution of uncertainty, making it difficult to accurately characterize the spatiotemporal correlation between shear and turbulence in real low-altitude wind fields. Therefore, the risk of model mismatch still exists in practical applications. In recent years, learning-based adaptive methods have shown potential for online adaptation to wind disturbances. However, they generally lack theoretical safety guarantees, and their performance is limited by the completeness of training data. Their safety is also difficult to guarantee when facing extreme wind conditions outside of distribution. Furthermore, the common hierarchical control architecture decouples trajectory planning from tracking control. While this simplifies the design, it prevents the planning layer from fully considering the dynamic characteristics of the underlying controllers and the propagation of uncertainties. This can easily lead to a disconnect between planning and execution, resulting in poor overall performance.
[0004] In summary, existing methods often fall into a dilemma when dealing with complex low-altitude wind disturbances: the difficulty of balancing conservatism and efficiency, the mismatch between model simplification and actual wind field, and the lack of a systematic integrated prevention and correction mechanism. There is an urgent need for an innovative solution that can effectively balance robustness and economy while strictly ensuring safety. Summary of the Invention
[0005] This invention provides a two-stage robust trajectory optimization method, apparatus, and medium for UAVs under complex low-altitude wind disturbances. The trajectory optimization problem for UAVs under complex low-altitude wind disturbances is constructed as a min-max robust optimization problem. This method is solved through an iterative approach consisting of an outer master problem (prevention phase) and inner sub-problems (correction phase), ultimately outputting the optimal trajectory and control strategy that theoretically withstands worst-case wind conditions while balancing flight safety and operational efficiency.
[0006] The objective of this invention can be achieved through the following technical solutions: A two-stage robust trajectory optimization method for UAVs facing complex low-altitude wind disturbances, the method includes the following steps: Step S1: Construct a composite wind disturbance model and a UAV dynamics model; Step S2: Initialize and set parameters for the main loop that generates columns and constraints, and set the worst-case wind condition sample set; Step S3: Enter the main loop for generating the composite wind disturbance model and UAV dynamics model and constraints, initialize the upper and lower bounds, and execute S4; Step S4: Based on solving the inner sub-problems, obtain the worst-case wind conditions under the current strategy; Step S5: Solve the outer principal problem based on the worst-case wind conditions under the current strategy to obtain a new reference track and wind disturbance control gain; Step S6: Determine the convergence of the new reference track and the wind disturbance control gain. If convergence is achieved, take the new reference track and the wind disturbance control gain as the optimal track and control gain, respectively, and execute S7; otherwise, execute S4. Step S7: Load the obtained optimal trajectory and control gain into the UAV flight control system.
[0007] Furthermore, the specific steps of step S4 are as follows: In the given first Under the reference trajectory obtained in the next iteration, solve the optimization problem; The upper bound is updated based on the worst-case wind conditions under the current strategy obtained from the optimization problem.
[0008] Furthermore, the optimization problem is: in, Indicates the inner sub-problem. This represents the worst-case scenario cost under the current strategy. This represents the worst-case wind scenario sample set. Represents the cost function, This represents the reference track for the k-th iteration. Let represent the wind disturbance in the k-th iteration. The worst-case wind condition is the specific wind disturbance scenario in the worst-case wind condition sample set obtained by solving the problem.
[0009] Furthermore, the updated upper bound is: in, Indicates the current upper bound. This represents the updated upper bound.
[0010] Furthermore, the specific steps of step S5 are as follows: Solve the master problem based on the worst-case wind conditions to obtain a new reference trajectory and wind disturbance control gain.
[0011] Furthermore, the main problem is: MP: Among them, the outer principal problem of MP This represents the wind disturbance control gain under worst-case wind conditions. It is an auxiliary variable.
[0012] Furthermore, the updated lower bound is: in, For the updated lower bound, For the current and next terms.
[0013] Furthermore, the specific steps for determining the convergence of the new reference track and the wind disturbance control gain are as follows: like ,in The interval between current iterations, or the number of iterations. , If the threshold for the number of iterations is set, then convergence occurs; otherwise, convergence does not occur, and the number of iterations is incremented by one to execute S4.
