CN115145295A - Online autonomous flight path optimization control method for unmanned aerial vehicle in dynamic environment - Google Patents
Online autonomous flight path optimization control method for unmanned aerial vehicle in dynamic environment Download PDFInfo
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Abstract
The invention provides an online autonomous flight path optimization control method for an unmanned aerial vehicle in a dynamic environment, which is characterized in that on the basis of a traditional method, various constraint conditions of the unmanned aerial vehicle are considered, and a nonlinear optimal control model of the unmanned aerial vehicle is constructed; dividing the whole autonomous trajectory control interval of the unmanned aerial vehicle into a plurality of rolling optimization time windows by using a rolling time domain control strategy, and reasonably optimizing each section of trajectory; and meanwhile, establishing an objective function according to the flight time when the unmanned aerial vehicle reaches a target area and the threat probability, and continuously performing online calculation by using a self-adaptive Radau pseudo-spectrum method to realize the online track real-time control optimization of the unmanned aerial vehicle. The invention can carry out the ground penetration combat mission in the uncertain complex battlefield environment containing factors such as complex terrain obstacles, dynamic threat sources, time sensitive targets and the like, and greatly improves the timeliness, the accuracy and the degree of autonomy of the unmanned aerial vehicle penetration track control; meanwhile, the lower flight cost, the higher survival probability and the task completion probability of the unmanned aerial vehicle in the defense burst task are ensured.
Description
Technical Field
The invention belongs to the technical field of automatic cruising of unmanned aerial vehicles, and particularly relates to an online autonomous flight path optimization control method of an unmanned aerial vehicle in a dynamic environment.
Background
The unmanned aerial vehicle gradually becomes important supporting force on the current information battlefield by virtue of unique performance advantages of excellent body structure, high overload, good pneumatic efficiency, low radar/infrared characteristic signals and the like, and along with the continuous improvement of communication technology and load performance, the capability of the unmanned aerial vehicle in the aspects of tasks such as detection and early warning, monitoring and evaluation, communication support, electronic countermeasure, target penetration and the like is gradually matured. The ground penetration combat mission is carried out in an uncertain complex battlefield environment containing factors such as complex terrain obstacles, dynamic threat sources and time-sensitive targets, and higher requirements are provided for timeliness, accuracy and autonomy degree of unmanned aerial vehicle penetration track control. In order to simultaneously guarantee the lower flight cost, the higher survival probability and the task completion probability of the unmanned aerial vehicle in the defense penetration task, the unmanned aerial vehicle is required to calculate a flight path capable of flying in real time under the constraint of various conditions according to information such as local terrain, obstacles and threats and the limitation of self maneuverability, and simultaneously the flight path is followed to complete the flight task. Meanwhile, when the unmanned aerial vehicle senses that the battlefield environment information changes, online autonomous flight path optimization control can be performed according to new information.
In order to realize the ground defense task of the unmanned aerial vehicle, the prior art scheme mainly focuses on a flight path planning technology, which is one of key technologies for successfully realizing the attack. At present, there are many methods for Planning the flight Path of Unmanned Aerial vehicle, and the paper "Mission Planning for Unmanned Aerial vehicle Based on Voronoi Diagram-Tabu Genetic Algorithm" (Tan W, hu Y, zhao Y, et al. Wireless Communications and Mobile Computing,2021,2021.) adopts Voronoi graph paper, A novel real-time competition Path Planning UAV in 3D complex dynamic environment (Zhang Z, wu J, dai J, et al. IEEE Access,2020,8: 2021-1920) using sparse A Algorithm, paper "A dynamic identification positional field (D-apf) u _ Path Planning technique for following and moving targets" (Jayaweera H M, hand S. IEEE Access,2020,8, the algorithms plan the path of the unmanned aerial vehicle, and then carry out constraint and smoothing treatment on the path condition, so that the planned path is close to reality. The paper (Hao Zhen, zhang Jian, zhu Fan, chua satisfied flight mechanics, 2010,28 (01): 47-52.) provides a method for planning low-altitude penetration three-dimensional flight path by applying an A algorithm in a radar threat environment, and only considers a simplified threat model of a distance factor.
