Unmanned aerial vehicle energy optimal trajectory planning method in industrial internet of things environment

Abstract

The application discloses a kind of unmanned aerial vehicle energy optimal trajectory planning method under industrial internet of things environment.The present application includes the following steps: first, according to the task demand setting fixed waypoint state constraint and optimization waypoint state under industrial internet of things environment;Then, construct the constrained trajectory optimization problem about minimizing the energy consumption of unmanned aerial vehicle;Then according to the gradient analytical expression of objective function about optimization waypoint state, calculate gradient, apply gradient descent algorithm to solve the optimal value of optimization waypoint state;Finally, the optimal full waypoint state is obtained according to the optimal value of optimization waypoint state and fixed waypoint state, and then the energy optimal trajectory that meets the dynamics of unmanned aerial vehicle and satisfies the constraint of fixed waypoint state is calculated.Compared with prior art, the present application can effectively reduce the energy consumption of unmanned aerial vehicle trajectory under industrial internet of things environment, reduce the dimension of solution space, improve the calculation efficiency and optimization performance.

Description

Technical Field

[0001] This invention relates to a method for optimal trajectory planning of unmanned aerial vehicles (UAVs) in the field of UAV motion planning technology, and more particularly to a method for optimal energy trajectory planning of UAVs in an industrial Internet of Things (IoT) environment. Background Technology

[0002] With the rapid development of communication and Internet of Things (IoT) technologies, the Industrial Internet of Things (IIoT) has been widely applied in manufacturing, energy, transportation, and other fields. Many factories and departments have deployed industrial sensor devices and industrial sensor networks, greatly improving industrial automation and production efficiency. However, due to the limited resources and performance of IIoT systems, problems exist such as weak computing power, communication data security, and real-time data transmission. Drone technology offers a good solution to these problems. Drones possess high mobility, enabling them to quickly reach designated locations and provide wide-area network signal coverage. Furthermore, their high-performance computing devices can assist in data acquisition tasks for IIoT devices and perform computationally intensive tasks that are difficult for IIoT devices to handle on their own, effectively addressing the performance limitations of IIoT devices. However, for drones, especially rotary-wing drones, endurance remains a significant factor restricting their operational capabilities. The flight trajectory of a drone has a significant impact on its energy consumption; therefore, many scholars have begun to focus on how to minimize energy consumption by optimizing flight trajectories. In current research on UAV energy-optimal trajectory planning, most existing methods are based on torque vector optimization and rely on existing solvers such as ACADO, GPOSP, and genetic algorithms to solve nonlinear optimization problems with UAV dynamic constraints and no intermediate waypoints. From the perspective of existing UAV energy-optimal trajectory planning algorithms, the following limitations exist: (1) Since the torque vector is a time-dependent vector, the degree of dispersion in the numerical calculation process directly affects the optimization effect. Furthermore, the high dimensionality of the time-varying parameter solution space easily leads to huge computational loads, long solution times, and poor real-time performance. (2) In the industrial IoT environment, most trajectory planning scenarios involve multiple intermediate waypoint state constraints, and existing methods cannot be directly applied. (3) Relying on existing optimization solvers limits the computing power and programming language support of the machine. Summary of the Invention

[0003] To address the problems existing in the prior art, the present invention aims to provide an energy-optimal trajectory planning method for unmanned aerial vehicles (UAVs) in an industrial Internet of Things (IIoT) environment. This method overcomes the shortcomings of existing methods, such as slow speed and long processing time based on moment vector optimization, reliance on optimization solvers, and inapplicability to scenarios with multiple intermediate waypoint state constraints. It solves the energy-optimal trajectory planning problem with fixed waypoint state constraints and UAV dynamic constraints.

[0004] The technical solution of the present invention is as follows:

[0005] I. A method for energy-optimal trajectory planning of unmanned aerial vehicles (UAVs) in an industrial Internet of Things (IoT) environment

[0006] Step 1: Set the fixed waypoint status and the waypoint status to be optimized for the drone based on the data acquisition tasks and edge computing service requirements of the industrial IoT devices;

[0007] Step 2: Establish the dynamics model and energy consumption model of the UAV, and construct a UAV trajectory optimization problem with minimizing UAV energy consumption as the objective function and UAV dynamics and fixed waypoint states as constraints.

