A dynamic optimization method for unmanned aerial vehicle online trajectory planning

Abstract

The application discloses a dynamic optimization method for unmanned aerial vehicle online trajectory planning, and belongs to the technical field of unmanned aerial vehicle autonomous control, and comprises the following steps: constructing a finite time domain optimal control problem containing a target function and multiple constraints at each sampling time; converting continuous control input into a segmented function by control parameterization technology, converting an infinite dimension problem into a finite dimension nonlinear programming problem; converting time-varying speed and obstacle avoidance constraints into integral penalty items for processing by using a constraint transcription method; introducing a terminal controller and a terminal area constraint to ensure recursive feasibility and asymptotic stability of the system; solving the nonlinear programming problem on-line, and applying the first control instruction to the unmanned aerial vehicle. The application realizes real-time, safe and efficient trajectory generation of the unmanned aerial vehicle in a complex environment by optimizing problem reconstruction and calculation simplification, and provides reliable technical support for unmanned aerial vehicle autonomous tasks under the premise of strictly ensuring constraint satisfaction and closed loop stability.

Description

Technical Field

[0001] This invention relates to the field of autonomous control technology for unmanned aerial vehicles (UAVs), and more specifically, to a dynamic optimization method for online trajectory planning of UAVs. Background Technology

[0002] Unmanned aerial vehicles (UAVs) are increasingly used in reconnaissance and surveillance, search and rescue, and logistics delivery, becoming a key component of modern intelligent systems. The autonomous flight capability of UAVs heavily relies on trajectory planning technology, which requires generating safe, efficient, and dynamically constrained flight trajectories in real time within complex dynamic environments, directly impacting the reliability and efficiency of mission execution. Currently, UAV trajectory planning methods mainly include graph search algorithms, sampling-based methods, evolutionary algorithms, artificial intelligence methods, and optimal control strategies.

[0003] In optimal control strategies, Model Predictive Control (MPC) has become an important method for UAV trajectory planning due to its ability to explicitly handle system dynamics and constraints. MPC solves for control commands online through rolling time-domain optimization, balancing dynamic performance and safety, making it particularly suitable for UAV applications requiring rapid response. Depending on the system modeling method, MPC can be divided into linear MPC and nonlinear MPC. The advantage of nonlinear MPC over linear MPC lies in its direct handling of the system's nonlinear dynamics and constraints, generating more accurate trajectories that better reflect actual flight conditions while strictly ensuring constraint satisfaction. In contrast, linear MPC, due to its linearization approximation, may result in suboptimal trajectories or constraint violations.

[0004] Despite the advantages of nonlinear MPC in trajectory planning, existing research still has the following limitations: (1) Existing methods are difficult to meet real-time computing requirements in complex environments; (2) Existing research has not provided sufficient theoretical analysis of the stability and recursive feasibility of closed-loop systems. Summary of the Invention

[0005] This invention provides a dynamic optimization method for online trajectory planning of unmanned aerial vehicles (UAVs). By reconstructing the optimization problem and simplifying the calculation, it achieves real-time trajectory generation in complex environments while ensuring recursive feasibility, constraint satisfaction, and closed-loop stability, thus providing efficient and reliable technical support for autonomous UAV missions.

[0006] To solve the above problems, the technical solution adopted by the present invention is as follows:

[0007] A dynamic optimization method for online trajectory planning of unmanned aerial vehicles (UAVs) includes:

[0008] Obtain the current state information of the UAV and, based on the preset dynamic model of the UAV translation subsystem, establish a predictive model for predicting the future state.

[0009] At each sampling time, a finite-time optimal control problem is constructed, which includes an objective function for minimizing the state error and control input, as well as constraints, including UAV dynamics constraints, velocity constraints, acceleration constraints, and obstacle avoidance constraints.

[0010] The continuous control input in the optimal control problem is parameterized and represented as a piecewise function determined by the control parameters to be optimized in the prediction time domain, so as to transform the infinite-dimensional optimal control problem into a finite-dimensional nonlinear programming problem.