The flight path planning algorithm in the prior art has advantages, but high-precision control of the defense process is difficult to realize, and the flight path planning property is difficult to ensure; most researches stay in the field of offline track planning, and have the defects of large calculated amount, poor robustness and the like. The problem of flight path optimization for drones can be abstracted as solving a set of nonlinear optimal control problems including differential-algebraic constraints and inequality constraints, while the premise of such real-time, on-line flight path generation is actually the real-time computation of the nonlinear control system. Meanwhile, most researches establish that the radar scattering cross section (RCS) in a threat model is kept constant, and actually the RCS can dynamically change along with the angle change of a fuselage relative to incident waves of the radar. In addition, the current unmanned aerial vehicle track planning research mainly focuses on static task scenes with known local threat information, the actual situation is often a dynamically-changed complex battlefield environment, the time-sensitive requirement on target attack in the environment is high, and the scheme in the prior art cannot meet the requirement of automatic cruising of the unmanned aerial vehicle.
Disclosure of Invention
In order to solve the problems in the prior art, the invention provides an online autonomous flight path optimization control method for an unmanned aerial vehicle in a dynamic environment. The technical problem to be solved by the invention is realized by the following technical scheme:
the invention provides an online autonomous flight path optimization control method of an unmanned aerial vehicle in a dynamic environment, which comprises the following steps:
step 1: establishing initial unmanned aerial vehicle kinematics and a kinetic equation according to flight parameters of the unmanned aerial vehicle in a dynamic environment;
step 2: adding conditional constraints to the kinematics and the dynamic equation of the initial unmanned aerial vehicle to obtain a nonlinear optimal control model;
the condition constraint comprises an initial constraint condition, a terminal condition constraint condition and a flight performance constraint condition, and the nonlinear optimal control model comprises the following steps: control variables and state variables;
and step 3: calculating the detection probability of the unmanned aerial vehicle detected by all the radars according to the correlation parameters between the current position of the unmanned aerial vehicle and the radars;
and 4, step 4: calculating a first performance index with minimum threat to the unmanned aerial vehicle according to the detection probability, and calculating a second performance index with minimum flight time of the unmanned aerial vehicle;
and 5: comprehensively weighting and optimizing the first performance index and the second performance index, and taking the optimized result as a target function;
step 6: optimizing the objective function by using the local planning control windows to convert the global minimum problem of the objective function into solving the objective function minimum problem in each local planning control window, obtain guide sub-objective functions of each local planning control window and establish unmanned aerial vehicle avoidance sub-objective functions;
and 7: mapping a time interval from the starting time to the ending time of the unmanned aerial vehicle to obtain a numerical value interval;
and step 8: and in the numerical interval according to the time sequence, solving the control variable, the state variable, the constraint condition, the first performance index and the second performance index of the unmanned aerial vehicle of the next local planning control window by using an adaptive Radau pseudo-spectrum method under the guidance of the guidance subfunction and the avoidance subfunction according to the control variable, the state variable, the constraint condition, the first performance index and the second performance index of the unmanned aerial vehicle of the previous local planning control window, and generating the global track of the unmanned aerial vehicle.