[0008] Step 3: Based on the differential flatness property of the UAV and the UAV dynamics model, combined with the waypoint state to be optimized and the UAV trajectory optimization problem in Step 2, the gradient analytical expression of the objective function with respect to the waypoint state to be optimized is obtained;

[0009] Step 4: Calculate the gradient using the analytical expression of the gradient of the objective function with respect to the state of the waypoint to be optimized, and then use the gradient descent algorithm to iteratively solve for the optimal value of the state of the waypoint to be optimized.

[0010] Step 5: Obtain the optimal total waypoint state by using the optimal value of the waypoint state to be optimized and the fixed waypoint state. Based on the optimal total waypoint state, solve for the polynomial coefficients of the UAV flight trajectory, and then obtain an energy-optimal trajectory.

[0011] The fixed waypoint status of the UAV includes the initial state of the start point of the UAV flight path, the initial state of the end point, the intermediate waypoint positions that need to be passed through to perform the mission, and the motion state that needs to be satisfied at that position.

[0012] The state of waypoints to be optimized includes the state of the starting point to be optimized, the state of the ending point to be optimized, and the operational state that can be adjusted and optimized at intermediate waypoints that need to be passed through to execute the mission.

[0013] When the initial state of the starting point and the initial state of the ending point contain position and yaw angle, then the initial state to be optimized at the starting point and the initial state to be optimized at the ending point contain at least the first derivative of velocity and yaw angle; when the initial state of the starting point and the initial state of the ending point contain position and its lower derivative as well as yaw angle and its lower derivative, then the initial state to be optimized at the starting point and the initial state to be optimized at the ending point contain the higher derivative of position and the higher derivative of yaw angle.

[0014] In step two, when the drone is a quadcopter, the specific formula for the drone trajectory optimization problem is as follows:

[0015]

[0016]

[0017] In the formula, E represents the energy consumed by the drone; min indicates taking the minimum value; ω j (t) represents the angular velocity of the j-th motor; J, κ τ and D v These represent the motor's moment of inertia, air resistance coefficient, and viscous damping coefficient, respectively; t0 and t f represent the start and end times of the trajectory, respectively; z(t) is the position and state of the planned trajectory at time t, t = t0, t... f ,t i ; This represents the initial state of the starting point in a fixed waypoint state. This represents the initial state of the destination in a fixed waypoint state. represents the motion state of the i-th intermediate waypoint; M represents the number of intermediate waypoints. and φ(t), θ(t), and ψ(t) represent the acceleration of the UAV in the x, y, and z directions in the geodetic coordinate system, respectively; φ(t), θ(t), and ψ(t) represent the roll angle, pitch angle, and yaw angle, respectively. and These represent the first derivatives of the roll angle, pitch angle, and yaw angle, respectively. and represent the second derivatives of the roll, pitch, and yaw angles, respectively; m represents the mass of the UAV, and g represents the acceleration due to gravity; I x I y and I z τ represents the moments of inertia of the UAV in the x, y, and z directions, respectively; T(t) is the total thrust of the motor; τ x (t), τ y (t) and τ z (t) represents the first torque vector, the second torque vector, and the third torque vector, respectively.

[0018] In step three, when the UAV is a quadcopter, the gradient expression of the objective function with respect to the waypoint state to be optimized is as follows:

[0019]

[0020]

[0021] Among them, g j (t) represents the square of the j-th motor angular velocity at time t, d P This indicates the status of waypoints that need optimization. This represents the gradient of the objective function with respect to the waypoint state to be optimized; ω represents the angular velocity ω of the j-th motor at time t. j The gradient of the square of (t) with respect to the waypoint state to be optimized.

