A UAV 3D Printing System and Method Combining Trajectory Curvature Optimization and End-Flight Compensation

Abstract

This invention discloses a UAV 3D printing system and method combining trajectory curvature optimization and end-effector compensation. The system includes a trajectory optimization module, a dynamic feasibility verification module, an end-effector compensation allocation module, and an execution and closed-loop control module. First, the original printing trajectory, containing sharp features such as right angles and acute angles, is optimized. Under deviation constraints, curvature constraints, and boundary constraints, a sequential quadratic programming algorithm is used to generate a smooth trajectory that satisfies the dynamic constraints. Then, the smooth trajectory is time-parameterized, limiting the acceleration and jerk of the flight platform and achieving synchronous control of the extrusion flow rate and trajectory speed. Further, the remaining geometric error of the optimized trajectory relative to the original trajectory is calculated, and this error is allocated to the end-effector compensation mechanism for correction within its effective travel range. Through the coordinated control of the flight platform and the end-effector compensation mechanism, high-precision trajectory following and stable printing are achieved.

Description

Technical Field

[0001] The present invention relates to the technical field of unmanned aerial vehicles (UAVs), and in particular to a method and system for 3D printing of unmanned aerial vehicles that combines trajectory curvature optimization and end-effector compensation. Background Technology

[0002] Currently, trajectory planning for drones in 3D printing (especially architectural or large-scale structure printing) often follows the designed path directly, including sharp geometric features such as right angles. Existing technologies use secondary positioning systems to correct the position and attitude deviations of the drone caused by airflow drift in real time (CN115520406A). Other solutions improve printing accuracy by setting positioning markers along the drone's flight path and correcting the path in real time based on the collected position information (CN109113343B). However, due to the inertia of the flight platform, attitude adjustment lag, and dynamic constraints, such trajectories are prone to the following problems at sharp corners:

[0003] Large path deviation: When making right-angle turns, the aircraft has difficulty completing attitude adjustments within a short distance, and the actual printed path deviates significantly from the theoretical trajectory.

[0004] Poor molding quality: Problems such as material accumulation, broken wires, and wire pulling often occur at sharp corners, affecting molding accuracy and surface quality.

[0005] Insufficient compensation: Even if an end-effector compensation mechanism (such as Delta parallel arm) is integrated into the flight platform, the compensation mechanism cannot completely eliminate errors due to the excessive instantaneous curvature of the original trajectory, insufficient working space and dynamic response capability.

[0006] Lack of systematic optimization: Existing solutions often optimize flight trajectory or terminal compensation separately, lacking a holistic collaborative design of "trajectory-dynamics-compensation mechanism".

[0007] Therefore, there is an urgent need for a collaborative optimization method that can fundamentally eliminate dynamically infeasible trajectories during the trajectory planning stage and combine it with an end-effector compensation mechanism for residual correction. Summary of the Invention

[0008] The purpose of this invention is to provide a UAV 3D printing system and method that combines trajectory curvature optimization and end-effector compensation. This is achieved by actively introducing controllable geometric deviations during the trajectory planning stage to transform the original design trajectory containing sharp features into a smooth trajectory that meets the dynamic constraints of the UAV. The system also incorporates an end-effector compensation mechanism for residual correction, thereby systematically solving problems such as large path deviations, poor molding quality, and insufficient compensation at sharp corners for UAVs, and improving printing accuracy and reliability.

[0009] To achieve the above objectives, the present invention adopts the following technical solution:

[0010] A drone 3D printing system combining trajectory curvature optimization and end-effector compensation includes a trajectory optimization module, a dynamic feasibility verification module, an end-effector compensation allocation module, an execution and closed-loop control module, and a sensing system.

