An unmanned aerial vehicle end-to-end trajectory planning method combining optimal control and deep learning

Abstract

The application discloses a kind of unmanned aerial vehicle end-to-end trajectory planning methods combining optimal control and deep learning, including S1, the polynomial representation of unmanned aerial vehicle trajectory is constructed, and several initial trajectories are formed by sampling to different directions, current state and network predicted end state are mapped into polynomial coefficient;S2, the multiple steps of motion planning are unified into a neural network, with depth map, current unmanned aerial vehicle state and target direction as input, with the offset of each initial trajectory end point and the like steps.The application parameterizes the representation of unmanned aerial vehicle trajectory by constructing three independent one-piece polynomials, and combines the strategy of uniformly sampling to different directions to form multiple initial trajectories, converts the trajectory generation problem into end state prediction problem, which not only ensures that the trajectory representation has sufficient flexibility to adapt to complex environment, but also significantly reduces the dimension of network prediction space, effectively improves the efficiency and feasibility of trajectory generation.

Description

Technical Field

[0001] This invention relates to the field of unmanned aerial vehicle (UAV) technology, specifically to an end-to-end trajectory planning method for UAVs that combines optimal control and deep learning. Background Technology

[0002] Autonomous navigation and trajectory planning for unmanned aerial vehicles (UAVs) is an important research direction in the field of robotics. Traditional methods typically employ a modular architecture, sequentially executing steps such as mapping, localization, path planning, and trajectory generation. However, these methods have significant shortcomings in terms of real-time performance, robustness, and high dependence on high-precision mapping and manually labeled data.

[0003] To overcome the limitations of explicit mapping and manually labeled data, researchers have recently explored an end-to-end learning paradigm that backpropagates trajectory cost gradients to neural network parameters using a chain rule. Optimal control combined with deep learning methods constructs a cost function that includes collision penalties, trajectory smoothness, and dynamic feasibility. It calculates the numerical gradient of the trajectory cost with respect to the trajectory parameters and further backpropagates this gradient to the network weights, directly guiding network parameter updates. During training, this method utilizes an environment representation containing privileged information to generate high-quality cost gradients, while during inference, it relies solely on depth sensor observations. This achieves real-time trajectory generation without explicit mapping, significantly improving planning efficiency and system real-time performance.

[0004] However, the existing methods described above still have the following shortcomings: First, existing research largely focuses on local planning or relies on idealized physical models, and research on the robustness of systems under complex dynamic environments, uncertainty perception, and real sensor noise conditions remains limited. In actual flight, UAVs face a variety of uncertainties such as wind disturbance, sensor noise, and dynamic obstacles, which existing methods struggle to address effectively.

[0005] Second, a complete framework combining high-order dynamic constraints of UAVs, environmental uncertainty modeling, and safety assurance mechanisms under real flight conditions has not yet been established. UAVs possess high-order dynamic characteristics such as differential flatness, and existing methods do not adequately model these constraints, potentially rendering the generated trajectories unenforceable in actual flight.

[0006] Third, mathematical modeling methods for collision costs, smoothness costs, and dynamic constraint costs, as well as the differentiability design of cost functions and gradient stability issues, still require in-depth research. Existing methods struggle to directly embed physical and safety constraints into the network optimization process, and lack a comprehensive loss function that can be used for neural network training and takes into account multiple constraints.

[0007] In summary, existing methods still have technical shortcomings, such as difficulty in dealing with uncertain disturbances such as wind disturbances, sensor noise and dynamic obstacles in actual flight, imperfect flight safety assurance mechanisms, and incomplete construction of loss functions in trajectory planning, which urgently need to be improved. Summary of the Invention

[0008] The purpose of this invention is to overcome the technical shortcomings of current UAVs in autonomous navigation and trajectory planning, such as difficulty in coping with uncertain disturbances in actual flight, such as wind disturbances, sensor noise and dynamic obstacles, imperfect flight safety assurance mechanisms, and incomplete construction of loss functions in trajectory planning. This invention provides an end-to-end trajectory planning method for UAVs that combines optimal control and deep learning.