[0011] The constraint transcription method is used to transform the time-varying velocity constraints and obstacle avoidance constraints into integral penalty terms, which are then integrated into the nonlinear programming problem for solution.

[0012] Terminal constraints are introduced into the optimal control problem. These terminal constraints include terminal controller constraints and terminal region constraints, in order to ensure the recursive feasibility and asymptotic stability of the closed-loop system.

[0013] The nonlinear programming problem is solved online to obtain the optimal control parameter sequence, and the first control command is generated based on the sequence to control the flight of the UAV.

[0014] Furthermore, the objective function includes an integral term and a terminal cost term; the integral term is the integral of the weighted sum of the second norm of the UAV state error in the prediction time domain and the second norm of the control input; the terminal cost term is the second norm of the predicted terminal state error in the prediction time domain, and the terminal state is penalized by introducing a positive definite terminal weight matrix to enhance the stability of the system.

[0015] Furthermore, the method for parameterizing the control input includes: uniformly dividing the prediction time domain into multiple sub-intervals; within each sub-interval, setting the three-dimensional acceleration control input of the UAV as a constant vector, which is the control parameter to be optimized; the control input in the entire prediction time domain is composed of the sequential splicing of the control parameter sequences in all sub-intervals, so as to transform the problem of solving the continuous control function into the optimization problem of solving the finite-dimensional control parameter vector.

[0016] Furthermore, the constraint transcription method includes: defining scalar functions for velocity constraints and each obstacle avoidance constraint to quantify the degree to which the current state violates the corresponding constraint; introducing a preset smoothing penalty function, which performs a nonlinear mapping on the output value of the scalar function, such that when the constraint is satisfied, its function value is zero or close to zero, and when the constraint is violated, its function value smoothly increases positively with the increase of the degree of violation; integrating the smoothing penalty function over the entire prediction time domain, and requiring the integral value to be less than a preset positive threshold to form an integral form of the penalty term.

[0017] Furthermore, the terminal controller is designed as a linear state feedback controller, which generates control commands based on the state error at the end of the predicted time domain. By designing the feedback gain matrix of the controller offline, it is ensured that when the UAV enters the terminal area, the system state can asymptotically converge to the target state under the action of the terminal controller, and all dynamic and safety constraints of the UAV are satisfied during the convergence process.

[0018] Furthermore, the terminal region constraint is defined as a set of state spaces surrounding the target state, requiring that the state at the end of the predicted time domain must fall within this set of state spaces. The size and shape of this set of state spaces are jointly determined based on the Lyapunov stability theory of the system, the dynamic characteristics of the UAV, the boundaries of various constraints, and the performance of the terminal controller. Its upper bound is determined by the Lyapunov function value that ensures state convergence, and its lower bound is determined by the condition that ensures the UAV maintains the minimum safe distance from all obstacles, thus forming an invariant set that can guarantee recursive feasibility.

[0019] Furthermore, to ensure the recursive feasibility of the method, an alternative feasible solution can be constructed for each sampling time t+Δ in the optimization problem. The alternative feasible solution is constructed as follows: for the time interval [t+Δ, t+T], the part of the corresponding time period in the optimal control sequence calculated at sampling time t is used, while for the newly added time interval [t+T, t+T+Δ], the control input generated by the terminal controller based on the state is adopted. This construction method ensures that at any sampling time, there exists at least one feasible solution that satisfies all constraints in the optimization problem.

[0020] Furthermore, the asymptotic stability of the dynamic optimization method is proven by selecting the objective function as the Lyapunov function of the entire closed-loop system. Theoretical derivation proves that at each sampling time, the Lyapunov function value corresponding to the calculated optimal control strategy is monotonically non-increasing relative to the Lyapunov function value at the previous time. Thus, it can be concluded that when time approaches infinity, the state error of the closed-loop error system will converge to zero, thereby strictly ensuring the long-term operational reliability of the control system.

