Any three-dimensional terrain vision coverage unmanned aerial vehicle energy optimization trajectory generation method

Abstract

The invention discloses an arbitrary three-dimensional terrain visual coverage unmanned aerial vehicle energy optimization trajectory generation method, which comprises the following steps of: generating visual coverage air route points: selecting a mountain region, acquiring a rough digital elevation model by utilizing a geographic information system or level flight shooting, calculating the air route points based on photogrammetry constraints, and calculating the visual coverage air route points; traversing the waypoints according to a predetermined sequence to complete a coverage task; modeling the energy consumption of the motor of the unmanned aerial vehicle: taking the brushless direct current motor as an object, carrying out mathematical modeling in combination with torque dynamics and electromagnetic equations of the motor, constructing a physical information neural network model, and training and optimizing flight data; and track optimal prediction control input mapping: designing an optimal prediction control method based on unmanned aerial vehicle dynamics, and calculating a mapping relation between the track and control input. According to the invention, the coverage efficiency can be obviously improved, so that the single flight coverage range of the unmanned aerial vehicle is expanded.

Description

Technical Field

[0001] The present invention relates to the technical field of visual coverage trajectory planning for unmanned aerial vehicles, and particularly to a method for generating an energy-optimized trajectory of an unmanned aerial vehicle for visual coverage of arbitrary three-dimensional terrains. Background Art

[0002] The execution of regional visual coverage by autonomous unmanned systems is an effective means for dynamic monitoring of the wild environment. Multi-rotor unmanned aerial vehicles have advantages such as autonomous takeoff and landing, mobility, and flexibility, and have great advantages when used to perform tasks such as ecological monitoring and disaster relief.

[0003] The battery energy density, weight, and load of unmanned aerial vehicles limit the limit of endurance ability and restrict the efficiency of completing tasks. Current research on improving the endurance and efficiency of unmanned aerial vehicles based on energy optimization mostly focuses on structural optimization or simple linear simplified modeling of energy consumption, and it is difficult to correspond theoretical modeling and simulation with real situations.

[0004] Most current research focuses on modeling unmanned aerial vehicles using kinematic equations, while often ignoring the importance of dynamic equations. Since kinematic equations do not consider the forces driving motion, the designed trajectories obtained through them are difficult to directly implement in practical applications. In addition, some existing work assumes that unmanned aerial vehicles fly in a two-dimensional horizontal plane, and it is difficult to guarantee the effectiveness of the energy consumption model due to different application scenarios.

[0005] Under the condition that the battery energy of a quadrotor unmanned aerial vehicle is limited, we construct the regional visual coverage problem as a joint optimization problem of coverage trajectory generation and non-linear trajectory energy consumption prediction under multiple constraints. This method takes the geographical information model of the area of interest as input, calculates the aerial waypoints based on photogrammetry constraints, and then uses a trajectory optimization algorithm to solve the optimal coverage traversal order and parameterized spatio-temporal trajectory, so that the unmanned aerial vehicle visits all waypoints according to this trajectory to complete the coverage task.

[0006] Therefore, in view of the above problems, a method for generating an energy-optimized trajectory of an unmanned aerial vehicle for visual coverage of arbitrary three-dimensional terrains is proposed. Summary of the Invention

[0007] The purpose of the present invention is to provide a method for generating an energy-optimized trajectory of an unmanned aerial vehicle for visual coverage of arbitrary three-dimensional terrains, including the following steps:

[0008] Step 1: Generate visual coverage aerial waypoints: Select a mountainous area, use a geographic information system or level flight shooting to obtain a rough digital elevation model, calculate aerial waypoints based on photogrammetry constraints, and traverse these waypoints in a predetermined order to complete the coverage task;

[0009] Step 2: UAV motor energy consumption modeling: Taking the brushless DC motor as the object, combining the torque dynamics and electromagnetic equations of the motor for mathematical modeling, constructing a physics-informed neural network model, and training and optimizing the flight data.

[0010] Step 3: Trajectory optimal prediction control input mapping: Designing an optimal prediction control method based on the UAV dynamics and calculating the mapping relationship between the trajectory and the control input.

[0011] Step 4: Parameterized trajectory generation and energy consumption optimization: Using a fifth-order B-spline curve to parameterize the trajectory modeling, calculating the trajectory energy consumption as the optimization goal, and finally optimizing the trajectory parameters to obtain the flight trajectory parameters with the optimal energy consumption.