[0009] To achieve the above objectives, the present invention employs the following technical solution: an end-to-end trajectory planning method for unmanned aerial vehicles (UAVs) combining optimal control and deep learning, comprising the following steps: S1. Construct a polynomial representation of the UAV trajectory, sample in different directions to form several initial trajectories, and map the current state and the network-predicted terminal state to polynomial coefficients. S2. Unify multiple steps of motion planning into a neural network, taking the depth map, current UAV status and target direction as input, and the offset of the end point of each initial trajectory, the terminal derivative and the corresponding score as output; S3. Construct a trajectory cost function that includes smoothing cost, safety cost, and target cost, and use real environment information to calculate the numerical gradient of the trajectory cost with respect to the network output. Then, backpropagate this numerical gradient to the network parameters to guide network training.

[0010] Furthermore, the "construction of a polynomial representation of the UAV trajectory" mentioned in step S1 specifically refers to representing the UAV trajectory with three independent one-part polynomials, corresponding to the x, y, and z directions in the body coordinate system, respectively. The trajectory in each direction is a time-parameterized polynomial, and all the coefficients of the trajectory form a polynomial coefficient vector A.

[0011] The expression for the "time-parameterized polynomial" is as follows: ,in, fm ( t ) is the first m Position functions in each direction t Let a0, a1, a2, ... a be time variables. n For polynomial coefficients, n Let be the order of the polynomial.

[0012] The expression for "all coefficients of the trajectory form a polynomial coefficient vector A" is as follows: .

[0013] Furthermore, the "sampling in different directions to form several initial trajectories" mentioned in step S1 specifically refers to: uniformly sampling the vertical and horizontal directions from the location of the UAV, determining a set of spatial points as the trajectory end point p, and forming a set of initial trajectory directions.

[0014] The specific method for "mapping the current state to the network-predicted terminal state as polynomial coefficients" in step S1 is as follows: first, the radius and angle of the initial trajectory terminal point are corrected by adjusting the offset predicted by the network to obtain the final terminal position. p Network synchronous prediction of terminal speed and terminal acceleration Then, the current state and the final state are used as the boundary conditions for the starting and ending points of the trajectory, respectively, and arranged into a boundary condition vector. d Use a predefined constant matrix M The boundary condition vector d The mapping is to a polynomial coefficient vector A.

[0015] The “neural network” mentioned in step S2 uses ResNet-18 as the backbone network to extract features from the depth map and employs 1×1 convolutional layers to independently predict trajectories at each location in the depth map.

[0016] The “real environment information” mentioned in step S3 includes at least the Euclidean symbolic distance field, complete point cloud data, and accurate UAV status information.

[0017] Compared with the prior art, the beneficial effects of the present invention are: (1) This invention constructs three independent single-segment polynomials to parameterize the UAV trajectory and combines them with a strategy of uniformly sampling in different directions to form multiple initial trajectories, transforming the trajectory generation problem into an end-state prediction problem. This ensures that the trajectory representation has sufficient flexibility to adapt to complex environments and significantly reduces the dimensionality of the network prediction space, effectively improving the efficiency and feasibility of trajectory generation.

[0018] (2) This invention unifies multiple steps of motion planning into a single neural network. With depth map, current UAV status and target direction as input, it directly outputs the end state and corresponding score of multiple candidate trajectories, realizing end-to-end mapping from sensor observation to trajectory generation. It eliminates the need for explicit mapping and modular cascading, significantly improving the real-time performance and computational efficiency of the planning system.

[0019] (3) This invention constructs a differentiable trajectory cost function that integrates smoothing cost, safety cost and target cost. It uses real environment information to calculate the numerical gradient of the cost relative to the network output and directly updates the network parameters through backpropagation. This enables the network to explicitly learn physical constraints and environmental safety constraints during training, and solves the technical problem of incomplete loss function construction in existing methods.