[0011] The trajectory optimization module smooths the original trajectory to generate a smooth trajectory that meets dynamic constraints. The dynamic feasibility verification module parameterizes the smoothed trajectory over time and limits the acceleration and jerk of the flight platform. The end-effector compensation allocation module allocates the remaining geometric error after smoothing the trajectory to the end-effector compensation mechanism to ensure that the error is corrected within the maximum travel range of the end-effector compensation mechanism. The execution and closed-loop control module controls the flight platform and the end-effector compensation mechanism to execute the optimized trajectory and perform real-time closed-loop feedback adjustments. The sensing system includes a positioning module, attitude sensor, mechanical state sensor, and displacement sensor to monitor the position, attitude, and mechanical state of the flight platform and provide feedback for closed-loop control.

[0012] In addition, the present invention also provides a method for a UAV 3D printing system based on a combination of trajectory curvature optimization and end-effector compensation, comprising the following steps:

[0013] Step S1: Obtain the original trajectory:

[0014] Obtain the original design printing path of the flight platform, including sharp geometric features such as right angles, acute angles, and folds;

[0015] Step S2, Trajectory Pre-optimization:

[0016] The original design printing path is optimized by using a curvature constraint algorithm to transform the path containing sharp features into a smooth trajectory, eliminating instantaneous turning actions that the flight platform cannot perform and improving the executability of the trajectory.

[0017] Step S3, Time-parameterized pre-dynamic feasibility verification:

[0018] The smooth flight trajectory is parameterized in time and its dynamic feasibility is verified, and corresponding velocity and acceleration planning information is generated to ensure that the flight platform can execute smoothly according to the trajectory in actual operation.

[0019] Step S4, End-of-line compensation error allocation:

[0020] The remaining geometric error after trajectory optimization is calculated and allocated to the end-effector compensation mechanism. The error allocation strategy ensures that the compensation mechanism can correct the remaining error within its maximum effective stroke range;

[0021] Step S5: Based on the optimized trajectory from Steps S2 to S4, control the flight platform to execute the flight trajectory, and simultaneously adjust the error through real-time closed-loop control feedback.

[0022] Preferably, the trajectory optimization includes deviation constraints, curvature constraints, and boundary constraints;

[0023] The deviation constraint is used to ensure that the maximum deviation between the optimized trajectory and the original trajectory does not exceed a predetermined value, thereby ensuring the fidelity of the trajectory.

[0024] The curvature constraint ensures that the curvature of the trajectory does not exceed the preset maximum curvature value, in order to avoid excessively sharp turns during flight.

[0025] The boundary constraints ensure that the starting and ending positions of the trajectory are fixed to maintain the global consistency of the flight path.

[0026] ,

[0027] in, The spatial coordinates of the position corresponding to the original design printing trajectory; These are the spatial coordinates of the discrete points corresponding to the optimized trajectory. This is the preset maximum allowable trajectory deviation;

[0028] The curvature constraint includes transforming the original trajectory γ0(s) of the original design printing path into a smooth trajectory γ(s) that satisfies dynamic constraints, wherein the curvature κ(s) satisfies:

[0029] ,

[0030] Where, a lat,max The maximum lateral acceleration is determined by the thrust-to-weight ratio and attitude margin of the flight platform; v(s) is the trajectory velocity along the arc length s. For maximum curvature;

[0031] The boundary constraints are as follows:

[0032] ; ,

[0033] in: The starting coordinates of the optimized trajectory; This is the starting point of the original trajectory; The coordinates of the endpoint of the optimized trajectory; This is the endpoint of the original trajectory.

[0034] Preferably, the trajectory optimization, while satisfying curvature constraints, achieves a balance between flight feasibility and smoothness by optimizing the changes in adjacent points of the smooth trajectory and the differences between the trajectory and the original design trajectory.

[0035] Preferably, the optimized smooth trajectory γ(s) is obtained by minimizing the maximum deviation between the smooth trajectory and the original trajectory:

[0036] ,

[0037] in, The objective function value optimized for trajectory smoothing; Summing all adjacent pairs of points in the trajectory; Optimized smooth trajectory The coordinates of a discrete point; Trajectory No. From point 1 to point 2 +1 point displacement vector; It is the square of the Euclidean norm.