[0012] Preferably, in Step 1, the photogrammetry constraint method is as follows:

[0013] Based on the digital elevation model, a quasi-uniform B-spline surface is used for terrain surface fitting. The calculated geometric center point is used as the center of the gimbal camera's field of view, and it is extended a fixed distance d along the normal vector direction to obtain an aerial viewpoint. The B-spline basis function is derived through the Cox-de Boor regression formula:

[0014]

[0015] where B ij is the control point derived from the predetermined digital terrain elevation data, N i,p (u) and N j,p (v) are B-spline basis functions that can be derived through the Cox-deBoor regression formula. According to the horizontal and vertical overlap rates of the camera's field of view, the surface is divided into several image acquisition areas using a uniform grid. The aerial waypoint position can be expressed as:

[0016]

[0017] where d is the equidistant constraint, is the unit normal vector at the surface s ij . At each waypoint, the attitude angles of the gimbal camera can be expressed as:

[0018]

[0019] Specifically, in Step 2, the mathematical modeling of the energy consumption model is as follows:

[0020] Considering a quadrotor UAV powered by a lithium battery, the rotor power structure uses a brushless DC motor. Considering the energy consumption of the resistive winding and inductive winding in the motor and the energy loss of overcoming internal friction and load friction, the energy loss caused by the electronic speed controller effect and battery efficiency is ignored. Therefore, the voltage of a single rotor motor can be expressed as:

[0021]

[0022] Among them, R and L are the resistance and inductance of the motor winding respectively, represents the derivative of the current at time t with respect to t, that is, the rate of change of the current, ω(t) represents the angular velocity of the rotor motor at time t, k e is the motor voltage constant. The loss in the motor magnetic circuit is usually greater than the inductance loss, so the influence of inductance is often ignored;

[0023] The dynamic equation for the brushless DC motor is:

[0024] i(t) = (T F + T L (ω ∧ (t)) + B ∧ (ω ∧ (t)) + J ∧ (ω ∧ (t)) / k T );

[0025] Among them, i(t) is the motor current, T F is the torque generated by the propeller friction, ω ∧ is the rotor angular velocity, k T is the motor torque constant, B ∧ is the viscous damping coefficient, J ∧ is the moment of inertia of the motor and the rotor load, T L (ω ∧ ) is the load friction torque generated by the propeller resistance. Ignoring the torque generated by friction, a basic energy consumption model is constructed based on this.

[0026] Since the current is controlled by the electronic speed controller fast enough, it can be assumed to be in a steady-state condition, and the terms related to the derivative can be omitted. Then the energy consumption of the system during a trajectory time T n can be expressed in the following form:

[0027]

[0028] Specifically, in step 2, the physical information neural network model is as follows:

[0029] Collect data on standard flight states through flight experiments, including hovering, uniform horizontal, climbing, and variable-speed arc motions. Considering the noise caused by environmental uncertainty and high-speed motor motion, the moving average method is used to preprocess the data to improve the accuracy and reliability of the model.

[0030] The physical-information neural network is used for energy consumption modeling. The input is the rotor angular velocity, and the output is the motor power. A multi-layer perceptron with a hidden layer is used to train the model, and the loss function combines the data-driven loss and the physical equation loss.

[0031] Specifically, in step 3, the trajectory optimal prediction control input mapping algorithm is as follows:

[0032] For the generated trajectory, by differentiating the trajectory, the position, velocity, and acceleration are calculated, and then the mapping between the trajectory state space and the control input is obtained. The control input is adjusted to minimize the cost function J, and the optimal trajectory input is obtained through optimization to ensure the recursive feasibility of the controller and the system stability.

[0033] The optimization objective functional is expressed as:

[0034]

[0035] It includes the trajectory error term, the input error term, and the penalty term for control variation. W represents the weights of these terms to indicate different influence degrees. The entire calculation process can be expressed as the following equation;

[0036]

[0037] γ 0 =γ s ;

[0038]

[0039] Where, is the trajectory position predicted by the model predictive control at time t for k steps, β(Δu k|t ) represents the input change amount predicted k steps forward at time t, β is the weight coefficient, u k|t represents the control input predicted at the kth step at time t, represents the actual input required to reach the predicted state , γ 0 =γ s represents the starting point constraint of the trajectory, represents that the trajectory at time t is set as the predicted value of the trajectory at time t in the model predictive control, represents the state transition of the system, γ t ∈R d is the UAV state variable, u t ∈R m is the system input at time step t, G is the system dynamics matrix, represent the nominal state and the corresponding input respectively.