[0020] (4) In the training phase, the present invention uses privileged information such as Euclidean symbolic distance field, complete point cloud and accurate state of UAV to generate high-quality numerical gradients, while in the inference phase, trajectory generation can be completed by relying only on noise information such as depth map observation and inertial measurement unit. The privileged learning mechanism enhances the robustness of the network to sensor noise and observation uncertainty, making the method engineering deployable. Attached Figure Description

[0021] Figure 1 This is a schematic diagram of the overall process of the present invention. Detailed Implementation

[0022] 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. Example

[0023] like Figure 1 As shown in this embodiment, an end-to-end trajectory planning method for unmanned aerial vehicles (UAVs) combining optimal control and deep learning includes the following steps: S1. Construct a polynomial representation of the UAV trajectory, sample in different directions to form several initial trajectories, and map the current state and the network-predicted terminal state to polynomial coefficients.

[0024] This step transforms the complex problem of generating continuous trajectories into a "state prediction" problem that neural networks can easily learn, thereby reducing the learning difficulty and ensuring the feasibility of the trajectory. The construction of the polynomial representation of the UAV trajectory refers to representing the UAV trajectory using three independent one-part polynomials, corresponding to the x, y, and z directions in the body coordinate system, respectively. The trajectory in each direction is a time-parameterized polynomial, expressed as: The coefficients of the trajectory form a polynomial coefficient vector A, whose expression is: .in, f μ ( t ) is the first m Position functions in each direction t Let a0, a1, a2…a be time variables. n For polynomial coefficients, n Let be the order of the polynomial.

[0025] The aforementioned sampling in different directions to form several initial trajectories refers to: uniformly sampling the vertical and horizontal directions from the location of the UAV, determining a set of spatial points as trajectory endpoints p, and forming a set of initial trajectory directions. The formula for the trajectory endpoint p is: .

[0026] The method for mapping the current state to the network-predicted terminal state as polynomial coefficients is as follows: first, the radius and angle of the initial trajectory terminal point are corrected by adjusting the offset predicted by the network to obtain the final terminal position. p Network synchronous prediction of terminal speed and terminal acceleration Then, the current state and the final state are used as the boundary conditions for the starting and ending points of the trajectory, respectively, and arranged into a boundary condition vector. d Use a predefined constant matrix M The boundary condition vector d This is mapped to a polynomial coefficient vector A. The expression for the polynomial coefficients A is: .

[0027] The constant matrix M It is a 6×6 matrix, and the total time of the trajectory is given. T and polynomial order n Predetermined, specifically M = B -1 ,in B This is the transformation matrix from boundary conditions to polynomial coefficients.

[0028] The above p ij For the ( i , j The position vector of the sampling endpoint represents the distance from the current position of the UAV along the path of the sampling endpoint. i The horizontal direction and the first j The three-dimensional coordinates of the end point obtained by sampling in each vertical direction; r The sampling radius is the straight-line distance from the current position of the drone to the endpoint, which is the length of the initial trajectory. yaw angle is the horizontal direction angle, corresponding to the horizontal rotation direction of the UAV, and i represents different horizontal sampling directions; i is the vertical angle (pitch angle), which is the angle in the vertical direction and corresponds to the pitch direction of the UAV. j represents different vertical sampling directions. x, y, and z are three coordinate components, representing the spatial position of the endpoint in the three directions of the body coordinate system.

[0029] The expressions for the boundary condition vector d in the x, y, and z directions are as follows: , , .

