Method for planning air-drop trajectory of tensegrity unmanned aerial vehicle

Abstract

The invention discloses a tensegrity unmanned aerial vehicle air-drop trajectory planning method, and belongs to the technical field of unmanned aerial vehicle control, and the method comprises the steps: unconstrained analytical solution: constructing a trajectory planning problem into a time-optimal minimization Jerk problem under the condition of neglecting the kinematics constraints such as speed, and solving the minimization Jerk problem; obtaining the theoretically optimal trajectory and the shortest time T0 thereof by solving a quintic polynomial; and carrying out constrained iterative optimization, taking T0 as a search lower bound under the condition that all kinematic constraints are met, adjusting the total duration of the trajectory through iterative methods such as binary search until the shortest feasible time T * meeting all the constraints is found, and generating a final trajectory. According to the method, the complex non-convex optimization problem is decomposed into two stages of analytical solution and iterative optimization, the strict requirement for accurate control of the tail end speed when the tensegrity unmanned aerial vehicle executes the air-drop task is met, and the task success rate and safety are improved.

Description

Technical Field

[0001] This invention belongs to the field of unmanned aerial vehicle (UAV) control technology, specifically relating to a method for planning the airdrop trajectory of a tensioned integral UAV. Background Technology

[0002] Tensile integral unmanned aerial vehicles (UAVs) are a new type of flexible structure aircraft that can absorb and dissipate impact energy through structural deformation, thereby achieving highly survivable impact landings. This unique impact resistance provides a novel solution for deploying UAVs in complex and unknown environments.

[0003] Since the airdrop impact landing of a tensioned monolithic UAV relies on a preset precise velocity, planning its flight trajectory transforms into a time-optimal control problem that strictly satisfies the terminal velocity constraint. Existing trajectory planning methods suffer from insufficient computational efficiency and solution reliability when addressing the precise velocity control requirements of tensioned monolithic UAVs. Therefore, developing a computationally efficient, reliable method that can accurately generate time-optimal trajectories is crucial for leveraging the unique advantages of tensioned monolithic UAVs and improving their mission success rate. Summary of the Invention

[0004] In view of this, this invention addresses the shortcomings of existing trajectory planning methods in terms of computational efficiency, result reliability, and precise control of terminal velocity when tensioned unmanned aerial vehicles (UAVs) perform airdrop missions. It proposes a computationally efficient and reliable time-optimal trajectory planning method.

[0005] The technical solution for implementing the present invention is as follows:

[0006] A method for planning the trajectory of a tensioned integral UAV airdrop, the method comprising the following steps:

[0007] Step 1: Solve for the theoretically optimal trajectory under no kinematic constraints;

[0008] Step 2: Determine whether the theoretical optimal trajectory obtained in Step 1 satisfies the kinematic constraints. If it does, the theoretical optimal trajectory obtained in Step 1 is used as the UAV airdrop trajectory. If it does not, the theoretical optimal trajectory obtained in Step 1 is optimized using an iterative method based on binary search, with the total flight time T as the search variable. The initial value of the total flight time T is the time of the theoretical optimal trajectory. During optimization, the total flight time is increased, and a modified boundary value problem is resolved for each new total time until a minimum feasible time T that satisfies all kinematic constraints is found. * The drone's airdrop trajectory was obtained;

[0009] The maximum total flight time is 2-3 times the initial value, and all kinematic constraints include velocity and acceleration constraints.

[0010] In step 1, the kinematic constraints of the aircraft are ignored, and the problem is transformed into a classic optimal boundary value problem. Using a numerically stable analytical solver based on the adjoint matrix, a theoretically time-optimal trajectory and its corresponding execution time are calculated for a given initial and terminal state.