The invention provides an online autonomous flight path optimization control method for an unmanned aerial vehicle in a dynamic environment. Dividing the whole autonomous trajectory control interval of the unmanned aerial vehicle into a plurality of rolling optimization time windows by using a rolling time domain control strategy, and reasonably optimizing each section of trajectory; meanwhile, the flight time of the unmanned aerial vehicle reaching the target area and the threat probability are used as target functions, and a method capable of adaptively adjusting the weighting performance index and switching the sub-target functions is provided. And (3) continuously calculating on line by using a self-adaptive Radau pseudo spectrum method to realize the real-time control optimization of the online track of the unmanned aerial vehicle. The invention can carry out the ground penetration combat mission in the uncertain complex battlefield environment containing factors such as complex terrain obstacles, dynamic threat sources, time sensitive targets and the like, and greatly improves the timeliness, the accuracy and the degree of autonomy of the unmanned aerial vehicle penetration track control; meanwhile, the lower flight cost, the higher survival probability and the task completion probability of the unmanned aerial vehicle in the defense burst task are ensured, a new track can be readjusted according to new information, the algorithm has high convergence speed and high calculation precision, and the practical scene has strong practicability.
The present invention will be described in further detail with reference to the accompanying drawings and examples.
Drawings
Fig. 1 is a schematic flow chart of an online autonomous flight path optimization control method for an unmanned aerial vehicle in a dynamic environment according to an embodiment of the present invention;
fig. 2 is a simulation diagram of online autonomous flight path optimization control of case 1 and case 2 unmanned aerial vehicles according to an embodiment of the present invention;
fig. 3 is a simulation top view of scenario 1 and scenario 2 unmanned aerial vehicle online autonomous trajectory optimization control provided in an embodiment of the present invention.
Detailed Description
The present invention will be described in further detail with reference to specific examples, but the embodiments of the present invention are not limited thereto.
As shown in fig. 1, the method for online autonomous trajectory optimization control of an unmanned aerial vehicle in a dynamic environment provided by the present invention comprises:
step 1: establishing initial unmanned aerial vehicle kinematics and a kinetic equation according to flight parameters of the unmanned aerial vehicle in a dynamic environment;
the initial unmanned aerial vehicle kinematics and kinetic equations are:
wherein (x, y, z) is the position coordinate of the unmanned aerial vehicle, V is the vacuum speed of the unmanned aerial vehicle, theta is the track inclination angle,
is the track drift angle; n is x For tangential overload, n z Normal overload and gamma roll angle.
Step 2: adding conditional constraints to the kinematics and the dynamic equation of the initial unmanned aerial vehicle to obtain a nonlinear optimal control model;
the condition constraint comprises an initial constraint condition, a terminal condition constraint condition and a flight performance constraint condition, and the nonlinear optimal control model comprises the following steps: control variables and state variables;
wherein, the state variable and the control variable of the unmanned aerial vehicle are respectively
U(t)＝[n x ,n z ,γ] T
In the formula, X (t) is an unmanned aerial vehicle state variable matrix, and U (t) is an unmanned aerial vehicle control variable matrix.
The initial constraint conditions are as follows:
wherein, t 0 For the initial time of flight of the unmanned aerial vehicle, (x) 0 ,y 0 ,z 0 ) Is the coordinate of the initial position of the unmanned aerial vehicle, V 0 、θ 0 And
respectively the initial speed, initial track inclination angle and initial track deflection angle of the unmanned aerial vehicle, gamma 0 The initial roll angle;
the terminal constraints of the unmanned aerial vehicle are:
(x w ,y w ,z w ) For unmanned aerial vehicle weapon launch position coordinates, (x) f ,y f ,z f ) Terminal position coordinates for unmanned aerial vehicle trajectory control, t f For the time of flight terminal of the unmanned aerial vehicle, Δ x, Δ y and Δ z are allowable drop errors, V f 、θ f And
respectively the tail end speed, the tail end track inclination angle and the tail end track deflection angle of the unmanned aerial vehicle;
the flight performance constraint condition is
In the formula, t is the flight time of the unmanned aerial vehicle, z min And z max Minimum and maximum flying heights, V, of the unmanned aerial vehicle, respectively min And V max Minimum and maximum flight speeds, θ, respectively, of the drone min And theta max Are respectively unmanned aerial vehiclesThe minimum and maximum track inclination angles,
and
minimum and maximum flight path drift angles, gamma, respectively, for the drone min And gamma max Respectively the minimum and maximum roll angles of the drone,
is the maximum roll angle rate of change, n, of the UAV xmax For maximum tangential overload of the drone, n zmax And the unmanned aerial vehicle is overloaded maximally normally.