[0022] In step four, the gradient descent algorithms include SGD, Adam, BFGS, and L-BFGS.

[0023] In step five, the optimal all-waypoint state D is... * Substituting these values ​​into the polynomial trajectory parameter solving equation, the polynomial coefficients p of the UAV flight trajectory are obtained. * Then, based on the polynomial coefficients p of the human-machine flight trajectory * Separate the optimal trajectory coefficients in the x-dimensional dimension Optimal trajectory coefficients in the y-dimension Optimal trajectory coefficients in the z-dimensional dimension Optimal trajectory coefficients in ψ dimension Thus, an energy-optimal trajectory that satisfies the fixed waypoint state constraints and conforms to UAV dynamics is obtained, and the specific formula is as follows:

[0024]

[0025]

[0026] in, Let d be the optimal value of the waypoint state to be optimized. F For fixed waypoint states, T stands for transpose. Let be the augmented mapping matrix of the polynomial trajectory.

[0027] II. A computer device

[0028] The computer device includes a memory and a processor, the memory storing a computer program, and the processor executing the computer program to implement the steps of the method.

[0029] III. A computer-readable storage medium

[0030] The computer-readable storage medium stores a computer program that, when executed by a processor, implements the steps of the method.

[0031] IV. A computer program product

[0032] The computer program product includes a computer program / instruction that, when executed by a processor, implements the steps of the method.

[0033] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0034] (1) The optimization variable of the present invention is waypoint state, and the solution space dimension is much lower than that of the existing nonlinear optimization method based on torque vector as optimization variable. The algorithm requires less computing power, less computation, and has a significantly improved solution speed, with better real-time performance and reliability.

[0035] (2) This invention combines the analytical expression of the objective function gradient with the gradient descent algorithm for optimization. Compared with heuristic algorithms such as genetic algorithm, ant colony algorithm, and particle swarm algorithm, this method has higher computational efficiency and optimization efficiency in the problem of optimal energy trajectory planning for UAVs.

[0036] (3) This invention does not rely on a nonlinear optimization solver, the algorithm is easy to implement, and it has a wide range of applications.

[0037] (4) This invention can be used in conjunction with different gradient descent algorithms and has great practicality.

[0038] (5) This invention utilizes the differential flatness property of UAV and waypoint state to obtain the energy-optimal trajectory. This trajectory has the good property of naturally satisfying the fixed waypoint state constraint and UAV dynamics constraint. Therefore, when solving the optimization problem, there is no need to consider and verify the fixed waypoint state constraint and UAV dynamics constraint, resulting in low solution complexity and faster convergence speed. Attached Figure Description

[0039] Figure 1 This is a flowchart of the present invention.

[0040] Figure 2 This is a schematic diagram of a drone working in an industrial Internet of Things environment according to the present invention.

[0041] Figure 3 This is a comparison chart of energy optimization in this invention.

[0042] Figure 4 This is a comparison chart of trajectory planning in this invention. Detailed Implementation

[0043] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0044] It should be noted that, unless otherwise specified, the embodiments and features described in the present invention can be combined with each other.

[0045] like Figure 1 As shown, the present invention includes the following steps:

[0046] Step 1: Based on the data acquisition tasks and edge computing service requirements of the industrial IoT devices, set the fixed waypoint status and the waypoint status to be optimized for the drone, such as... Figure 2 As shown;

[0047] The fixed waypoint status of the UAV includes the initial state of the start point of the UAV flight path, the initial state of the end point, the intermediate waypoint positions that need to be passed through to perform the mission, and the motion state that needs to be satisfied at that position.

[0048] The state of waypoints to be optimized includes the state of the origin to be optimized, the state of the destination to be optimized, and the operational state that can be adjusted and optimized at intermediate waypoints that need to be passed through to execute the mission.