[0011] In step 2, based on the constraint satisfaction and iterative optimization of binary search, this stage checks whether the theoretically optimal trajectory generated in step 1 satisfies all kinematic constraints. If the trajectory satisfies all constraints, then the trajectory is the final optimal feasible solution. If the trajectory is unreasonable, it indicates that the theoretically optimal time is too short. At this time, an iterative optimization framework based on binary search is initiated, using the total flight time T as the search variable. By iterating between the theoretically optimal time and a conservative upper limit time, the flight time is systematically increased, and a modified boundary value problem is resolved for each new time T until a minimum feasible time T that satisfies all constraints is found. * .

[0012] Beneficial effects

[0013] 1. This invention presents an innovative two-stage planning framework that decouples the problem into analytical solution and iterative optimization, achieving a balance between computational efficiency and solution reliability. Compared to traditional integrated nonlinear optimization methods, this invention utilizes analytical solutions as a high-quality starting point and combines them with efficient binary search, avoiding complex global optimization, sensitivity to initial values, and the risk of convergence failure, thus ensuring millisecond-level computational efficiency and deterministic planning results.

[0014] 2. The planning results of this invention combine time optimization with precise constraint satisfaction, intelligently balancing the two. When there are no constraints or constraints are not activated, the solution is the theoretically optimal solution; when constraints are present, the solution found through iteration is the feasible solution that satisfies the constraint boundaries and takes the shortest time. This ensures that the trajectory is both optimal within the feasible region and strictly satisfies the terminal state constraint of the impact velocity, perfectly resolving the contradiction that traditional methods struggle to achieve both.

[0015] 3. This invention discloses a trajectory planning method for airdropping from a tensioned integral UAV, belonging to the field of UAV control technology. The method includes: unconstrained analytical solution, where the trajectory planning problem is constructed as a time-optimal minimization Jerk problem under the condition of ignoring kinematic constraints such as velocity; the theoretically optimal trajectory and its shortest time T0 are obtained by solving a fifth-order polynomial; and constrained iterative optimization, where, under the condition of satisfying all kinematic constraints, with T0 as the lower bound of the search, the total trajectory duration is adjusted using iterative methods such as binary search until the shortest feasible time T satisfying all constraints is found. *The invention decomposes the complex non-convex optimization problem into two stages: analytical solution and iterative optimization. This solves the stringent requirement for precise end-effector velocity control when a tensioned unmanned aerial vehicle (UAV) performs an airdrop mission, thereby improving mission success rate and safety. Attached Figure Description

[0016] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0017] Figure 1 The flowchart shows the time-optimal trajectory planning method.

[0018] Figure 2 This is a graph showing the data from the simulation experiment.

[0019] Figure 3 This is a graph showing sensor data from a physical experiment.

[0020] Figure 4 This is a diagram of a physical experiment. Detailed Implementation

[0021] The present invention will now be described in detail with reference to the accompanying drawings and embodiments. Obviously, the described embodiments are merely some, not all, of the embodiments of the present invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.

[0022] A method for planning the trajectory of a tensioned integral UAV airdrop includes the following steps:

[0023] Step 1: Analytical solution of the unconstrained time-optimal trajectory. Without considering kinematic constraints, a theoretically optimal time is obtained.

[0024] Step 2: Based on the constraint satisfaction and iterative optimization of binary search, check whether the trajectory generated according to the theoretical optimal time satisfies the kinematic constraints; if yes, then the theoretical optimal time is the final optimal feasible time; if not, then using the total flight time as the search variable, find the minimum feasible time that satisfies all kinematic constraints through iterative search as the final optimal feasible time.

[0025] In step one, the trajectory connecting the start and end states is modeled as an optimization problem with the goal of minimizing Jerk. Its optimal solution is a fifth-degree polynomial. A cost function with respect to the total time T is established by solving the coefficients of the fifth-degree polynomial. Then, a higher-degree polynomial equation with respect to time T is obtained by differentiating the cost function. The adjoint matrix method is used to solve the higher-degree polynomial equation f(T) = 0, and its smallest positive real root is selected as the theoretical optimal time T0.