[0030] in, p x (0) represents the initial position coordinates of the UAV in the x-direction. x (0) represents the initial velocity of the UAV in the x direction (the first derivative of its position). x (0) represents the initial acceleration of the UAV in the x direction (the second derivative of its position). p x (T) represents the position coordinates of the endpoint in the x-direction after network prediction and correction. x (T) represents the velocity of the endpoint predicted by the network in the x-direction. x (T) represents the acceleration of the network-predicted endpoint in the x-direction; correspondingly, p y (0) and p z (0) represents the starting position coordinates of the UAV in the y and z directions, respectively, and so on, without further explanation.

[0031] S2. Unify multiple steps of motion planning into a neural network, taking the depth map, current UAV status and target direction as input, and the offset of the end point of each initial trajectory, the terminal derivative and the corresponding score as output.

[0032] The purpose of this step is to compress the traditional serial process of "mapping, planning, and control" into a neural network, enabling end-to-end real-time mapping from the depth map directly to the feasible trajectory. This solves the shortcomings of traditional modular methods, such as high latency, reliance on the global map, and inability to cope with dynamic and unknown environments.

[0033] The neural network in this embodiment uses ResNet-18 as the backbone to extract features from the depth map and employs 1×1 convolutional layers to independently predict the trajectory at each location in the depth map. The depth map is a distance image captured in real-time by an onboard camera of the UAV; it is a two-dimensional image where the value of each pixel represents the distance from the sensor to the corresponding spatial object.

[0034] The output of this step consists of three items. The first is the offset of the end point of each initial trajectory, i.e., the offset for each pre-sampled end point p of the initial trajectory. ij The network predicts its corrections in radius and angle. , , ), its corrected end position =Sampling(r+ , + θ j + ).

[0035] The second is the terminal derivative, which is the velocity and acceleration at the terminal point (i.e., the terminal velocity). and terminal acceleration The purpose is to form a complete end state together with the end position p, so that the trajectory satisfies the continuity of velocity / acceleration at the end point, ensuring that the UAV can stop smoothly at the end point.

[0036] Thirdly, there is the corresponding score, which is the network's evaluation score (scalar value) of the quality of the trajectory. In this embodiment, among multiple candidate trajectories, this score is used for comparison and filtering, and the trajectory with the highest score is usually selected as the final execution plan.

[0037] S3. Construct a trajectory cost function that includes smoothing cost, safety cost, and target cost, and use real environment information to calculate the numerical gradient of the trajectory cost with respect to the network output. Then, backpropagate this numerical gradient to the network parameters to guide network training.

[0038] The purpose of this step is to enable the network to learn how to generate safe, smooth, and flyable trajectories through the "physical cost" of environmental feedback, without "human-labeled data".

[0039] The smoothing cost penalizes sharp turns and abrupt acceleration changes, forcing the network-generated trajectory to be smooth and continuous, ensuring the drone's motors and flight control can physically execute commands and avoiding severe attitude jitter. Its mathematical definition is: acceleration on the trajectory. (t) (corresponding to UAV thrust) and jerk The square of (t) (corresponding to the rate of change of thrust, which is related to the motor response) in time T The integral over is expressed as: .

[0040] The security cost mentioned above is calculated based on the Euclidean Symbolic Distance Field (ESDF). This ESDF can give the distance from any point in space to the nearest obstacle. d ( p (Negative values ​​are found inside obstacles). When the trajectory point is too close to an obstacle (distance less than the safety threshold)... d th When this condition is met, a high penalty is imposed. Its purpose is to push the trajectory away from obstacles such as walls and trees, ensuring physical safety during flight. If the safety constraints are not met, the cost increases dramatically, causing the trajectory to be abandoned. The expression for this safety cost is: .

[0041] The target cost is the penalty trajectory endpoint. p ( T The deviation from the target direction or position serves to guide the drone towards the predetermined target direction, preventing it from spinning in place or flying into irrelevant areas. The expression for this target cost is: ,in, p target The target location coordinates specified by the user.