[0021] Furthermore, the translational subsystem dynamics model defines the UAV's state vector as a six-dimensional vector containing three-dimensional position coordinates and three-dimensional velocity components, and defines the control input as a three-dimensional acceleration command; the acceleration constraint is derived from the maximum total thrust that the UAV rotor can generate, specifically by limiting the Euclidean modulus of the sum of the acceleration command vector and the gravitational acceleration vector to an upper limit determined by the ratio of the maximum total thrust to the mass of the UAV.

[0022] Furthermore, the dynamic optimization method is executed online using a rolling time-domain optimization approach: at each sampling time, based on the current state fed back by the UAV's sensors as the initial condition, the nonlinear programming problem is solved to obtain the optimal control parameter sequence covering the entire prediction time domain; the control command corresponding to the first control parameter in the optimal control parameter sequence is applied to the UAV system to drive it to fly for one sampling interval; at the next sampling time, the updated state of the UAV is obtained, and this is used as the new initial condition to repeat the optimization solution and control application process, so as to achieve continuous online correction and closed-loop control of the UAV trajectory.

[0023] Compared with the prior art, the beneficial effects of the present invention are:

[0024] (1) By introducing control parameterization technology, this invention successfully transforms the original infinite-dimensional optimal control problem into a finite-dimensional nonlinear programming problem. This dimensionality reduction greatly reduces the computational complexity of online solution, enabling UAVs to make rapid decisions in dynamically changing environments, achieving millisecond-level single-step computation time, and meeting the stringent real-time requirements of highly dynamic tasks.

[0025] (2) This invention, through careful design of the terminal controller and terminal region constraints within the model predictive control framework, and analysis combined with Lyapunov stability theory, rigorously proves the recursive feasibility and asymptotic stability of the closed-loop system. This effectively solves the problem of insufficient theoretical analysis in existing research, ensuring that the UAV will not fail due to the unsolvable optimization problem during long-term operation, and can stably converge to the target state, greatly enhancing the reliability and safety of the control system.

[0026] (3) This invention not only strictly considers the model characteristics of the UAV itself, but also cleverly transforms time-varying state constraints (such as speed limits and dynamic obstacle avoidance) into integral penalty terms through a constraint transcription method. This approach reduces the dimensionality of the optimization problem while effectively and strictly ensuring that the UAV always meets all safety and physical constraints throughout the entire flight process, thus ensuring the feasibility and safety of the generated trajectory.

[0027] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, embodiments of the present invention are described below in detail with reference to the accompanying drawings. Attached Figure Description

[0028] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of the present invention and should not be regarded as a limitation on the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.

[0029] Figure 1 This is a flight trajectory diagram of the UAV in an embodiment of the present invention;

[0030] Figure 2 This is a speed constraint diagram of the UAV in an embodiment of the present invention;

[0031] Figure 3 This is a diagram showing the input of UAV control quantities in an embodiment of the present invention;

[0032] Figure 4 This is an obstacle avoidance constraint diagram for the UAV in an embodiment of the present invention;

[0033] Figure 5 This is a diagram showing the single-step calculation time of the UAV in an embodiment of the present invention. Detailed Implementation

[0034] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are some embodiments of the present invention, but not all embodiments.

[0035] This invention discloses a dynamic optimization method for online trajectory planning of unmanned aerial vehicles (UAVs). This method employs nonlinear model predictive control (NMPC) to optimize the UAV's maneuver decisions. Considering practical engineering problems, UAVs need to take off from a designated starting point, avoid multiple obstacles, and ultimately reach a preset target location.