[0026] The fifth-order polynomial model of the trajectory is:

[0027] p(t) = c5t 5 +c4t 4 +c3t 3 +c2t 2 +c1t+c0

[0028] Where t is time, and c0 to c5 are the coefficients of the trajectory, whose values ​​are uniquely determined by six boundary conditions: the position, velocity, and acceleration of the starting and ending points of the trajectory.

[0029] The adjoint matrix method constructs an adjoint matrix C for the high-order polynomial equation f(T) = 0. f :

[0030]

[0031] The eigenvalues ​​of the adjoint matrix are all the roots of the polynomial f(T), thus allowing for a stable solution.

[0032] In step two, the minimum feasible time T that satisfies all kinematic constraints is found. * The process is constructed as a single-variable constrained optimization problem:

[0033] T * =min{T|(T≥T0)∧(v max (T)≤v max _ limit )}

[0034] Among them, v max (T) represents the maximum velocity value of the generated trajectory under a given total duration T, v max _ limit The maximum speed limit is preset, and the problem is solved efficiently using a binary search algorithm.

[0035] Example

[0036] This invention proposes a method for planning the trajectory of a tensioned integral UAV airdrop, such as... Figure 1 As shown, its detailed implementation method is as follows:

[0037] Step 1: Analytical solution of the unconstrained time-optimal trajectory

[0038] The specific process is as follows:

[0039] Consider the motion of the UAV in a single dimension. The trajectory state vector x(t) is defined as a triple containing position, velocity, and acceleration:

[0040] x(t) = [ p (t),v(t),a(t)] T

[0041] Where p(t), v(t), and a(t) are the position, velocity, and acceleration at time t, respectively.

[0042] The optimization objective is to find a trajectory with the shortest total time T to ensure the system can quickly reach the target point, which is crucial for real-time performance and efficiency. This trajectory should also be as flat as possible (to minimize Jerk's algorithm) and meet maximum speed limits throughout the motion to ensure the agent operates within its physical capabilities.

[0043]

[0044] ex t s. t .p(0)=p extstart ,p( T ) = p extend

[0045]

[0046] Where w is the trajectory smoothness weight value;

[0047] This is a time-optimal control problem with non-convex kinematic constraints. Direct solutions are very difficult. At this stage, neglecting velocity constraints, we seek the Jerk-minimum trajectory connecting the start and end states. According to optimal control theory, the trajectory solution minimizing the Jerk integral is a fifth-degree polynomial:

[0048] p(t) = c5t 5 +c4t 4 +c3t 3 +c2t 2 +c1t+c0

[0049] This trajectory consists of 6 coefficients c = [c0,...,c5] T The only certainty is that these six coefficients can be solved using six boundary conditions (p, v, a at the start and end points). Substituting the boundary conditions into the fifth-degree polynomial and its first and second derivatives yields a system of linear equations concerning the coefficient c:

[0050]

[0051] Where M(T) is a 6x6 matrix related to the total time T.

[0052] Solving this system of equations yields a coefficient expression c(T) with T as the variable. Substituting c(T) into Jerk's integral objective, we obtain a cost function J(T) in T. To find the time T that minimizes Jerk's objective, we set its derivative dJ / dT = 0, which derives a high-order polynomial equation in T:

[0053] f(T) = k n T n +k n-1 T n-1 +…+k0=0

[0054] Directly solving for the roots of this high-order polynomial equation (i.e., the candidate optimal time T) may be numerically unstable. To obtain a more robust solution, the adjoint matrix method is used. For the polynomial f(T) = 0, an adjoint matrix C of the following form is constructed. f :

[0055]

[0056] The eigenvalues ​​of this adjoint matrix are exactly polynomials. f All roots of (T). By calculating C f By analyzing the eigenvalues, we can stably find all candidate optimal times. We then select the smallest positive real root as the theoretically optimal time T0 under unconstrained conditions. This step provides an idealized and most compact lower bound for subsequent iterative optimization.