And 3, step 3: calculating the detection probability of the unmanned aerial vehicle detected by all the radars according to the correlation parameters between the current position of the unmanned aerial vehicle and the radars;
as an optional implementation manner of the present invention, the step 3 includes:
step 31: establishing a radar threat model according to the correlation parameters of the unmanned aerial vehicle and the air defense radar;
the radar threat model is represented as:
in the formula (x) r ,y r ,z r ) The position coordinate of the enemy air defense radar is shown, and r is the relative distance between the unmanned aerial vehicle and the enemy air defense radar;
step 32: establishing an unmanned aerial vehicle circumferential RCS model under the radar threat model;
the unmanned aerial vehicle circumferential RCS model is as follows:
wherein sigma is the scattering cross section area of the unmanned aerial vehicle radar, a, b and c are the characteristic parameters of the radar,
step 33: and calculating the detection probability of the unmanned aerial vehicle detected by the thunder according to the circumferential RCS model of the unmanned aerial vehicle.
Wherein the probability that the instant of the drone is captured at a time is
P t ＝1/[1+(c 2 R t 4 /σ t ) c1 ]
In the formula, c 1 、c 2 Configuring parameters, R, for the radar itself t For the relative distance, σ, of the drone and the radar at that moment t The radar scattering cross section of the unmanned aerial vehicle at the moment;
when n air defense radar sites of enemies form the combined air defense system, the detection probability of the air defense system to the unmanned aerial vehicle is
In the formula, i represents the serial number of the air defense radars, n represents the total number of the air defense radars, P T (i) Representing the probability that each air defense radar is instantaneously captured.
And 4, step 4: calculating a first performance index with minimum threat to the unmanned aerial vehicle according to the detection probability, and calculating a second performance index with minimum flight time of the unmanned aerial vehicle;
the performance index of the unmanned aerial vehicle with the shortest flight time is as follows:
J time ＝t f -t 0
the minimum threatened performance indexes of the unmanned aerial vehicle are as follows:
and 5: comprehensively weighting and optimizing the first performance index and the second performance index, and taking the optimized result as a target function;
it is worth mentioning that: comprehensively considering the flight time of the unmanned aerial vehicle arriving at the combat area and being threatened, weighting the first performance index and the second performance index to obtain:
in the formula, ω 1 、ω 2 As a weighting coefficient, P (X (t)) is the probability of being captured by all radars in the current time state of the drone;
the weighted result is optimized in a segmentation way to obtain an objective function of
In the formula, r (t) is the distance between the position of the unmanned aerial vehicle at the current moment and the attack target reference point, and v (t) is the approaching speed of the unmanned aerial vehicle and the attack target reference point at the moment.
And 6: optimizing the objective function by using the local planning control windows to convert the global minimum problem of the objective function into solving the objective function minimum problem in each local planning control window, obtain a guide sub-objective function of each local planning control window and establish an unmanned aerial vehicle avoidance sub-objective function;
the method can convert the optimal track problem of the unmanned aerial vehicle from the initial position to the target position into a multi-window solving problem in a sliding window mode. Similar to the global optimal trajectory control optimization problem, the optimal trajectory control optimization problem for the first local programming control window may be described as:
where g is a non-linear function to be optimized in relation to the parameters in brackets, in relation to the entire control process,
heuristic functions for residual cost, C k In order to be able to update the environmental constraints,
state feedback obtained for sensor sampling.
Selecting the shortest residual attack time as a guidance sub-target function, namely:
in the formula, r (kT) c +T p ) Optimizing the distance, v, between the position of the drone and the target position for the kth rolling window terminal moment c (kT c +T p ) The approaching speed of the unmanned aerial vehicle and the target position at the moment.