[0036] The implementation steps of this invention are as follows:

[0037] Step A: Establishment of UAV dynamics modeling and prediction model

[0038] First, this method acquires the current state information of the UAV and, based on a pre-defined dynamic model of the UAV's translational subsystem, establishes a predictive model for predicting future states. The dynamic system of a quadcopter UAV can be decoupled into a translational subsystem and a rotational subsystem. This patent focuses on the modeling of the translational subsystem, whose dynamic equations are described as follows:

[0039] (1)

[0040] Wherein, the state vector Represents the state variables of the translation subsystem. The coordinates of the drone's position. For the velocity vector, specifically, the UAV's translational subsystem dynamics model defines the UAV's state vector η as a six-dimensional vector containing three-dimensional position coordinates p and three-dimensional velocity components v, and defines the control input as a three-dimensional acceleration command, i.e. m is the total mass of the drone. This represents the total thrust generated by the quadcopter. Based on the aforementioned dynamic equations of the translational subsystem, the total thrust T can be derived. F The expression is:

[0041] (2)

[0042] Step B: Constructing the Finite-Time Optimal Control Problem

[0043] At each sampling time, this method constructs a finite-time optimal control problem. This optimal control problem includes an objective function aimed at minimizing the state error and control input, as well as a set of constraints, including UAV dynamics constraints, velocity constraints, acceleration constraints, and obstacle avoidance constraints.

[0044] Considering the physical limits of the UAV's propulsion system and flight safety requirements, it is necessary to perform constraint modeling on flight speed, acceleration, and obstacles.

[0045] Velocity constraints can be represented in the following set form:

[0046] (3)

[0047] in, A positive number indicates the maximum permissible flight speed.

[0048] The acceleration constraint is derived from the maximum total thrust that the UAV rotor can generate, specifically by interpolating the acceleration command vector 'a' with the gravitational acceleration vector. The Euclidean modulus of the sum is limited to the maximum total thrust. Within the upper limit determined by the ratio of the mass m of the UAV. Its constraint expression is:

[0049] (4)

[0050] in, This indicates the maximum total thrust that the four rotors of the drone can generate.

[0051] To ensure the safe flight of drones in complex environments, obstacle avoidance must be considered. Obstacle avoidance constraints can be expressed as:

[0052] (5)

[0053] in, This represents the coordinates of the center position of the l-th obstacle. This represents the safe radius of the obstacle. This constraint ensures that the drone maintains a safe distance from all obstacles.

[0054] Next, the objective function is constructed. Based on the dynamic equation (1) of the UAV translation subsystem, a prediction model is established:

[0055] (6)

[0056] Define state error Position error Speed ​​error The corresponding error dynamic equation is:

[0057] (7)

[0058] To optimize the flight trajectory of the UAV, the following objective function is designed:

[0059] (8)

[0060] The objective function constructed in step B includes an integral term and a terminal cost term. The integral term is the integral of the weighted sum of the second norm of the UAV state error in the prediction time domain and the second norm of the control input. The terminal cost term is the second norm of the predicted terminal state error in the prediction time domain. A positive definite terminal weight matrix is ​​introduced to penalize the terminal state, thereby enhancing the stability of the system. Here, Q and R are semi-positive definite weight matrices, used to adjust the weights of the state error and the control input, respectively; P is a positive definite weight matrix used to ensure terminal stability.

[0061] Based on the above constraints and objective function, the UAV trajectory planning problem can be formulated as the following optimal control problem:

[0062] (9)

[0063] Here, Ω represents the terminal area constraint, ensuring that the drone can eventually stabilize near the target state.

[0064] Step C: Control parameterization processing

[0065] Within the framework of nonlinear model predictive control algorithms, step C is then executed to parameterize the continuous control input in the optimal control problem. This parameterization transforms the original infinite-dimensional optimal control problem into a finite-dimensional nonlinear programming problem. Specifically, the prediction time domain is uniformly divided into multiple sub-intervals (M segments). Within each sub-interval, the three-dimensional acceleration control input of the UAV is set as a constant vector, which is the control parameter σ to be optimized. i The control input in the entire prediction time domain is composed of the sequential splicing of control parameter sequences from all sub-intervals, thus transforming the problem of solving the continuous control function into the optimization problem of solving the finite-dimensional control parameter vector.