[0057] Step 2: Constraint Satisfaction and Iterative Optimization Based on Binary Search

[0058] The theoretically optimal time T0 and trajectory obtained by the unconstrained solution are ideal results without considering kinematic constraints such as maximum velocity. In practical applications, this may cause the velocity at certain points on the trajectory to exceed the physical limits of the system. Therefore, adjusting the trajectory duration to satisfy all kinematic constraints is a necessary step to ensure the feasibility of the trajectory.

[0059] For this type of time-optimal trajectory, there is a key monotonically decreasing relationship between its maximum speed and trajectory duration T: the shorter the trajectory duration T, the higher the maximum speed required to complete the same state transition. Therefore, if the trajectory generated at time T0 exhibits speeding, the trajectory time T must be extended to reduce the maximum speed within the constraints. The goal is to find a minimum feasible time T that satisfies the speed limit while being as close as possible to the theoretical optimum. * .

[0060] This search process is structured as a single-variable constrained optimization problem. Let the function v max (T) represents the maximum velocity value of the generated trajectory given a total time T, then the optimal feasible time T * The solution can be precisely described as:

[0061] T * =min{T|(T≥T0)∧(v max (T)≤v max_limit )}

[0062] Among them, T * This represents the minimum value selected from all flight times T that satisfy the conditions. These conditions require that a feasible flight time must not only be greater than or equal to the theoretically optimal time under unconstrained conditions, but also that the maximum speed v of the trajectory generated based on that time T is... max (T) must also strictly adhere to the system's maximum speed limit v max_limit .

[0063] To solve this problem efficiently, v is used. max To investigate the monotonicity of (T), an iterative algorithm based on binary search was designed. This algorithm first checks v... max Does (T0) satisfy the constraint? If not, then within a defined search interval [T]... low ,T high The iteration is performed within [T], where the lower bound is T. low Initialized to T0, with an upper bound of T. high This is a conservative time value that ensures the constraints are met. In the k-th iteration, the algorithm calculates the test time point. And according to T mid The search interval for the next round is updated based on whether the generated trajectory exceeds the speed limit.

[0064]

[0065] This iterative process continues until the interval width is reached. The convergence tolerance is less than the preset value. Ultimately, the optimal feasible time is determined to be the upper bound T of the converged interval. high This ensures the time optimality and kinematic feasibility of the generated trajectory.

[0066] Finally, simulations and physical experiments were conducted to analyze the proposed unconstrained time-optimal trajectory and to perform constraint satisfaction and iterative optimization based on binary search. First, the core capabilities of the framework were rigorously quantitatively evaluated in a high-fidelity simulation environment based on ROS / Gazebo. The experimental task was set as a standard Iris quadcopter UAV performing a vertical descent maneuver under strict maximum speed constraints (8 m / s). The results show that the time-optimal execution time T can be automatically solved. * =8.3s. For example... Figure 2 As shown, its speed rapidly accelerates to the maximum speed limit, maintains a constant speed while gliding, and then decelerates to its maximum, fully utilizing the dynamic potential of the aircraft. After successfully verifying the basic capabilities of the framework in simulation, it was deployed in a more challenging physical task to test its applicability under real, non-ideal conditions. A precision airdrop mission was performed using a custom-designed tensioned integral aircraft, requiring the aircraft to impact the ground with a precise non-zero terminal velocity (-8 m / s). By setting the target state, the time-optimal (T) time was successfully generated on the onboard computer. * A smooth trajectory with a time limit of 1.3s and a stringent end-velocity constraint. For example... Figure 3 and Figure 4 The aircraft successfully completed a high-impact landing according to the planned trajectory, and the impact velocity recorded by the onboard sensors was highly consistent with the expected value.