[0040] Specifically, in step 4, the trajectory parameterization modeling method is as follows:

[0041] To generate a smooth flight trajectory, the characteristics of Bezier curves are used for trajectory modeling. The trajectory γ can be divided into N - 1 segments by N air waypoints. The Bernstein polynomial is used for trajectory modeling, and its expression is as follows:

[0042]

[0043] where, represents the general equation of the segmented trajectory. For our task, there are N - 1 segments of trajectories, and each segment of trajectory P i (j) is represented by the superscript j, and the subscript i represents the i-th control point trajectory of the Bezier curve. The vector of all control points for j ∈ {1, 2, …, N - 1} is And B(ζ) is the basis function of the Bernstein polynomial, and this expression can be rewritten as:

[0044]

[0045] where, r is the order of the polynomial, is the binomial coefficient. Since the Bezier curve is defined on the fixed interval [0, 1], therefore, for each segment of the trajectory, we need a scale factor ζ to scale the parameter time t to the arbitrarily assigned time of that segment of the trajectory. We set a fifth-order polynomial curve as a monotonically increasing function of time t for the scale factor of the Bezier curve:

[0046] ζ(t) = s 0 + s 1 t + s 2 t 2 + s 3 t 3 + s 4 t 4 + s 5 t 5 ∈ [0, 1];

[0047] Specifically, in step 4, the trajectory kinematic constraint planning method is as follows:

[0048] The trajectory must pass through multiple predetermined waypoints, and the starting and target positions and their derivatives of each segment of the trajectory satisfy equality constraints. For the l th -th order derivative of the j th -th waypoint (l ≤ 2), the constraint conditions are as follows:

[0049]

[0050] where, i = 1 or n represents the control point The i-th control point, or 1 represents the boundary condition of the ζ(t) polynomial. At the intersection of two adjacent Bézier curves, we require the position, velocity, and acceleration to be continuous. Therefore, the continuity constraints should also be satisfied at the trajectory endpoints, specifically:

[0051]

[0052] where is the l th -th derivative of the j th -th segment of the trajectory (0 ≤ l ≤ 2). To consider dynamic feasibility, we impose hard constraints on the higher-order derivatives of the trajectory. The velocity vector and acceleration vector of the quadrotor are restricted within and to make the generated trajectory dynamically feasible. This constraint can be expressed as:

[0053]

[0054] Specifically, in step 4, the trajectory energy consumption optimization method is as follows:

[0055] After obtaining the parameterized trajectory, combined with the optimal predictive control input mapping and the motor energy consumption model, calculate the energy consumption of the current trajectory, transform the problem into an optimization problem, use the energy consumption as the objective function, and use the genetic algorithm to optimize the waypoint sequence and trajectory parameters to finally obtain a smooth trajectory with the optimal energy consumption;

[0056]

[0057] ξ ij ∈ {0, 1}, i, j ∈ {1, 2, …, N};

[0058]

[0059] γ k+1|t = G(γ k|t , u k|t ), k ∈ K, t ∈ T;

[0060] 0 ≤ ω Λ ≤ ω max , Λ ∈ 1, 2, 3, 4;

[0061] |θ(t)| ≤ θ max , t ∈ T;

[0062]

[0063] where represents the power at time k of the n-th segment of the trajectory, ξ ij represents 1 if flying from the i-th point to the j-th point and 0 otherwise, Represents the total trajectory length constraint, Represents the power constraint for all segments of the trajectory, γ k+1|t = G(γ k|t , u k|t ) indicates that the trajectory at the (k + 1)-th moment is calculated by the dynamic equation, 0 ≤ ω Λ ≤ ω max |θ(t)| ≤ θ max , t ∈ T represents the rotor angular velocity constraint, are the UAV attitude constraints, representing the pitch angle and roll angle respectively.

[0064] Compared with the prior art, the beneficial effects of the present invention are as follows: The present invention proposes a method for generating and optimizing a UAV coverage trajectory based on power consumption modeling, which can generate a trajectory with the optimal energy consumption for any three-dimensional target area, ensuring a certain image overlap rate, and taking into account the dynamic model of the UAV rotor motor and the actual flight state. Combining with the proposed method for real-time power loss modeling of a quadrotor UAV enabled by physical information, a cascaded optimization algorithm is introduced, which combines Bezier smooth trajectory generation and optimal trajectory energy consumption prediction, and can significantly improve the coverage efficiency, thereby expanding the single-flight coverage range of the UAV. Brief Description of the Drawings