[0038] Preferably, the trajectory optimization adopts a multi-objective weighted optimization form, and its comprehensive objective function is:

[0039] ,

[0040] Where α is the path length smoothness weight; β is the curvature smoothness weight; and γ is the trajectory fidelity weight. Let i be the i-th discrete point in the original design trajectory; Let be the trajectory curvature at the corresponding discrete point.

[0041] Preferably, the trajectory optimization is solved using the Sequential Quadratic Programming (SQP) algorithm, which reconstructs the original nonlinear constraint optimization problem into the following quadratic programming subproblem:

[0042] ,

[0043] st ,

[0044] in, For the search direction, An approximation of the Hessian matrix. These are the trajectory curvature constraints and dynamic constraints.

[0045] The sequential quadratic programming algorithm includes the following steps:

[0046] Using the discrete points of the original trajectory as the initial solution ;

[0047] Construct the Lagrangian function:

[0048] ,

[0049] At the current iteration point Calculate the approximation of the Hessian matrix at this point. And linearize the constraints;

[0050] Solve the quadratic programming subproblem to obtain the search direction. ;

[0051] The step size is determined by a line search method. And update the trajectory solution:

[0052] ,

[0053] When the convergence condition is met When the iteration ends, the iteration is terminated.

[0054] Preferably, in step S3, the smooth flight trajectory is parameterized over time and its dynamic feasibility is verified to generate corresponding velocity and acceleration planning information;

[0055] Limit the acceleration 'a' and jerk 'j' of the flight platform to ensure it can execute the trajectory smoothly.

[0056] ,

[0057] The extrusion flow rate Q(s) and the trajectory velocity v(s) are synchronously controlled, satisfying the following relationship:

[0058] ,

[0059] in, Where is the nozzle cross-sectional area, and k is the material flow coefficient.

[0060] Preferably, in step S4, the remaining geometric error after trajectory optimization is calculated to measure the spatial deviation between the optimized smooth trajectory and the original design trajectory.

[0061] ,

[0062] in, For the first The remaining geometric error vector of each trajectory point; For the original design trajectory, the first The coordinates of the points; To optimize the smooth trajectory The coordinates of the points; This represents the total number of discrete points on the trajectory.

[0063] Preferably, the end-effector compensation mechanism is capable of fine-tuning the position and attitude of the flight platform at the millimeter level to compensate for residual errors generated in the smooth trajectory;

[0064] The flight platform uses a multi-rotor drone, which has stable hovering and trajectory following capabilities.

[0065] Compared with the prior art, the present invention has the following beneficial effects:

[0066] This invention optimizes the curvature constraint of the original trajectory through a trajectory pre-optimization module, solving the problem that UAVs cannot perform instantaneous turning maneuvers at sharp corners, and fundamentally improving trajectory executability. By converting sharp features such as right angles and acute angles into smooth trajectories that meet dynamic constraints, the path deviation caused by inertia and attitude adjustment lag of the flight platform is eliminated at the source, reducing the maximum tracking error from 97.2mm to 14.8mm, an improvement of 84.8%.

[0067] This invention solves the problem of saturation failure of the compensation mechanism due to excessive error in traditional solutions by coordinating the end-effector compensation allocation module with trajectory optimization, thus achieving a systematic improvement in molding accuracy. By allocating the remaining small-amplitude, gradually changing error after optimization to the end-effector compensation mechanism, it ensures that the mechanism always operates within its workspace, reducing the maximum error of the final printing path from 45.3mm to 6.7mm and increasing the molding pass rate from 65% to 95%.

[0068] This invention solves the forming defects such as material accumulation, filament breakage, and filament pulling at sharp corners by synchronously controlling time parameterization and extrusion flow rate, achieving a significant improvement in print quality. By limiting acceleration and jerk and optimizing them synchronously with the material extrusion flow rate, the printhead movement is matched with the material extrusion speed, effectively reducing material accumulation at corners and reducing the surface ripple height from 2.8mm to below 0.5mm.