[0049] When the initial state of the starting point and the initial state of the ending point contain position and yaw angle, then the initial state to be optimized at the starting point and the initial state to be optimized at the ending point must contain at least the first derivative of velocity and yaw angle, and may also contain multiple derivatives of velocity and higher derivatives of yaw angle. When the initial state of the starting point and the initial state of the ending point contain position and lower derivatives of position and yaw angle, then the initial state to be optimized at the starting point and the initial state to be optimized at the ending point contain higher derivatives of position and higher derivatives of yaw angle. That is, the operating parameters in the initial state of the starting point / initial state of the ending point and the initial state to be optimized at the starting point / initial state of the ending point do not overlap, and at least one operating parameter must be set in each state. For example, the highest order of the derivative of the displacement state (i.e., the highest order of the trajectory state) is 3. The fixed starting state includes position and yaw angle; the starting state to be optimized includes velocity and acceleration, jerk, and the first derivative of the yaw angle. The fixed starting state includes position and initial velocity, as well as the yaw angle and its first derivative; the starting state to be optimized includes acceleration, jerk, and the second and third derivatives of the yaw angle. Define the fixed waypoint state as d. F The waypoint status to be optimized is d. P The fixed waypoint state and the waypoint state to be optimized together constitute the total waypoint state D, satisfying D = [d]. F dP ] T .

[0050] Step 2: Establish the dynamics model and energy consumption model of the UAV, and construct a UAV trajectory optimization problem with minimizing UAV energy consumption as the objective function and UAV dynamics and fixed waypoint states as constraints.

[0051] In step two, when the drone is a quadcopter, the specific formula for the drone trajectory optimization problem is as follows:

[0052]

[0053]

[0054] Among them, the total thrust of the motor is T(t), and the first torque vector is τ. x (t), the second torque vector τ y (t) and the third moment vector τ z The formula for calculating (t) is:

[0055]

[0056]

[0057]

[0058]

[0059] In the formula, E represents the energy consumed by the drone, which is also the objective function of the optimization problem; min indicates taking the minimum value; ω j (t) represents the angular velocity of the j-th motor, j = 1, 2, 3, 4; J, κ τ and D v These represent the motor's moment of inertia, air resistance coefficient, and viscous damping coefficient, respectively; t0 and t f represent the start and end times of the trajectory, respectively; z(t) is the position and state of the planned trajectory at time t, t = t0, t... f ,t i ; This represents the initial state of the starting point in a fixed waypoint state. This represents the initial state of the destination in a fixed waypoint state. represents the motion state of the i-th intermediate waypoint; M represents the number of intermediate waypoints. and φ(t), θ(t), and ψ(t) represent the acceleration of the UAV in the x, y, and z directions in the geodetic coordinate system, respectively; φ(t), θ(t), and ψ(t) represent the roll angle, pitch angle, and yaw angle, respectively. and These represent the first derivatives of the roll angle, pitch angle, and yaw angle, respectively. and represent the second derivatives of the roll, pitch, and yaw angles, respectively; m represents the mass of the UAV, and g represents the acceleration due to gravity; I x I y and I z τ represents the moments of inertia of the UAV in the x, y, and z directions, respectively; T(t) is the total thrust of the motor; τ x (t), τ y (t) and τ z (t) represent the first, second, and third torque vectors, respectively; K F K represents the thrust coefficient. M represents the drag coefficient; l represents the distance from the center of mass of the UAV to the center of the motor.

[0060] Step 3: Based on the differential flatness property of the UAV and the UAV dynamics model, combined with the waypoint state to be optimized and the UAV trajectory optimization problem in Step 2, the gradient analytical expression of the objective function with respect to the waypoint state to be optimized is obtained;

[0061] In step three, when the UAV is a quadcopter, the gradient expression of the objective function with respect to the waypoint state to be optimized is as follows:

[0062]

[0063]

[0064] Among them, g j (t) represents the square of the j-th motor angular velocity at time t, d P This indicates the status of waypoints that need optimization. This represents the gradient of the objective function with respect to the waypoint state to be optimized; ω represents the angular velocity ω of the j-th motor at time t. j The gradient of the square of (t) with respect to the waypoint state to be optimized is calculated as follows:

[0065]