[0065] Figure 1 is the overall flowchart of the present invention;

[0066] Figure 2 is the schematic diagram of the photogrammetry constraint of the present invention;

[0067] Figure 3 is the brushless DC motor system diagram of the present invention;

[0068] Figure 4 is the schematic diagram of the physical information neural network model of the motor model of the present invention;

[0069] Figure 5 is the schematic diagram of the visual comparison of the trajectories of the four methods of the present invention;

[0070] Figure 6 is the schematic diagram of the data comparison result of the present invention. Detailed Embodiment

[0071] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0072] Example 1:

[0073] As shown in the attached Figure 1 The present invention provides a method for generating an energy-optimized trajectory of an unmanned aerial vehicle for visual coverage of any three-dimensional terrain;

[0074] In this embodiment, simulation saddle-shaped mountain trajectory planning experimental data is used for verification and analysis. The computer CPU used in the experiment is an i9-12900@2.4GHz hexadec-core with a memory of 16GB.

[0075] The specific steps are as follows:

[0076] Step 1: Select a mountain-viewing area, use a geographic information system (GIS) or level flight shooting to obtain a rough digital elevation model, verify the experiment on the simulated mountain body, directly use a mathematical equation to generate the mountain surface model, calculate the aerial waypoints based on photogrammetry constraints and set an equidistant constraint, calculate the gimbal camera view angle according to the front-view constraint, and traverse these waypoints in the order obtained by solving with the genetic algorithm to complete the coverage task;

[0077] Step 2: Take a brushless DC motor as the object, combine the torque dynamics and electromagnetic equations of the motor for mathematical modeling, construct a physical information neural network model, and the loss function includes data-driven loss and physical loss that satisfies the electromagnetic equation and torque dynamics, and is trained and optimized through flight data;

[0078] Step 3: Design an optimal predictive control method based on the dynamics of the unmanned aerial vehicle, divide each smooth trajectory into 100 discrete trajectory points, and calculate the mapping relationship between the trajectory and the control input;

[0079] Step 4: Use a fifth-order B-spline curve to parameterize the trajectory modeling, calculate the trajectory energy consumption as the optimization goal, and finally optimize the trajectory parameters to obtain the flight trajectory with the optimal energy consumption;

[0080] In this embodiment, the photogrammetry constraint in the above step 1 is implemented by the following preferred scheme:

[0081] Based on the digital elevation model, a quasi-uniform B-spline surface is used for terrain surface fitting. For the simulated mountain body, the mountain surface model can be directly obtained. Set the horizontal overlap rate of the image to 0.3 and the vertical overlap rate to 0.2, use a uniform grid to divide to obtain multiple photogrammetry areas, calculate the geometric center point according to the equidistant and front-view constraints as the center of the gimbal camera field of view, and extend a fixed distance of 30m along the normal vector direction to obtain the aerial view point. As Figure 2 shown, the B-spline basis function is derived through the Cox-de Boor recurrence formula.

[0082]

[0083] where B ij is a control point derived from predetermined digital terrain elevation data, N i,p (u) and N j,p (v) are B-spline basis functions that can be derived through the Cox-deBoor recurrence formula. According to the horizontal and vertical overlap rates of the camera's field of view, the surface is divided into several image acquisition regions using a uniform grid. The position of the aerial waypoint can be expressed as:

[0084]

[0085] where d is the equidistant constraint, is the unit normal vector at the surface s ij . At each waypoint, the attitude angles of the pan-tilt camera can be expressed as:

[0086]

[0087] Specifically, in step 2, the mathematical modeling of the energy consumption model is as follows:

[0088] In this embodiment, the mathematical modeling of the energy consumption model in the above step 2 is implemented using the following preferred solution:

[0089] Considering a quadrotor UAV powered by a lithium battery, the rotor power structure uses a brushless DC motor. The energy consumption of the resistive winding and inductive winding in the motor, as well as the energy loss caused by overcoming internal friction and load friction, are considered, while the energy loss caused by the influence of the electronic speed controller and battery efficiency is ignored, as Figure 3 shown. Therefore, the voltage of a single rotor motor can be expressed as:

[0090]

[0091] where R and L are the resistance and inductance of the motor winding respectively, represents the derivative of the current at time t with respect to t, that is, the rate of change of the current, ω(t) represents the angular velocity of the rotor motor at time t, and k e is the motor voltage constant. The loss in the motor magnetic circuit is usually greater than the inductance loss, so the influence of the inductance is often ignored;