[0069] This invention solves the problems of poor system stability and large attitude disturbances through a hierarchical control architecture of "coarse adjustment of the UAV + fine adjustment of the compensator", and realizes reliable operation of the printing process. The smooth flight trajectory reduces the attitude disturbance and load impact of the flight platform. Combined with the high-frequency and precise correction of the end compensation mechanism, the tracking error of the system under different environmental conditions varies by about 10mm, and the compensation effect remains stable. Attached Figure Description

[0070] Figure 1 This is a schematic diagram illustrating curvature comparison, curvature distribution, trajectory comparison, and deviation in a UAV 3D printing system that combines trajectory curvature optimization and end-effector compensation, provided as an embodiment of the present invention.

[0071] Figure 2 This is a schematic diagram illustrating curvature comparison, curvature distribution, trajectory comparison, and deviation in a method for a UAV 3D printing system combining trajectory curvature optimization and end-effector compensation, provided as an embodiment of the present invention.

[0072] Figure 3 This is a schematic diagram illustrating curvature comparison, curvature distribution, trajectory comparison, and deviation in a method for a UAV 3D printing system combining trajectory curvature optimization and end-effector compensation, provided as an embodiment of the present invention.

[0073] Figure 4 This is a schematic diagram illustrating curvature comparison, curvature distribution, trajectory comparison, and deviation in a method for a UAV 3D printing system combining trajectory curvature optimization and end-effector compensation, provided as an embodiment of the present invention.

[0074] Figure 5 This is a schematic diagram illustrating curvature comparison, curvature distribution, trajectory comparison, and deviation in a method for a UAV 3D printing system combining trajectory curvature optimization and end-effector compensation, provided as an embodiment of the present invention.

[0075] Figure 6 A flowchart of a method for a drone 3D printing system combining trajectory curvature optimization and end-effector compensation, provided as an embodiment of the present invention.

[0076] The serial numbers in the diagram are as follows:

[0077] 1. Quadcopter drone; 2. End-effector compensation mechanism; 3. 3D printing extruder; 4. 3D printing feed tube; 5. Desired path of drone; 6. Actual path of drone; 7. Desired path of print head; 8. Actual path of print head. Detailed Implementation

[0078] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments.

[0079] This embodiment provides a UAV 3D printing system that combines trajectory curvature optimization and end-effector compensation, including a trajectory optimization module, a dynamic feasibility verification module, an end-effector compensation allocation module, an execution and closed-loop control module, and a sensing system.

[0080] The trajectory optimization module smooths the original trajectory to generate a smooth trajectory that meets dynamic constraints. The dynamic feasibility verification module parameterizes the smoothed trajectory over time and limits the acceleration and jerk of the flight platform. The end-effector compensation allocation module distributes the remaining geometric error after smoothing the trajectory to the end-effector compensation mechanism, ensuring that the error is corrected within the maximum travel range of the end-effector compensation mechanism. The execution and closed-loop control module controls the flight platform and the end-effector compensation mechanism to execute the optimized trajectory and perform real-time closed-loop feedback adjustments. The sensing system, including a positioning module, attitude sensors, mechanical state sensors, and displacement sensors, monitors the position, attitude, and mechanical state of the flight platform and provides feedback for closed-loop control.

[0081] In addition, such as Figure 6 As shown, the present invention also provides a method for a UAV 3D printing system based on a combination of trajectory curvature optimization and end-effector compensation, comprising the following steps:

[0082] Step S1: Obtain the original trajectory:

[0083] Obtain the original design printing path of the flight platform, including sharp geometric features such as right angles, acute angles, and folds;

[0084] Step S2, Trajectory Pre-optimization:

[0085] The original design printing path is optimized by using a curvature constraint algorithm to transform paths with sharp features into smooth trajectories, eliminating instantaneous turning maneuvers that the flight platform cannot perform and improving the executability of the trajectory.