[0042] Therefore, the trajectory cost function is derived from the smoothing cost. C s Security costs C safe and target cost C goal The weighted summation yields the expression: .in, , and These are the weighting coefficients for each cost, used to balance the relative importance of trajectory smoothness, safety, and goal orientation in the total cost. Their specific values ​​are preset according to task requirements.

[0043] The real environmental information mentioned includes at least the Euclidean symbolic distance field, complete point cloud data, and accurate UAV status information.

[0044] As described above, the present invention can be well implemented.

Claims

1. An end-to-end trajectory planning method for unmanned aerial vehicles (UAVs) combining optimal control and deep learning, characterized in that, Includes the following steps: S1. Construct a polynomial representation of the UAV trajectory, sample in different directions to form several initial trajectories, and map the current state and the network-predicted terminal state to polynomial coefficients. S2. Unify multiple steps of motion planning into a neural network, taking the depth map, current UAV status and target direction as input, and the offset of the end point of each initial trajectory, the terminal derivative and the corresponding score as output; S3. Construct a trajectory cost function that includes smoothing cost, safety cost, and target cost, and use real environment information to calculate the numerical gradient of the trajectory cost with respect to the network output. Then, backpropagate this numerical gradient to the network parameters to guide network training.

2. The end-to-end trajectory planning method for unmanned aerial vehicles (UAVs) combining optimal control and deep learning according to claim 1, characterized in that, The "construction of polynomial representation of UAV trajectory" mentioned in step S1 specifically refers to representing the UAV trajectory with three independent one-part polynomials, corresponding to the x, y, and z directions in the body coordinate system, respectively. The trajectory in each direction is a time-parameterized polynomial, and all the coefficients of the trajectory form a polynomial coefficient vector A.

3. The end-to-end trajectory planning method for unmanned aerial vehicles (UAVs) combining optimal control and deep learning according to claim 2, characterized in that, The phrase "sampling in different directions to form several initial trajectories" in step S1 specifically refers to: uniformly sampling the vertical and horizontal directions from the location of the UAV, determining a set of spatial points as the trajectory end point p, and forming a set of initial trajectory directions.

4. The end-to-end trajectory planning method for unmanned aerial vehicles (UAVs) combining optimal control and deep learning according to claim 3, characterized in that, The specific method for "mapping the current state to the network-predicted terminal state as polynomial coefficients" in step S1 is as follows: first, the radius and angle of the initial trajectory terminal point are corrected by adjusting the offset predicted by the network to obtain the final terminal position. p Network synchronous prediction of terminal speed and terminal acceleration Then, the current state and the final state are used as the boundary conditions for the starting and ending points of the trajectory, respectively, and arranged into a boundary condition vector. d Use a predefined constant matrix M The boundary condition vector d The mapping is to a polynomial coefficient vector A.

5. The end-to-end trajectory planning method for unmanned aerial vehicles (UAVs) combining optimal control and deep learning according to claim 1, characterized in that, The "neural network" mentioned in step S2 uses ResNet-18 as the backbone network to extract features from the depth map and employs 1×1 convolutional layers to independently predict trajectories at each location in the depth map.

6. The end-to-end trajectory planning method for unmanned aerial vehicles (UAVs) combining optimal control and deep learning according to claim 5, characterized in that, The "real environment information" mentioned in step S3 includes at least the Euclidean symbolic distance field, complete point cloud data, and accurate UAV status information.

7. The end-to-end trajectory planning method for unmanned aerial vehicles (UAVs) combining optimal control and deep learning according to claim 2, characterized in that, The expression for the "time-parameterized polynomial" is: ,in, fμ ( t ) is the first μ Position functions in each direction t Let a0, a1, a2, ... a be time variables. n For polynomial coefficients, n Let be the order of the polynomial.

8. The end-to-end trajectory planning method for unmanned aerial vehicles (UAVs) combining optimal control and deep learning according to claim 7, characterized in that, The expression for "all coefficients of the trajectory form a polynomial coefficient vector A" is: .

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