[0092] The dynamic equation of the brushless DC motor is:

[0093] i(t) = (T F + T L (ω ∧ (t)) + B ∧ (ω ∧ (t)) + J ∧ (ω ∧ (t)) / k T );

[0094] Among them, \(i(t)\) is the motor current, and \(T\) F is the torque generated by the propeller friction, and \(\omega\) ∧ is the angular velocity of the rotor, \(k\) T is the motor torque constant, \(B\) ∧ is the viscous damping coefficient, \(J\) ∧ is the moment of inertia of the motor and the rotor load, \(T\) L (\(\omega\) ∧ ) is the load friction torque generated by the propeller resistance. Ignoring the torque generated by friction, a basic energy consumption model is constructed based on this.

[0095] Since the current is controlled by the electronic speed controller fast enough, it can be assumed to be in a steady-state condition, and the terms related to derivatives can be omitted. Then, the energy consumption of the system during a trajectory time \(T\) n can be expressed in the following form:

[0096]

[0097] Collect data of standard flight states through flight experiments, including hovering, uniform horizontal, climbing, and variable-speed arc motions. Considering the noise caused by environmental uncertainties and the high-speed movement of the motor, the moving average method is used to preprocess the data, and the adjacent 20 data are taken for moving average filtering to improve the accuracy and reliability of the model;

[0098] As Figure 4 shown, a physics-informed neural network is used for energy consumption modeling. The input is the angular velocity of the rotor, and the output is the motor voltage and current. A multi-layer perceptron with a hidden layer is used to train the model. The model includes 3 fully connected layers, with 64 neurons in each layer. ReLU is used as the activation function after each layer. The loss function combines the data-driven loss and the physical equation loss. The data loss is the MSE loss between the predicted value and the actual value, and the physical equation loss is the voltage equation and the torque equation;

[0099] \(L\) PNN =(1 - \(\lambda\) f )\(L\) M +\(\lambda\) f \(L\) f ;

[0100] In this embodiment, the trajectory optimal prediction control input mapping algorithm in step 3 above is implemented by the following preferred scheme:

[0101] For the generated trajectory, by differentiating the trajectory, calculate the position, velocity, and acceleration, and then obtain the mapping between the trajectory state space and the control input. Adjust the control input to minimize the cost function \(J\), and obtain the optimal trajectory input through optimization to ensure the recursive feasibility and system stability of the controller.

[0102] The optimization objective functional is expressed as:

[0103]

[0104] It includes a trajectory error term, an input error term, and a penalty term for control variation. W represents the weights of these terms to indicate different degrees of influence. The entire calculation process can be expressed as the following equation;

[0105]

[0106] γ 0 = γ s ;

[0107]

[0108] Among them, is the predicted trajectory position of the model predictive control for k steps at time t. β(Δu k|t ) represents the input change amount predicted k steps forward at time t. β is the weight coefficient. u k|t represents the control input predicted at the k-th step at time t. represents the actual input required to reach the predicted state . γ 0 = γ s represents the starting point constraint of the trajectory. represents that the trajectory at time t is set as the predicted value of the trajectory at time t in the model predictive control. represents the state transition of the system. γ t ∈R d is the UAV state variable. u t ∈R m is the system input at time step t. G is the system dynamics matrix. represent the nominal state and the corresponding input respectively.

[0109] Specifically, in step 4, the trajectory parameterization modeling method is as follows:

[0110] To generate a smooth flight trajectory, the characteristics of the Bezier curve are used for trajectory modeling. For the simulated mountain trajectory γ, it can be divided into 59 segments by 60 air waypoints. The Bernstein polynomial is used for trajectory modeling, and its expression is as follows:

[0111]

[0112] Among them, represents the general equation of the segmented trajectory. For our task, there are N - 1 segments of trajectories. Each segment of trajectory P i (j)Denoted by superscript \(j\) and subscript \(i\) representing the \(i\)-th control point locus of the Bezier curve, all control point vectors for \(j\in\{1,2,\cdots,N - 1\}\) are and \(B(\zeta)\) is the basis function of the Bernstein polynomial, and this expression can be rewritten as:

[0113]

[0114] where \(r\) is the order of the polynomial, is the binomial coefficient. Since the Bezier curve is defined on the fixed interval \([0,1]\), therefore, for each segment of the locus, we need a scale factor \(\zeta\) to scale the parameter time \(t\) to the arbitrarily assigned time of that segment of the locus. We set a fifth-order polynomial curve as a monotonically increasing function of time \(t\) for the scale factor of the Bezier curve:

[0115] \(\zeta(t)=s\) 0 +s 1 t + s 2 t 2 +s 3 t 3 +s 4 t 4 +s 5 t 5 \(\in[0,1]\);

[0116] The scale factor parameter is obtained by algorithm calculation, and it is necessary to ensure the dynamic feasibility and time feasibility of the locus;

[0117] Specifically, in step 4, the kinematic constraint planning method for the locus is as follows:

[0118] The locus must pass through multiple predetermined waypoints, and the starting and target positions and their derivatives of each segment of the locus satisfy the equality constraints. For the \(l\) th -th order derivative of the \(j\) th -th waypoint (\(l\leq2\)), the constraint conditions are as follows:

[0119]

[0120] where \(i = 1\) or \(n\) represents the \(i\)-th control point of the control point , or 1 represents the boundary condition of the \(\zeta(t)\) polynomial. At the intersection of two adjacent Bezier curves, we require its position, velocity and acceleration to be continuous. Therefore, the continuity constraints should also be satisfied at the locus endpoints, specifically:

[0121]

[0122] where is the \(l\) th -th order derivative of the \(j\) th(0 ≤ l ≤ 2) - order derivative. To consider the dynamic feasibility, we impose hard constraints on the higher - order derivatives of the trajectory. The velocity vector and acceleration vector of the quadrotor are restricted within and so that the generated trajectory is dynamically feasible. In this embodiment, is set to 5 m / s, is set to 10 m / s². This constraint can be expressed as:

[0123]

[0124] Specifically, in step 4, the trajectory energy consumption optimization method is as follows:

[0125] After obtaining the parameterized trajectory, combined with the optimal predictive control input mapping and the motor energy consumption model, calculate the energy consumption of the current trajectory, transform the problem into an optimization problem, use the energy consumption as the objective function, and use the genetic algorithm to optimize the waypoint sequence and trajectory parameters to finally obtain a smooth trajectory with the optimal energy consumption;

[0126]

[0127] ξ ij ∈ {0, 1}, i, j ∈ {1, 2, …, N};

[0128]

[0129] γ k+1|t = G(γ k|t , u k|t ), k ∈ K, t ∈ T;

[0130] 0 ≤ ω Λ ≤ ω max , Λ ∈ 1, 2, 3, 4;

[0131] |θ(t)| ≤ θ max , t ∈ T;

[0132]

[0133] Among them, represents the power at the k - th moment of the n - th segment of the trajectory, ξ ij represents that the value is 1 when flying from the i - th point to the j - th point and 0 otherwise, represents the total length constraint of the trajectory, represents the power constraint of all segments of the trajectory, γ k+1|t = G(γ k|t , u k|t ) represents that the trajectory at the (k + 1) - th moment is calculated by the dynamic equation, 0 ≤ ω Λ ≤ ωmax |θ(t)| ≤ θ max , where t ∈ T represents the angular velocity constraint of the rotor are the attitude constraints of the UAV, representing the pitch angle and roll angle respectively.

[0134] In the genetic algorithm, the population size is set to 100, the number of iterations is 400, and the speed and acceleration limits are given by the dynamic constraints. The attitude limit is π / 2, and the angular velocity limit of the UAV rotor is 800 rad / s. As Figure 5 shown, the lower part is the simulation mountain model, and the upper part is the trajectory obtained by our algorithm.

[0135] As shown in the appendix Figure 6 , it can be seen from the simulation experiment trajectory data of 60 waypoints that although the trajectory length obtained by this application is not optimal compared with the benchmark method, the trajectory time and trajectory energy consumption are both better than the benchmark method.

[0136] Among them, the trajectory energy consumption obtained by the algorithm EO-TP of this application is less than that of the benchmark methods WP&CPP, and the energy consumption optimization ratio reaches 10.4%, which proves the effectiveness of the method.

[0137] Using the technical solution described in the present invention, or those skilled in the art designing similar technical solutions inspired by the technical solution of the present invention and achieving the above technical effects shall fall within the protection scope of the present invention.