[0067] In summary, the above are merely preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. 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 method for trajectory planning of an integral tensile unmanned aerial vehicle air-drop, characterized in that The steps of the method include: Step 1, solving the theoretical optimal trajectory without kinematic constraints; Step 2, judging whether the theoretical optimal trajectory obtained in step 1 satisfies the kinematic constraints, if yes, the theoretical optimal trajectory obtained in step 1 is taken as the UAV air-drop trajectory, if not, the theoretical optimal trajectory obtained in step 1 is optimized by using an iterative method based on dichotomy, the total flight time is increased during the optimization, and a modified boundary value problem is solved again for each new total time until a minimum feasible time T satisfying all kinematic constraints is found * , to obtain the UAV air-drop trajectory.

2. The tension integral whole unmanned aerial vehicle air-drop trajectory planning method according to claim 1, characterized in that: In step 1, when solving the theoretical optimal trajectory without kinematic constraints, the kinematic constraints of the aircraft are ignored, the problem is converted into a classic optimal boundary value problem, and a numerical stable analytical solver based on an adjoint matrix is used to obtain a theoretically optimal time trajectory and its corresponding execution time for a given initial and terminal state.

3. The tension integral whole unmanned aerial vehicle air-drop trajectory planning method according to claim 2, characterized in that: The trajectory connecting the start and end states is modeled as an optimization problem aiming to minimize the jerk, and the optimal solution is a quintic polynomial, and a cost function about the total time T is established by solving the coefficients of the quintic polynomial, and a high-order polynomial equation about the time T is obtained by taking the derivative of the cost function, the high-order polynomial equation f(T) = 0 is solved by using the adjoint matrix method, and the minimum positive real root of the equation is selected as the theoretical optimal time T0.

4. The tension integral whole unmanned aerial vehicle air-drop trajectory planning method according to claim 3, characterized in that: The quintic polynomial model of the trajectory is: p(t) = c5t 5 + c4t 4 + c3t 3 + c2t 2 + c1t + c0 Where t is the time, c0 to c5 are the coefficients of the trajectory, and their values are uniquely determined by the positions, velocities and accelerations of the start and end points of the trajectory, i.e. 6 boundary conditions.

5. The tension integral whole unmanned aerial vehicle air-drop trajectory planning method according to claim 4, characterized in that: The companion matrix method constructs a companion matrix C for the high order polynomial equation f(T) = 0 f : The eigenvalues of the adjoint matrix are all the roots of the polynomial f(T), so the solution is stable.

6. The tension integral whole unmanned aerial vehicle air-drop trajectory planning method according to claim 5, characterized in that: In step 2, the constraint satisfaction based on binary search and iterative optimization, this stage checks whether the theoretical optimal trajectory generated in step 1 satisfies all kinematic constraints, if the trajectory satisfies all constraints, the trajectory is the final optimal feasible solution, if the trajectory is unreasonable, it indicates that the theoretical optimal time is too short, at this time, start an iterative optimization framework based on binary search, take the total flight time T as the search variable, through iteration between the theoretical optimal time and a conservative upper limit time, increase the flight time, and solve a revised boundary value problem for each new time T until a minimum feasible time T satisfying all constraints is found * , obtain the unmanned aerial vehicle air-drop trajectory.

7. The tension integral whole unmanned aerial vehicle air-drop trajectory planning method according to claim 6, characterized in that: The initial value of the total flight time is T0.

8. The tension integral whole unmanned aerial vehicle air-drop trajectory planning method according to claim 7, characterized in that: The maximum value of the total flight time is 2-3 times the initial value.

9. The tension integral whole unmanned aerial vehicle air-drop trajectory planning method according to claim 8, characterized in that: All kinematic constraints include velocity constraints and acceleration constraints.

10. The tension integral whole unmanned aerial vehicle air-drop trajectory planning method according to claim 9, characterized in that: In the second step, the minimum feasible time T satisfying all kinematic constraints is found * The process is constructed as a single-variable constrained optimization problem: T * = min{T | (T ≥ To) ∧ (v max (T) ≤ v max_limit )} where v max (T) is the maximum speed value of the generated trajectory for a given total duration T, v max_limit is the preset maximum speed limit, and the problem is efficiently solved by a binary search algorithm.

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