[0066] In the formula, the transformation matrix K -1 The formula for calculating the control input vector u is as follows:

[0067]

[0068]

[0069] in, This represents the gradient of the total thrust of the electric motors with respect to the waypoint state to be optimized. This represents the gradient of the first moment vector with respect to the waypoint state to be optimized. This represents the gradient of the second moment vector with respect to the waypoint state to be optimized. This represents the gradient of the third moment vector with respect to the waypoint state to be optimized. and The expression for the calculation is as follows:

[0070]

[0071]

[0072]

[0073]

[0074] Since the waypoint state to be optimized consists of the UAV's position in three-dimensional space and its derivative states, excluding the fixed waypoint state constraints, as well as the yaw angle and its derivative states, it is easy to obtain the gradients of the second derivatives of the trajectory states of x, y, z, and ψ with respect to the waypoint state to be optimized in the above expressions. The calculation method is as follows:

[0075]

[0076]

[0077]

[0078]

[0079] In the formula, and Let A represent the second derivatives of the time vectors of the polynomial loci of x, y, z, and ψ, respectively. x A y A z and A ψ denoted by , and denoted by , respectively, the mapping matrices representing the polynomial trajectories of x, y, z, and ψ.

[0080] The general expression for the gradient of the second derivative of the trajectory states of x, y, z, and ψ with respect to the state of the waypoint to be optimized is as follows:

[0081]

[0082] Where f is the general state parameter and n is the order of the derivative of the general state.

[0083] Based on the differential flatness property of the UAV, the total motor thrust T(t), roll angle φ, and pitch angle θ, along with their derivatives, can be represented by the trajectory states in the x, y, and z directions and the trajectory state of the yaw angle ψ. The expressions for the total motor thrust T(t), roll angle φ, and pitch angle θ are shown below:

[0084]

[0085]

[0086]

[0087] Therefore, the roll angle φ and pitch angle θ, as well as the gradients of their first and second derivatives with respect to the waypoint state to be optimized, can be further calculated as follows:

[0088]

[0089]

[0090]

[0091]

[0092] Among them, p1, p2, Let be the first intermediate variable, the second intermediate variable, the first derivative of the first intermediate variable, and the first derivative of the second intermediate variable, respectively; q1, q2, ... These are the third intermediate variable, the fourth intermediate variable, the first derivative of the third intermediate variable, and the first derivative of the fourth intermediate variable, respectively.

[0093] The formulas for calculating the intermediate variables required by the expression are shown in Table 1:

[0094] Table 1 shows the formulas for calculating intermediate variables.

[0095]

[0096]

[0097] In Table 1, The nth derivative of the input function S with respect to the waypoint state d to be optimized P The gradient function, S is The input function, i = 1, 2, ..., 8, j = 1, 2, ..., 6, k = 1, 2, 3, 4 represent the variable S with respect to the waypoint state d to be optimized. P gradient, Let be the first derivatives of the i-th and j-th beta-type intermediate variables, and the second derivative of the k-th beta-type intermediate variable, respectively. Since variable S depends only on the trajectory states of x, y, z, and ψ and their derivatives, therefore... The gradient of the nth derivative of the trajectory states of x, y, z, and ψ with respect to the state of the waypoint to be optimized can be obtained using the following formula:

[0098]

[0099] In the formula, A represents the nth derivative of the time vector of the polynomial trajectory f. f The mapping matrix representing the trajectory of the f-polynomial.

[0100] Step 4: Calculate the gradient of the objective function with respect to the state of the waypoint to be optimized using the analytical expression of the gradient. Then, use the gradient descent algorithm to iteratively solve for the optimal value of the state of the waypoint to be optimized, such as... Figure 3 As shown;

[0101] In step four, the gradient descent algorithms include SGD, Adam, BFGS, and L-BFGS. The gradient is calculated based on the analytical gradient expression from step three, and then applied to gradient descent algorithms such as SGD, Adam, BFGS, and L-BFGS. Finally, the optimal value of the waypoint state to be optimized is calculated. Since the gradient obtained by combining the differential flatness property of the UAV and the trajectory obtained by waypoint state optimization have the good property of naturally satisfying the fixed waypoint state constraints and UAV dynamic constraints, the limitations of the fixed waypoint state constraints and UAV dynamic constraints can be further eliminated in the process of solving the UAV energy-optimal trajectory optimization problem constructed in step two in step four.