[0014] Compared with the prior art, the present invention has the following beneficial effects: I. This invention proposes a two-stage prevention-correction deep integration decision-making method. Through closed-loop iteration of outer-layer planning and inner-layer adversarial mechanisms, it combines pre-emptive robust trajectory planning with real-time correction control strategies. This not only proactively avoids high-risk areas during the planning stage but also compensates for wind disturbances online in real time through optimized control laws. Thus, while strictly ensuring flight safety under worst-case conditions, it significantly reduces flight costs, achieving an optimal balance between safety and efficiency.
[0015] Second, this invention constructs a composite uncertain set model that integrates logarithmic wind shear profiles and three-dimensional bounded turbulence, more accurately characterizing the spatiotemporal structure and physical boundaries of low-altitude wind fields, making the description of uncertain sets more consistent with actual atmospheric physical laws. Optimization based on this model can fundamentally improve the reliability of the results, effectively avoiding the "pseudo-safety" or "ineffective optimization" problems caused by oversimplification of the model, and ensuring the effectiveness and credibility of the planned trajectory in actual complex wind fields.
[0016] Third, to address the complex min-max problem arising from the aforementioned methods, this invention employs the C&CG algorithm for solution. By iteratively generating key "worst-case" samples, it avoids the combinatorial explosion problem caused by exhaustive search. Furthermore, it performs targeted convex approximation processing for non-convex constraints, ensuring rapid convergence within a finite number of iterations. Therefore, it can meet the real-time requirements of rapid mission response for UAVs, providing a feasible technical path for the practical engineering deployment of robust autonomous flight in complex environments. It is applicable to various low-altitude UAV application scenarios such as urban logistics, inspection, and emergency response. Attached Figure Description
[0017] Figure 1 This is a schematic diagram of the process of the present invention; Figure 2 This is a schematic diagram of a composite wind disturbance model; Figure 3 The graph shows the convergence curve of the C&CG algorithm during iteration. Figure 4 A comparison chart of the flight paths for the three strategies; Figure 5 A bar chart comparing Monte Carlo performance. Detailed Implementation
[0018] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments. These embodiments are based on the technical solution of the present invention and provide detailed implementation methods and specific operating procedures. However, the scope of protection of the present invention is not limited to the following embodiments.
[0019] This invention proposes a two-stage prevention-correction robust trajectory optimization method for unmanned aerial vehicles (UAVs). The core idea is to construct the trajectory optimization problem for UAVs under complex low-altitude wind disturbances as a min-max robust optimization problem. This method is solved through an iterative approach consisting of an outer master problem (prevention phase) and inner sub-problems (correction phase), ultimately outputting the optimal trajectory and control strategy that theoretically withstands worst-case wind conditions while balancing flight safety and operational efficiency.
[0020] The specific steps of the method are as follows: Step S1: Construct a composite wind disturbance model and a UAV dynamics model.
[0021] First, a mathematical model is established to describe complex wind conditions at low altitudes. This model will incorporate total wind disturbance. Decomposed into wind shear and turbulence Two parts, namely The wind shear component is described using a logarithmic profile model that conforms to the physical laws of the atmospheric boundary layer; the turbulence component is defined with physically meaningful bounded fluctuation ranges in each direction of three-dimensional space. This composite model collectively defines the uncertainty set of wind disturbance. Simultaneously, a point mass dynamics equation for the UAV, incorporating wind disturbance terms, is established to describe the relationship between its position, velocity, and control input.
[0022] Step S2: Initialization and parameter setting.
[0023] Set the physical and mission constraints for the UAV flight, including the starting point, target point, total flight time or steps, maximum speed, maximum acceleration, and safe distance. Initialize the worst-case wind condition sample set and set the algorithm's convergence tolerance and maximum number of iterations. Generate an initial reference track that satisfies the basic constraints.
[0024] Step S3: Enter the main loop of Column and Constraint Generation (C&CG).
[0025] Set the iteration counter Upper bound of the initialization algorithm and the lower realm Then, repeat steps S4 and S5 until the convergence condition is met.
[0026] Step S4: Solve the inner subproblem (SP) – Identify the worst-case scenario under the current strategy.
[0027] In the given first Under the reference trajectory obtained in the next iteration, solve the following optimization problem: The problem aims to find a specific wind disturbance sequence from the wind disturbance uncertainty set defined in step S1 that maximizes the objective function. This is the "worst-case" wind disturbance scenario for the current trajectory and control strategy, and the worst-case wind condition sample is added to the sample set. After solving SP, the upper bound is updated.