[0086] Furthermore, in this embodiment, trajectory optimization includes deviation constraints, curvature constraints, and boundary constraints;

[0087] Deviation constraints are used to ensure that the maximum deviation between the optimized trajectory and the original trajectory does not exceed a predetermined value, thereby guaranteeing the fidelity of the trajectory.

[0088] Curvature constraint: Ensures that the curvature of the trajectory does not exceed the preset maximum curvature value to avoid excessively sharp turns during flight;

[0089] Boundary constraints: ensure that the starting and ending positions of the trajectory are fixed to maintain the global consistency of the flight path.

[0090] The deviation constraints are as follows:

[0091] ,

[0092] in, The spatial coordinates of the position corresponding to the original design printing trajectory; These are the spatial coordinates of the discrete points corresponding to the optimized trajectory. This is the preset maximum allowable trajectory deviation;

[0093] The curvature constraint involves transforming the original trajectory γ0(s) of the original design printing path into a smooth trajectory γ(s) that satisfies dynamic constraints, wherein the curvature κ(s) satisfies:

[0094] ,

[0095] Where, a lat,max The maximum lateral acceleration is determined by the thrust-to-weight ratio and attitude margin of the flight platform; v(s) is the trajectory velocity along the arc length s. This represents the maximum curvature.

[0096] The boundary constraints are as follows:

[0097] ; ,

[0098] in: The starting coordinates of the optimized trajectory; This is the starting point of the original trajectory; The coordinates of the endpoint of the optimized trajectory; This is the endpoint of the original trajectory.

[0099] Trajectory optimization, while satisfying curvature constraints, achieves a balance between flight feasibility and smoothness by optimizing the changes in adjacent points of the smooth trajectory and the differences between the trajectory and the original design trajectory. The optimized smooth trajectory γ(s) is obtained by minimizing the maximum deviation between the smooth trajectory and the original trajectory.

[0100] ,

[0101] in, The objective function value for trajectory smoothing optimization; Summing all adjacent pairs of points in the trajectory; Optimized smooth trajectory The coordinates of a discrete point; Trajectory No. From point 1 to point 2 +1 point displacement vector; It is the square of the Euclidean norm.

[0102] The trajectory optimization adopts a multi-objective weighted optimization approach, and its comprehensive objective function is:

[0103] ,

[0104] Where α is the path length smoothness weight; β is the curvature smoothness weight; and γ is the trajectory fidelity weight. Let i be the i-th discrete point in the original design trajectory; Let be the trajectory curvature at the corresponding discrete point.

[0105] Step S3, Time-parameterized pre-dynamic feasibility verification:

[0106] The smooth flight trajectory is parameterized over time and its dynamic feasibility is verified to generate corresponding velocity and acceleration planning information, ensuring that the flight platform can execute smoothly according to the trajectory in actual operation.

[0107] Specifically, the acceleration 'a' and jerk 'j' of the flight platform are limited to ensure that the flight platform can execute smoothly according to the trajectory.

[0108] ,

[0109] The extrusion flow rate Q(s) and the trajectory velocity v(s) are synchronously controlled, satisfying the following relationship:

[0110] ,

[0111] in, Where is the nozzle cross-sectional area, and k is the material flow coefficient.

[0112] Step S4, End-of-line compensation error allocation:

[0113] The residual geometric error after trajectory optimization is calculated and used to measure the spatial deviation between the optimized smooth trajectory and the original design trajectory.

[0114] ,

[0115] in, For the first The residual geometric error vector of each trajectory point; For the original design trajectory, the first The coordinates of the points; To optimize the smooth trajectory The coordinates of the points; This represents the total number of discrete points on the trajectory.

[0116] This error is then assigned to the end compensation mechanism. The error allocation strategy ensures that the compensation mechanism can correct the remaining error within its maximum effective travel range.