[0102] Step 5: Obtain the optimal full waypoint state by using the optimal value of the waypoint state to be optimized and the fixed waypoint state. Based on the optimal full waypoint state, solve for the polynomial coefficients of the UAV flight trajectory, and then obtain an energy-optimal trajectory that conforms to UAV dynamics and satisfies the constraints of the fixed waypoint state.

[0103] In step five, the optimal all-waypoint state D is... * Substituting these values ​​into the polynomial trajectory parameter solving equation, the polynomial coefficients p of the UAV flight trajectory are obtained. * Then, based on the polynomial coefficients p of the human-machine flight trajectory * Separate the optimal trajectory coefficients in the x-dimensional dimension Optimal trajectory coefficients in the y-dimension Optimal trajectory coefficients in the z-dimensional dimension Optimal trajectory coefficients in ψ dimension Thus, an energy-optimal trajectory that satisfies the fixed waypoint state constraints and conforms to UAV dynamics is obtained, and the specific formula is as follows:

[0104]

[0105]

[0106] in, Let d be the optimal value of the waypoint state to be optimized. F For fixed waypoint states, T stands for transpose. Let be the augmented mapping matrix of the polynomial trajectory.

[0107] Figure 4 The four subplots compare the trajectories before and after optimization in the x, y, z, and ψ dimensions, respectively. The three plots in each subplot are the trajectories before and after optimization for x, y, z, or ψ and their first and second derivatives, respectively. The dashed lines represent the trajectory before optimization, and the solid lines represent the trajectory after optimization.

[0108] The above description is merely a preferred embodiment of the present invention; however, the scope of protection of the present invention is not limited thereto. Therefore, it should be understood that many modifications can be made to the exemplary embodiments, and other arrangements can be designed, as long as they do not depart from the spirit and scope of the invention as defined by the appended claims. Any equivalent substitutions or changes made by those skilled in the art within the scope of the technology disclosed in this invention, based on the technical solutions and improved concepts of the present invention, should be covered within the scope of protection of this invention.

Claims

1. A method for energy-optimal trajectory planning of unmanned aerial vehicles (UAVs) in an industrial Internet of Things (IIoT) environment, characterized in that, Includes the following steps: Step 1: Set the fixed waypoint status and the waypoint status to be optimized for the drone based on the data acquisition tasks and edge computing service requirements of the industrial IoT devices; Step 2: Establish the dynamics model and energy consumption model of the UAV, and construct a UAV trajectory optimization problem with minimizing UAV energy consumption as the objective function and UAV dynamics and fixed waypoint states as constraints. Step 3: Based on the differential flatness property of the UAV and the UAV dynamics model, combined with the waypoint state to be optimized and the UAV trajectory optimization problem in Step 2, the gradient analytical expression of the objective function with respect to the waypoint state to be optimized is obtained; When the UAV is a quadcopter, the gradient expression of the objective function with respect to the waypoint state to be optimized is as follows: in, Representative at Time of the first The square of the angular velocity of the motor This indicates the status of waypoints that need optimization. This represents the gradient of the objective function with respect to the waypoint state to be optimized; Indicates in Time of the first angular velocity of each motor The gradient of the square of the waypoint with respect to the state of the waypoint to be optimized; , and These represent the moment of inertia, air resistance coefficient, and viscous damping coefficient of the motor, respectively. and These represent the start and end times of the trajectory, respectively. Step 4: Calculate the gradient using the analytical expression of the gradient of the objective function with respect to the state of the waypoint to be optimized, and then use the gradient descent algorithm to iteratively solve for the optimal value of the state of the waypoint to be optimized. Step 5: Obtain the optimal full waypoint state by using the optimal value of the waypoint state to be optimized and the fixed waypoint state. Based on the optimal full waypoint state, solve for the polynomial coefficients of the UAV flight trajectory, and then obtain an energy-optimal trajectory.