[0028] During the solution process, non-convex terms in the model are made convex.
[0029] Step S5: Solve the outer master problem (MP) – optimize the trajectory and control strategy.
[0030] Using the currently accumulated worst-case wind condition sample set, solve the following main problem: MP: This problem simultaneously optimizes the new reference track and wind disturbance control gain, and introduces auxiliary variables. Let MP represent the upper bound of the worst-case cost under the current sample set. The goal is to find a set of tracks and control gains that minimizes the maximum cost across all identified worst-case wind condition samples. After solving for MP, the lower bound is updated.
[0031] Similarly, non-convex constraints in MP, such as obstacle avoidance distance constraints, are linearized into convex approximations.
[0032] Step S6: Convergence assessment.
[0033] Calculate the gap of the current iteration like or number of iterations If the condition is met, the algorithm terminates and outputs the current optimal trajectory, optimal control gain, and the corresponding worst-case cost estimate. Otherwise, let... Then return to step S4 to continue the iteration.
[0034] Step S7: Track execution and online correction.
[0035] The final optimized reference trajectory and wind disturbance resistance control gain are then loaded into the UAV flight control system. During mission execution, the flight control system combines real-time perceived wind speed information and utilizes... The control commands are dynamically adjusted to achieve online wind disturbance compensation, ensuring that the actual flight trajectory closely follows the robustly optimized reference trajectory.
[0036] Through the above steps, this invention achieves a complete technical closed loop from offline planning to online correction, ensuring high safety, high economy and strong robustness of UAVs in complex low-altitude wind disturbance environments.
[0037] Areas for improvement: 1. A two-stage robust optimization method that deeply integrates prevention and correction is introduced, which unifies the modeling and solution of risk planning and real-time disturbance rejection control from a methodological perspective.
[0038] 2. A wind disturbance uncertainty set model that better reflects physical reality was constructed, taking into account both the profile characteristics of wind shear and the bounded randomness of turbulence, providing a more accurate input for robust optimization.
[0039] 3. An efficient solution process based on C&CG was designed. Instead of enumerating all possibilities, the critical worst-case scenario was generated iteratively, which reduced the computational complexity and made the algorithm practical for engineering applications.
[0040] To verify the effectiveness of this invention, we conducted simulation tests in a complex scenario simulating a real low-altitude environment. This scenario included nine obstacles: four spherical obstacles and five cubic obstacles. The UAV mission involved flying from a starting point [0, 0, 80] meters to a destination [120, 120, 80] meters, facing complex wind disturbances including logarithmic wind shear and bounded turbulence throughout the journey. Experiments compared three strategies: Strategy 1 (deterministic optimization), Strategy 2 (single-stage robust optimization), and the proposed Strategy 3 (two-stage prevention and correction robust optimization). The results clearly show that in 3000 Monte Carlo random wind disturbance tests, Strategy 3 achieved a 100% obstacle avoidance success rate and a 100% constraint satisfaction rate. Its average energy consumption (4.3822) and maximum energy consumption (8.3156) were significantly lower than the comparative strategies. Furthermore, the algorithm robustly converged within 12 iterations, demonstrating its engineering feasibility. This specific embodiment fully demonstrates that the present invention can effectively solve the problem of balancing safety and economy in actual complex low-altitude wind disturbance environments.
[0041] Figure 1 The invention systematically reveals the two-stage optimization framework and execution process of the deep integration of "prevention planning" and "online correction". Figure 2 It intuitively illustrates the constructed composite wind disturbance model that better fits the physical laws of the low-altitude atmosphere, integrating logarithmic wind shear and bounded turbulence. Figure 3 Using UB and LB as the vertical axis and the number of iterations as the horizontal axis, the convergence process of this algorithm is shown. Initially, the difference between the upper and lower bounds is large, but after several iterations, they quickly approach each other and eventually converge within the tolerance range, proving that the algorithm is efficient and reliable. Figure 4 This is a comparison chart of the flight paths of three strategies. Under the same complex obstacle scenario and wind disturbance, a three-dimensional view of the typical flight path of Strategy 1 (deterministic method), Strategy 2 (single-stage robust method), and Strategy 3 (the two-stage method of this invention) is drawn. It can be clearly seen that the Strategy 1 path deviates significantly, Strategy 2 is somewhat improved but still has deviations, and the Strategy 3 path closely follows the reference path and successfully avoids all obstacles. Figure 5 Monte Carlo simulation tests were used, and bar charts were used to compare the obstacle avoidance success rate and constraint satisfaction rate of the three strategies in multiple random wind disturbance tests, intuitively demonstrating the significant advantages of Strategy 3 in various indicators. These figures, from the method, model, algorithm to the results, comprehensively and powerfully illustrate the innovation and practicality of this invention.