[0066] The control input 'a' uses a piecewise constant function 'a'. p Discretize the representation:

[0067] (10)

[0068] (11)

[0069] in, For the control parameters to be optimized, Let be a basis function, meaning that it takes a value of 1 during the i-th time interval and 0 at other times.

[0070] Step D: Constrained Transcription

[0071] Subsequently, step D is executed, employing a constraint transcription method to transform the time-varying velocity constraints and obstacle avoidance constraints into integral penalty terms, which are then integrated into the nonlinear programming problem for solution.

[0072] First, we define a scalar function for both the velocity constraint and each obstacle avoidance constraint to quantify the degree to which the current state violates the constraint. We define the velocity constraint function. and obstacle avoidance constraint functions .

[0073] Secondly, a pre-defined smoothing penalty function Θ is introduced to perform a non-linear mapping on the output value of the scalar function. For velocity constraints, the following smoothing penalty function is used:

[0074] (12)

[0075] Where ε > 0. When the constraint is satisfied, its function value is zero or close to zero. When the constraint is violated, its function value increases smoothly and positively as the degree of violation increases.

[0076] Finally, the smoothing penalty function is integrated over the entire prediction time domain, and the integral value is required to be less than a preset positive threshold γ, thus forming an integral penalty term. The integral penalty term for the velocity constraint is expressed as:

[0077] (13)

[0078] Similarly, for each obstacle, the integral penalty term of the obstacle avoidance constraint can be expressed as:

[0079] (14)

[0080] Where γ > 0.

[0081] Therefore, we discretize the UAV trajectory planning problem into the following nonlinear programming problem:

[0082] (15)

[0083] in .

[0084] Step E: Introduce terminal constraints

[0085] To ensure the recursive feasibility and asymptotic stability of the closed-loop system, step E is executed, introducing terminal constraints into the optimal control problem. These terminal constraints include terminal controller constraints and terminal region constraints.

[0086] We designed the following terminal controller:

[0087] (16)

[0088] The terminal controller is designed as a linear state feedback controller, which predicts the state error η at the end of the time domain. e Generate a control command. is a constant feedback gain matrix.

[0089] Terminal area set to:

[0090] (17) Among them,

[0091] (18)

[0092] (19)

[0093] here, and It is a constant matrix. Representation matrix The minimum eigenvalue. The terminal region constraint is defined as a set of state spaces surrounding the target state, requiring that the state at the end of the predicted time domain must fall within this set of state spaces. The size and shape of this set of state spaces are jointly determined based on the Lyapunov stability theory of the system, the dynamic characteristics of the UAV, the boundaries of various constraints, and the performance of the terminal controller. Its upper bound is determined by the Lyapunov function value that ensures state convergence, and its lower bound is determined by the condition that ensures the UAV maintains the minimum safe distance from all obstacles, thus forming an invariant set that can guarantee recursive feasibility.

[0094] The terminal controller must satisfy the following properties:

[0095] (20)

[0096] That is, within the terminal region Ω, the terminal controller can make the system state satisfy all constraints and reduce the value of the Lyapunov function.

[0097] To ensure the recursive feasibility of the method in this invention, an alternative feasible solution can be constructed in the optimization problem at each sampling time t+Δ. We assume... For a feasible solution to problem (15), the corresponding state error is: To ensure feasibility in the time domain τ ∈ [t+Δ, t+T+Δ], we define the alternative feasible solution as:

[0098] (twenty one)

[0099] in Indicates time Feasible control inputs, and Indicates will This is applied to the state error generated by system (1). This construction method ensures that at any sampling time, the optimization problem has at least one feasible solution that satisfies all constraints.

[0100] The asymptotic stability of the method of this invention is proved by selecting the objective function as the Lyapunov function of the entire closed-loop system.

[0101] We consider defining the Lyapunov function as... ,make This represents the optimal control input. This represents the feasible control quantity, from which we can obtain:

[0102] (twenty two)

[0103] By integrating the fourth property condition of the terminal controller, we obtain the following inequality:

[0104] (twenty three)

[0105] And because:

[0106] (twenty four)

[0107] We can conclude that ΔJ ≤ 0. This indicates that as t→∞, the state error... The closed-loop error system exhibits asymptotic stability.