Claims

1. A method for generating energy-optimized trajectories of unmanned aerial vehicles with visual coverage of arbitrary three-dimensional terrain, characterized in that: The following steps are involved: Step 1: Generate visual coverage aerial waypoints: Select a mountainous area, use a geographic information system or level flight photography to obtain a rough digital elevation model, calculate aerial waypoints based on photogrammetric constraints, and traverse these waypoints in a predetermined order to complete the coverage task; Step 2: UAV motor energy consumption modeling: Take the brushless DC motor as the object, combine the torque dynamics and electromagnetic equations of the motor for mathematical modeling, build a physical information neural network model, and train and optimize the flight data; Step 3: Trajectory Optimal Predictive Control Input Mapping: Design an optimal predictive control method based on UAV dynamics and calculate the mapping relationship between trajectory and control input; Step 4: Parametric trajectory generation and energy consumption optimization: Use the fifth-order Bezier curve to parameterize the trajectory modeling, calculate the trajectory energy consumption and use it as the optimization target, and finally optimize the trajectory parameters to obtain the flight trajectory parameters with the best energy consumption.

2. The method for generating energy-optimized trajectories of drones with visual coverage of arbitrary three-dimensional terrain according to claim 1, characterized in that: In step 1, the photogrammetric constraint method is as follows: Based on the digital elevation model, the quasi-uniform B-spline surface is used to fit the terrain surface. The calculated geometric center point is used as the center of the gimbal camera field of view, and a fixed distance d is extended along the normal vector direction to obtain the aerial viewpoint. The B-spline basis function is derived through the Cox-de Boor regression formula: Among them B ij is the control point derived from the predetermined digital terrain elevation data, N i,p (u) and N j,p (v) is the B-spline basis function that can be derived from the Cox-deBoor regression formula. According to the lateral and longitudinal overlap ratios of the camera field of view, the surface is divided into several image acquisition areas using a uniform grid. The position of the aerial waypoint can be expressed as: Where d is the equal distance constraint, For the surface ij The unit normal vector at each waypoint, the attitude angle of the gimbal camera can be expressed as:

3. The method for generating energy-optimized trajectories of drones with visual coverage of arbitrary three-dimensional terrain according to claim 1, characterized in that: In step 2, the energy consumption model is mathematically modeled as follows: Consider a quad-rotor drone powered by a lithium battery. The rotor power structure uses a brushless DC motor. The energy consumption of the resistive winding and inductive winding in the motor and the energy loss of overcoming internal friction and load friction are taken into account. The energy loss caused by the influence of the electric control and battery efficiency is ignored. Therefore, the voltage of a single rotor motor can be expressed as: Among them, R and L are the resistance and inductance of the motor winding respectively, represents the derivative of the current at time t with respect to t, that is, the rate of change of the current, ω(t) represents the angular velocity of the rotor motor at time t, and k e is the motor voltage constant. The loss in the motor magnetic circuit is usually greater than the inductance loss, so the effect of inductance is often ignored. The dynamic equation for the brushless DC motor is: i(t)=(T F +T L (ω ∧ (t))+B ∧ (ω ∧ (t))+J ∧ (ω ∧ (t)) / k T ); Where i(t) is the motor current, T F is the torque generated by propeller friction, ω ∧ is the rotor angular velocity, k T is the motor torque constant, B ∧ is the viscous damping coefficient, J ∧ is the moment of inertia of the motor and rotor load, T L (ω ∧ ) is the load friction torque generated by the propeller resistance, ignoring the torque generated by friction, and the basic energy consumption model is constructed based on this; Since the current is controlled fast enough by the electronic speed regulator, a steady-state condition can be assumed and the terms related to the derivative can be omitted. Then the system moves in a trajectory time T n The energy consumption can be expressed as follows:

4. The method for generating energy-optimized trajectories of drones with visual coverage of arbitrary three-dimensional terrain according to claim 1, characterized in that: In step 2, the physical information neural network model is as follows: The data of standard flight conditions are collected through flight experiments, including hovering, uniform level, climbing and variable speed arc motion. Considering the noise caused by environmental uncertainty and high-speed motion of the motor, the moving average method is used to pre-process the data to improve the accuracy and reliability of the model. A physical information neural network is used for energy consumption modeling. The input is the rotor angular velocity and the output is the motor power. The model is trained using a multi-layer perceptron with hidden layers. The loss function combines data-driven loss and physical equation loss.