[0117] Furthermore, in this embodiment, the end-effector compensation mechanism can fine-tune the position and attitude of the flight platform at the millimeter level to compensate for residual errors generated in the smooth trajectory.

[0118] The flight platform uses a multi-rotor drone, which has the ability to hover stably and follow a trajectory.

[0119] Step S5: Based on the optimized trajectory from Step S2 to Step S4, control the flight platform to execute the flight trajectory, and at the same time adjust the error through real-time closed-loop control feedback.

[0120] Furthermore, in this embodiment, trajectory optimization is solved using the Sequential Quadratic Programming (SQP) algorithm, reconstructing the original nonlinear constraint optimization problem into the following quadratic programming subproblem:

[0121] ,

[0122] st ,

[0123] in, For the search direction, An approximation of the Hessian matrix. These are the trajectory curvature constraints and dynamic constraints.

[0124] The sequential quadratic programming algorithm includes the following steps:

[0125] Using the discrete points of the original trajectory as the initial solution ;

[0126] Construct the Lagrange function:

[0127] ,

[0128] At the current iteration point Calculate the approximation of the Hessian matrix at this point. And linearize the constraints;

[0129] Solve the quadratic programming subproblem to obtain the search direction. ;

[0130] The step size is determined by a line search method. And update the trajectory solution:

[0131] ,

[0132] When the convergence condition is met When the iteration ends, the iteration is terminated.

[0133] The following is a detailed description based on specific embodiments:

[0134] In this embodiment, an L-shaped path containing right-angle turns is used as the design trajectory experiment for the quadcopter UAV 1 for UAV 3D printing, and the implementation process of the trajectory optimization method is explained.

[0135] First, the original design trajectory is discretized to obtain a sequence of original trajectory points, and these discrete points are used as the initial solution for the sequence quadratic programming algorithm. The original design trajectory corresponds to the expected path 5 of the UAV.

[0136] Since the turning radius of the original design trajectory at the right-angle turn is 0, the instantaneous curvature at the corresponding position tends to be infinite. When the printing speed is 0.1 m / s, the actual flight path 6 of the quadcopter drone 1 in this area results in a trajectory deviation of about 100 mm relative to the expected path 5 of the drone. Furthermore, the end compensation mechanism 2 installed under the drone is insufficient to eliminate this deviation when trajectory optimization is not performed.

[0137] This embodiment uses the Sequential Quadratic Programming (SQP) algorithm to solve the trajectory optimization problem, transforming the original nonlinear constraint optimization problem, which includes curvature constraints and dynamic constraints, into a solution at the current iteration point. The problem can be restructured into the following quadratic programming subproblem:

[0138] ,

[0139] st ,

[0140] in, This represents the search direction for the current iteration step. This is an approximation of the Hessian matrix of the objective function. These are the trajectory curvature constraints and flight platform dynamics constraints.

[0141] The sequential quadratic programming algorithm includes the following steps:

[0142] Using the discrete points of the original trajectory as the initial solution ;

[0143] Construct the Lagrange function:

[0144] ,

[0145] The flight platform at the current iteration point Calculate the approximation of the Hessian matrix at this point. The constraints are linearized; based on this, a quadratic programming subproblem is solved to obtain the search direction. ;

[0146] Furthermore, the step size is determined using a line search method. And update the trajectory solution:

[0147] ,

[0148] The above iterative process is repeated continuously until the convergence condition is met. When the iteration ends, a smooth printing trajectory that satisfies both curvature and dynamic constraints is obtained.

[0149] Through the above trajectory optimization process, the instantaneous curvature at the right-angle turn in the original design trajectory is effectively reduced, and the actual flight trajectory deviation of the quadcopter UAV 1 is significantly reduced. At this time, driven by the end compensation mechanism 2, the 3D printing extruder 3 connected to its end and its print head move along the desired print head path 7, and form the corresponding actual print head path 8 under the compensation effect. Thus, with the cooperation of the continuous feeding of the 3D printing feed tube 4, the residual geometric error is finely corrected.