2. The method for optimal energy trajectory planning of unmanned aerial vehicles in an industrial Internet of Things environment according to claim 1, characterized in that, The fixed waypoint status of the UAV includes the initial state of the start point of the UAV flight path, the initial state of the end point, the intermediate waypoint positions that need to be passed through to perform the mission, and the motion state that needs to be satisfied at that position. The state of waypoints to be optimized includes the state of the starting point to be optimized, the state of the ending point to be optimized, and the operational state that can be adjusted and optimized at intermediate waypoints that need to be passed through to execute the mission. When the initial state of the starting point and the initial state of the ending point contain position and yaw angle, then the initial state to be optimized at the starting point and the initial state to be optimized at the ending point contain at least the first derivative of velocity and yaw angle; when the initial state of the starting point and the initial state of the ending point contain position and its lower derivative as well as yaw angle and its lower derivative, then the initial state to be optimized at the starting point and the initial state to be optimized at the ending point contain the higher derivative of position and the higher derivative of yaw angle.

3. The method for optimal energy trajectory planning of unmanned aerial vehicles in an industrial Internet of Things environment according to claim 1, characterized in that, In step two, when the drone is a quadcopter, the specific formula for the drone trajectory optimization problem is as follows: In the formula, This represents the energy consumed by the drone; This indicates taking the minimum value; Representing the The angular velocity of each motor; , and These represent the moment of inertia, air resistance coefficient, and viscous damping coefficient of the motor, respectively. and These represent the start and end times of the trajectory, respectively. The planned trajectory is in The position and state at each time step, ; This represents the initial state of the starting point in a fixed waypoint state. This represents the initial state of the destination in a fixed waypoint state. Representing the The motion status of each intermediate waypoint; This represents the number of intermediate waypoints; , and These represent the UAV in the geodetic coordinate system. , and Acceleration in the direction of; , and These represent roll angle, pitch angle, and yaw angle, respectively. , and These represent the first derivatives of the roll angle, pitch angle, and yaw angle, respectively. , and These represent the second derivatives of the roll angle, pitch angle, and yaw angle, respectively. Represents the quality of the drone. Represents gravitational acceleration; , and Representing drones in , and Moment of inertia in the direction of rotation; This refers to the total thrust of the motor. , and These represent the first, second, and third torque vectors, respectively.

4. The method for optimal energy trajectory planning of unmanned aerial vehicles in an industrial Internet of Things environment according to claim 1, characterized in that, In step four, the gradient descent algorithms include SGD, Adam, BFGS, and L-BFGS.

5. The method for optimal energy trajectory planning of unmanned aerial vehicles in an industrial Internet of Things environment according to claim 1, characterized in that, In step five, the optimal all waypoint state is... Substituting these values ​​into the polynomial trajectory parameter solving equation, the polynomial coefficients of the UAV flight trajectory are obtained. Then, based on the polynomial coefficients of the drone's flight trajectory Separate Dimensionally optimal trajectory coefficients , Dimensionally optimal trajectory coefficients , Dimensionally optimal trajectory coefficients , Dimensionally optimal trajectory coefficients Thus, an energy-optimal trajectory that satisfies the fixed waypoint state constraints and conforms to UAV dynamics is obtained, as shown in the following formula: in, The optimal value for the waypoint state to be optimized is... In fixed waypoint status, For transpose, Let be the augmented mapping matrix of the polynomial trajectory.

6. A computer device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, When the processor executes the computer program, it implements the steps of the method according to any one of claims 1 to 5.

7. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the steps of the method according to any one of claims 1 to 5.

8. A computer program product comprising a computer program / instructions, characterized in that, When the computer program / instructions are executed by the processor, they implement the steps of the method according to any one of claims 1 to 5.

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