[0108] Step F: Online Algorithm Validation

[0109] Finally, the method of the present invention is executed online using a rolling time-domain optimization approach: at each sampling time, based on the current state fed back by the UAV sensor as the initial condition, the nonlinear programming problem (15) is solved to obtain an optimal control parameter sequence σ covering the entire prediction time domain; then, only the control command corresponding to the first control parameter σ1 in the sequence is applied to the UAV system to drive it to fly for one sampling interval; at the next sampling time, the updated state of the UAV is obtained, and this is used as the new initial condition to repeat the above optimization solution and control application process, thereby realizing continuous online correction and closed-loop control of the UAV trajectory.

[0110] In a real-world flight scenario, the UAV navigates from a starting point to a target point, avoiding six obstacles along the way. The CasADi solver is used to solve the optimization problem in real time. The initial state of the UAV and related constraints are defined as follows:

[0111] The initial position of the drone is Maximum speed Maximum acceleration The target location is set to Six static obstacles were set up in the actual flight environment, with the following coordinates:

[0112]

[0113]

[0114]

[0115]

[0116]

[0117]

[0118] The safety radius of each obstacle is set as follows: The optimal control problem of drone trajectory planning The prediction time domain is T=0.8s, and the sampling interval is... ms.

[0119] Figure 1 The drone's flight path was shown, demonstrating that it successfully navigated from its initial position to the target point and autonomously avoided six obstacles. Figure 2 Real-time speed data recorded by the motion capture system , Figure 3 The acceleration control quantity calculated by the onboard computer at every moment As shown in the figure, both velocity and acceleration satisfy the preset constraints.

[0120] Figure 4 It shows the distances between the drone and various obstacles throughout the flight. , It always maintained a safe distance of 0.38 m, effectively achieving obstacle avoidance. Figure 5 The airborne computation time for single-step iteration was recorded. The computation time for single-step iteration of this algorithm was consistently controlled within 25 ms, with an average computation time of 7.51 ms, which meets the real-time requirements of UAV trajectory planning.

[0121] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A dynamic optimization method for online trajectory planning of unmanned aerial vehicles (UAVs), characterized in that, include: Obtain the current state information of the UAV and, based on the preset dynamic model of the UAV translation subsystem, establish a predictive model for predicting the future state. At each sampling time, a finite-time optimal control problem is constructed, which includes an objective function for minimizing the state error and control input, as well as constraints, including UAV dynamics constraints, velocity constraints, acceleration constraints, and obstacle avoidance constraints. The continuous control input in the optimal control problem is parameterized and represented as a piecewise function determined by the control parameters to be optimized in the prediction time domain, so as to transform the infinite-dimensional optimal control problem into a finite-dimensional nonlinear programming problem. The constraint transcription method is used to transform the time-varying velocity constraints and obstacle avoidance constraints into integral penalty terms, which are then integrated into the nonlinear programming problem for solution. Terminal constraints are introduced into the optimal control problem. These terminal constraints include terminal controller constraints and terminal region constraints, in order to ensure the recursive feasibility and asymptotic stability of the closed-loop system. The nonlinear programming problem is solved online to obtain the optimal control parameter sequence, and the first control command is generated based on the sequence to control the flight of the UAV.

2. The dynamic optimization method according to claim 1, characterized in that, The objective function includes an integral term and a terminal cost term. The integral term is the integral of the weighted sum of the second norm of the UAV state error in the prediction time domain and the second norm of the control input. The terminal cost term is the second norm of the predicted terminal state error in the prediction time domain. A positive definite terminal weight matrix is ​​introduced to penalize the terminal state, thereby enhancing the stability of the system.