[0150] like Figures 1 to 5 The diagram shown illustrates the curvature comparison, curvature distribution, trajectory comparison, and deviation under right-angled paths, obtuse-angled paths, acute-angled paths, zigzag paths, and undulating paths provided in this embodiment.

[0151] Table 1 shows the trajectory optimization data simulated by the computer (comparison between the original trajectory and the optimized trajectory), in which material accumulation is basically eliminated and the printed edges are smooth and continuous.

[0152] Table 1

[0153]

[0154] In the description of this invention, it should be understood that the terms "center," "longitudinal," "lateral," "length," "width," "thickness," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," "outer," "clockwise," and "counterclockwise," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limiting this invention.

[0155] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of this invention, "a plurality of" means two or more, unless otherwise explicitly specified.

[0156] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any equivalent substitutions or modifications made by those skilled in the art within the scope of the technology disclosed in the present invention, based on the technical solution and inventive concept of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. A method for a UAV 3D printing system combining trajectory curvature optimization and end-effector compensation, characterized in that, Includes the following steps: Step S1: Obtain the original trajectory: Obtain the original design printing path of the flight platform, including sharp geometric features such as right angles, acute angles, and folds; Step S2, Trajectory Pre-optimization: The original design printing path is optimized by using an algorithm to transform paths containing sharp features into smooth trajectories, eliminating instantaneous turning maneuvers that the flight platform cannot perform, and improving the executability of the trajectory. The trajectory optimization adopts a multi-objective weighted optimization form, and its comprehensive objective function is: ； Where α is the path length smoothness weight; β is the curvature smoothness weight; and γ is the trajectory fidelity weight. Let i be the i-th discrete point in the original design trajectory; The curve represents the trajectory curvature at the corresponding discrete point. The trajectory optimization is solved using a sequential quadratic programming algorithm, which reconstructs the original nonlinear constraint optimization problem into the following quadratic programming subproblem: ； s.t. ; in, For the search direction, An approximation of the Hessian matrix. These are the trajectory curvature constraints and dynamic constraints. The sequential quadratic programming algorithm includes the following steps: Using the discrete points of the original trajectory as the initial solution ; Construct the Lagrangian function: ； At the current iteration point Calculate the approximation of the Hessian matrix at this point. And linearize the constraints; Solve the quadratic programming subproblem to obtain the search direction. ; The step size is determined by a line search method. And update the trajectory solution: ； When the convergence condition is met When the iteration ends, proceed. Step S3, Time-parameterized pre-dynamic feasibility verification: The smooth flight trajectory is parameterized in time and its dynamic feasibility is verified, and corresponding velocity and acceleration planning information is generated to ensure that the flight platform can execute smoothly according to the trajectory in actual operation. Step S4, End-of-line compensation error allocation: The remaining geometric error after trajectory optimization is calculated and allocated to the end-effector compensation mechanism; the error allocation strategy ensures that the compensation mechanism can correct the remaining error within its maximum effective stroke range. Step S5: Based on the optimized trajectory from Steps S2 to S4, control the flight platform to execute the flight trajectory, and simultaneously adjust the error through real-time closed-loop control feedback.

2. The method for a UAV 3D printing system combining trajectory curvature optimization and end-effector compensation according to claim 1, characterized in that, In step S2, the trajectory optimization includes deviation constraints, curvature constraints, and boundary constraints; The deviation constraint is used to ensure that the maximum deviation between the optimized trajectory and the original trajectory does not exceed a predetermined value, thereby ensuring the fidelity of the trajectory. The curvature constraint ensures that the curvature of the trajectory does not exceed the preset maximum curvature value, in order to avoid excessively sharp turns during flight. The boundary constraints ensure that the starting and ending positions of the trajectory are fixed to maintain the global consistency of the flight path.