5. The method for generating energy-optimized trajectory of a drone with visual coverage of arbitrary three-dimensional terrain according to claim 1, characterized in that: In step 3, the trajectory optimal predictive control input mapping algorithm is as follows: For the generated trajectory, the position, velocity and acceleration are calculated by differentiating the trajectory, and then the mapping between the trajectory state space and the control input is obtained. The control input is adjusted to minimize the cost function J, and the optimal trajectory input is obtained through optimization to ensure the recursive feasibility of the controller and the stability of the system. The optimization objective functional is expressed as: It includes trajectory error term, input error term and control change penalty term. W is the weight of these terms to indicate the different degrees of influence. The whole calculation process can be expressed as the following equation; γ0=γ s ; in, The model predictive control predicts the k-step trajectory position at time t, β(Δu k|t ) represents the input change predicted k steps forward at time t, β is the weight coefficient, u k|t represents the control input predicted for the kth step at time t, In order to achieve the predicted state The actual input required, γ0 = γ s represents the starting point constraint of the trajectory, The trajectory at time t is defined as the predicted value of the trajectory at time t in the model predictive control. represents the state transition of the system, γ t ∈R d is the drone state variable, u t ∈R m is the system input at time step t, G is the system dynamics matrix, Represent the nominal state and the corresponding input, respectively.

6. The method for generating energy-optimized trajectories of drones with visual coverage of arbitrary three-dimensional terrain according to claim 1, characterized in that: In step 4, the trajectory parameterization modeling method is as follows: In order to generate a smooth flight trajectory, the characteristics of the Bezier curve are used for trajectory modeling. The trajectory γ can be divided into N-1 segments by N air waypoints. The Bernstein polynomial is used for trajectory modeling, and its expression is as follows: in, Represents the general equation of the segmented trajectory. For our task, there are N-1 segments of trajectory, and each segment of trajectory P i (j) The superscript j represents the trajectory of the i-th control point of the Bezier curve, and the subscript i represents the trajectory of the i-th control point of the Bezier curve. The vectors of all control points of j∈{1,2,…,N-1} are and is the basis function of Bernstein polynomials, the expression can be rewritten as: Where r is the order of the polynomial, is the binomial coefficient. Since the Bezier curve is defined on a fixed interval [0,1], we need a scaling factor for each segment of the trajectory. To scale the parameter time t to an arbitrarily assigned time for the segment, we set a fifth-order polynomial curve as a monotonically increasing function of time t for the Bezier curve's scaling factor:

7. The method for generating energy-optimized trajectory of a drone with visual coverage of arbitrary three-dimensional terrain according to claim 1, characterized in that: In step 4, the trajectory is planned under kinematic constraints as follows: The trajectory must pass through multiple predetermined waypoints, and the starting and target positions and their derivatives of each trajectory must satisfy the equality constraint; for the jth th The lth waypoint th (l≤2)-order derivative, the constraints are as follows: Where i = 1 or n represents a control point The i-th control point of The boundary conditions of the polynomial require that the position, velocity, and acceleration of two adjacent Bezier curves are continuous at their intersections. Therefore, the continuity constraint should also be satisfied at the endpoints of the trajectory. Specifically: in is the jth th The l of the segment trajectory th (0≤l≤2)-order derivatives. In order to consider the dynamic feasibility, we impose hard constraints on the high-order derivatives of the trajectory. The velocity vector and acceleration vector of the quadrotor are restricted to and Within the range of , so that the generated trajectory has dynamic feasibility, this constraint can be expressed as:

8. The method for generating energy-optimized trajectories of drones with visual coverage of arbitrary three-dimensional terrain according to claim 1 is characterized in that: In step 4, the trajectory energy consumption optimization method is as follows: After obtaining the parameterized trajectory, the energy consumption of the current trajectory is calculated by combining the optimal predictive control input mapping and the motor energy consumption model. The problem is transformed into an optimization problem. With energy consumption as the objective function, a genetic algorithm is used to optimize the waypoint sequence and trajectory parameters, and finally a smooth trajectory with optimal energy consumption is obtained. x ij ∈{0,1},i,j∈{1,2,…,N}; c k+1|t =G(γ k|t ,u k|t ),k∈K,t∈T; 0≤ω Λ ≤ω max ,Λ∈1,2,3,4; |θ(t)|≤θ max ,t∈T; in, represents the power at time k of the nth trajectory, ξ ij If it flies from the i-th point to the j-th point, the value is 1, otherwise it is 0. represents the total trajectory length constraint, |N-1|P max represents the power constraint of all segments of the trajectory, γ k+1|t =G(γ k|t ,u k|t ) indicates that the trajectory at the k+1th moment is calculated by the dynamic equation, 0≤ω Λ ≤ω max |θ(t)|≤θ max ,t∈T represents the rotor angular velocity constraint, are the attitude constraints of the UAV, representing the pitch angle and roll angle respectively.

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