3. The dynamic optimization method according to claim 1, characterized in that, The method for parameterizing the control input includes: uniformly dividing the prediction time domain into multiple sub-intervals; setting the three-dimensional acceleration control input of the UAV as a constant vector in each sub-interval, which is the control parameter to be optimized; the control input in the entire prediction time domain is composed of the sequential splicing of the control parameter sequences in all sub-intervals, so as to transform the problem of solving the continuous control function into the optimization problem of solving the finite-dimensional control parameter vector.

4. The dynamic optimization method according to claim 3, characterized in that, The constraint transcription method includes: defining scalar functions for velocity constraints and each obstacle avoidance constraint to quantify the degree to which the current state violates the corresponding constraint; introducing a preset smoothing penalty function, which performs a nonlinear mapping on the output value of the scalar function. When the constraint is satisfied, its function value is zero or close to zero, and when the constraint is violated, its function value increases smoothly and positively with the increase of the degree of violation; integrating the smoothing penalty function over the entire prediction time domain and requiring the integral value to be less than a preset positive threshold to form an integral penalty term.

5. The dynamic optimization method according to claim 1, characterized in that, The terminal controller is designed as a linear state feedback controller, which generates control commands based on the state error at the end of the predicted time domain. By designing the feedback gain matrix of the controller offline, it is ensured that when the UAV enters the terminal area, the system state can asymptotically converge to the target state under the action of the terminal controller, and all dynamic and safety constraints of the UAV are satisfied during the convergence process.

6. The dynamic optimization method according to claim 5, characterized in that, The terminal region constraint is defined as a set of state spaces surrounding the target state, requiring that the state at the end of the predicted time domain must fall within this set of state spaces. The size and shape of this set of state spaces are jointly determined based on the Lyapunov stability theory of the system, the dynamic characteristics of the UAV, the boundaries of various constraints, and the performance of the terminal controller. Its upper bound is determined by the Lyapunov function value that ensures state convergence, and its lower bound is determined by the condition that ensures the UAV maintains a minimum safe distance from all obstacles, thus forming an invariant set that can guarantee recursive feasibility.

7. The dynamic optimization method according to claim 1, characterized in that, In the optimization problem at each sampling time t+Δ, an alternative feasible solution can be constructed; The method for constructing the alternative feasible solution includes: for the time interval [t+Δ, t+T], using the portion of the corresponding time period in the optimal control sequence calculated at sampling time t, and for the newly added time interval [t+T, t+T+Δ], using the control input generated by the terminal controller based on the state.

8. The dynamic optimization method according to claim 1, characterized in that, The asymptotic stability of the dynamic optimization method is proven by selecting the objective function as the Lyapunov function of the entire closed-loop system. Theoretical derivation shows that at each sampling time, the Lyapunov function value corresponding to the calculated optimal control strategy is monotonically non-increasing relative to the Lyapunov function value at the previous time. Therefore, as time approaches infinity, the state error of the closed-loop error system will converge to zero, thus strictly ensuring the long-term operational reliability of the control system.

9. The dynamic optimization method according to claim 1, characterized in that, The translational subsystem dynamics model defines the UAV's state vector as a six-dimensional vector containing three-dimensional position coordinates and three-dimensional velocity components, and defines the control input as a three-dimensional acceleration command. The acceleration constraint is derived from the maximum total thrust that the UAV rotor can generate, specifically by limiting the Euclidean magnitude of the sum of the acceleration command vector and the gravitational acceleration vector to an upper limit determined by the ratio of the maximum total thrust to the mass of the UAV.

10. The dynamic optimization method according to claim 1, characterized in that, The dynamic optimization method employs a rolling time-domain optimization approach for online execution: at each sampling time, based on the current state fed back by the UAV's sensors as the initial condition, the nonlinear programming problem is solved to obtain the optimal control parameter sequence covering the entire prediction time domain; the control command corresponding to the first control parameter in the optimal control parameter sequence is applied to the UAV system to drive it to fly for one sampling interval; at the next sampling time, the updated state of the UAV is obtained, and this is used as the new initial condition to repeat the optimization solution and control application process, thereby achieving continuous online correction and closed-loop control of the UAV trajectory.

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