[0042] If the aforementioned functions are implemented as software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this invention, or the part that contributes to the prior art, or a part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of this invention. 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.
Claims
1. A two-stage robust trajectory optimization method for UAVs accommodating complex low-altitude wind disturbances, characterized in that, The method includes the following steps: Step S1: Construct a composite wind disturbance model and a UAV dynamics model; Step S2: Initialize and set parameters for the main loop that generates columns and constraints, and set the worst-case wind condition sample set; Step S3: Enter the main loop for generating the composite wind disturbance model and UAV dynamics model and constraints, initialize the upper and lower bounds, and execute S4; Step S4: Based on solving the inner sub-problems, obtain the worst-case wind conditions under the current strategy; Step S5: Solve the outer principal problem based on the worst-case wind conditions under the current strategy to obtain a new reference track and wind disturbance control gain; Step S6: Determine the convergence of the new reference track and the wind disturbance control gain. If convergence is achieved, take the new reference track and the wind disturbance control gain as the optimal track and control gain, respectively, and execute S7; otherwise, execute S4. Step S7: Load the obtained optimal trajectory and control gain into the UAV flight control system.
2. The two-stage robust trajectory optimization method for UAVs facing complex low-altitude wind disturbances as described in claim 1, characterized in that, The specific steps of step S4 are as follows: In the given first Under the reference trajectory obtained in the next iteration, solve the optimization problem; The upper bound is updated based on the worst-case wind conditions under the current strategy obtained from the optimization problem.
3. The two-stage robust trajectory optimization method for UAVs facing complex low-altitude wind disturbances as described in claim 2, characterized in that, The optimization problem is: in, Indicates the inner sub-problem. This represents the worst-case scenario cost under the current strategy. This represents the worst-case wind scenario sample set. Represents the cost function, This represents the reference track for the k-th iteration. Let represent the wind disturbance in the k-th iteration. The worst-case wind condition is the specific wind disturbance scenario in the worst-case wind condition sample set obtained by solving the problem.
4. The two-stage robust trajectory optimization method for UAVs facing complex low-altitude wind disturbances as described in claim 3, characterized in that, The updated upper bound is: in, Indicates the current upper bound. This represents the updated upper bound.
5. The two-stage robust trajectory optimization method for UAVs facing complex low-altitude wind disturbances according to claim 4, characterized in that, The specific steps of step S5 are as follows: Solve the master problem based on the worst-case wind conditions to obtain a new reference trajectory and wind disturbance control gain.
6. The two-stage robust trajectory optimization method for UAVs facing complex low-altitude wind disturbances as described in claim 5, characterized in that, The main question is: MP: Among them, the outer principal problem of MP This represents the wind disturbance control gain under worst-case wind conditions. It is an auxiliary variable.
7. A two-stage robust trajectory optimization method for UAVs facing complex low-altitude wind disturbances as described in claim 6, characterized in that, The updated lower bound is: in, For the updated lower bound, For the current and next terms.
8. The two-stage robust trajectory optimization method for UAVs facing complex low-altitude wind disturbances according to claim 7, characterized in that, The specific steps for determining the convergence of the new reference track and the wind disturbance control gain are as follows: like ,in The interval between current iterations, or the number of iterations. , If the threshold for the number of iterations is set, then convergence occurs; otherwise, convergence does not occur, and the number of iterations is incremented by one to execute S4.
9. A two-stage robust trajectory optimization device for UAVs facing complex low-altitude wind disturbances, comprising a memory, a processor, and a program stored in the memory, characterized in that, When the processor executes the program, it implements the method as described in any one of claims 1-8.
10. A storage medium having a program stored thereon, characterized in that, When the program is executed, it implements the method as described in any one of claims 1-8.