3. The method for a UAV 3D printing system combining trajectory curvature optimization and end-effector compensation according to claim 2, characterized in that, The deviation constraints are as follows: ， in, The spatial coordinates of the position corresponding to the original design printing trajectory; These are the spatial coordinates of the discrete points corresponding to the optimized trajectory. This is the preset maximum allowable trajectory deviation; The curvature constraint involves transforming the original trajectory γ0(s) of the original design printing path into a smooth trajectory γ(s) that satisfies dynamic constraints, wherein the curvature κ(s) satisfies: ， in, alat,max The maximum lateral acceleration is determined by the thrust-to-weight ratio and attitude margin of the flight platform. Sure; v(s) Let be the velocity along the trajectory of arc length s. For maximum curvature; The boundary constraints are as follows: ； ， in: The starting coordinates of the optimized trajectory; This is the starting point of the original trajectory; The coordinates of the endpoint of the optimized trajectory; This is the endpoint of the original trajectory.

4. The method for a UAV 3D printing system combining trajectory curvature optimization and end-effector compensation according to claim 3, characterized in that, The trajectory optimization, while satisfying curvature constraints, achieves a balance between flight feasibility and smoothness by optimizing the changes in adjacent points of the smooth trajectory and the differences between the trajectory and the original design trajectory.

5. The method for a UAV 3D printing system combining trajectory curvature optimization and end-effector compensation according to claim 4, characterized in that, By minimizing the maximum deviation between the smoothed trajectory and the original trajectory, the optimized smoothed trajectory γ(s) is obtained: ； in, The objective function value for trajectory smoothing optimization; Summing all adjacent pairs of points in the trajectory; Optimized smooth trajectory The coordinates of a discrete point; Trajectory No. From point 1 to point 2 +1 point displacement vector; It is the square of the Euclidean norm.

6. The method for a UAV 3D printing system combining trajectory curvature optimization and end-effector compensation according to claim 1, characterized in that, In step S3, the smooth flight trajectory is parameterized in time and its dynamic feasibility is checked to generate corresponding velocity and acceleration planning information. Limiting the acceleration of the flight platform a and accelerometer j (jerk) To ensure the flight platform can execute smoothly according to the trajectory: ， Extrusion flow Q(s) Synchronous control with the trajectory velocity v(s) satisfies the following relationship: ， in, The nozzle cross-sectional area is... k This represents the material flow coefficient.

7. The method for a UAV 3D printing system combining trajectory curvature optimization and end-effector compensation according to claim 1, characterized in that, In step S4, the remaining geometric error after trajectory optimization is calculated, which is used to measure the spatial deviation between the optimized smooth trajectory and the original design trajectory. ， in, For the first The remaining geometric error vector of each trajectory point; For the original design trajectory, the first The coordinates of the points; To optimize the smooth trajectory The coordinates of the points; This represents the total number of discrete points on the trajectory.

8. A system based on the method of a UAV 3D printing system combining trajectory curvature optimization and end-effector compensation as described in any one of claims 1-7, characterized in that, It includes a trajectory optimization module, a dynamics feasibility verification module, an end-point compensation allocation module, an execution and closed-loop control module, and a sensing system; The trajectory optimization module smooths the original trajectory to generate a smooth trajectory that meets dynamic constraints. The dynamic feasibility verification module parameterizes the smoothed trajectory over time and limits the acceleration and jerk of the flight platform. The end-effector compensation allocation module allocates the remaining geometric error after smoothing the trajectory to the end-effector compensation mechanism, ensuring that the error is corrected within the maximum travel range of the end-effector compensation mechanism. The execution and closed-loop control module controls the flight platform and the end-effector compensation mechanism to execute the optimized trajectory and perform real-time closed-loop feedback adjustments. The sensing system, including a positioning module, attitude sensor, mechanical state sensor, and displacement sensor, monitors the position, attitude, and mechanical state of the flight platform and provides feedback for closed-loop control.

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