Selecting an avoidance sub-target function, and guiding the unmanned aerial vehicle to advance towards the direction of avoiding the threat, namely:
wherein (x (t), y (t), z (t)) is the position coordinate of the drone at the current time, (x (t), y (t), z (t)) is the position coordinate of the drone at the current time threat ,y threat ,z threat ) Position coordinates, x, for sudden threats a 、y b And z c The safe distances from the sudden threat in the three coordinate directions are respectively.
And 7: mapping a time interval from the starting time to the ending time of the unmanned aerial vehicle to obtain a numerical value interval;
recording the time interval of the optimal control problem as t epsilon [ t ∈ 0 ,t f ]Converting to a Nonlinear Programming problem (NLP), converting the time interval to tau e [ -1, + 1)]And let t e [ t ∈ [ [ t ] 0 ,t f ]Is divided into K grids, an
Performing a mapping transformation
τ＝[2t-(t k +t k-1 )]/(t k -t k-1 ),t k-1 <t k
dτ/dt＝2/(t k -t k-1 ),k＝1,2,...,K
And 8: and solving the control variable, the state variable, the constraint condition, the first performance index and the second performance index of the unmanned aerial vehicle of the next local planning control window by using an adaptive Radau pseudo-spectrum method under the guidance of the guidance subfunction and the avoidance subfunction according to the control variable, the state variable, the constraint condition, the first performance index and the second performance index of the unmanned aerial vehicle of the previous local planning control window in the numerical interval according to the time sequence to generate the global track of the unmanned aerial vehicle.
The first performance index is J time ＝t f -t 0 The second performance index is
The first performance index and the second performance index are comprehensively weighted as follows:
as an alternative embodiment of the present invention, step 8 includes:
step 81: grid division is carried out on each local planning control window by adopting an interval division network, and discretization is carried out on a control variable, a state variable, a constraint condition, a first performance index and a second performance index by adopting a fixed M-order interpolation polynomial;
step 82: according to the divided grids, under the guidance of the guide sub-function and the avoidance sub-target function, solving the optimal control problem of the control variable, the state variable, the constraint condition, the first performance index and the second performance index of the unmanned aerial vehicle of the next local planning control window, converting the optimal control problem into an NLP problem, and solving the NLP problem by adopting a sequence quadratic programming method;
step 83: taking a sign =1, if the grid k meets the error criterion, making k = k +1, and repeating the step 83; if K = K and sign =1, the algorithm is completed to obtain the calculated track; if K = K and sign =0, jumping to step 82, otherwise let sign =0;
step 84: if r k ≥r max Or N k >M, dividing a sub-network for the network K, enabling K = K +1, jumping to the Step 83, and jumping to Step2 if K = K;
and step 85: increasing the order of the interpolation polynomial of the kth sub-network, jumping to Step2 if K = K, otherwise jumping to Step 83;
step 86: and repeating the steps 81 to 85 to obtain the global track of the unmanned aerial vehicle.
The global interpolation polynomial approximation is carried out on the state variable and the control variable at a series of discrete points, and the state variable can be approximately expressed as K discrete point
In the formula (I), the compound is shown in the specification,
for the Lagrange interpolation polynomial,
for Lagrange-Gauss-Radau (LGR) configuration points of the kth grid,
the non-allocated point indicates the end time.
Control variables were measured at 1,2, K-1 grids with N k An approximation of a Lagrange polynomial of order,
interpolating a polynomial for Lagrange
Due to terminal time t f Not configured, the control variable of the Kth grid being N k -Lagrange polynomial approximation of order 1,
interpolating a polynomial for Lagrange
For state X (k) (tau) is derived
Substituting the state variable into a kinetic differential equation, and performing discrete processing on an LGR point to obtain
In the formula (I), the compound is shown in the specification,
is N at the k grid k ×(N k + 1) order Radau pseudo-spectral differential matrix.
Inequality constraint on Kth grid using N k Discretizing the LGR points to obtain
The edge value constraint can be approximately expressed as
The performance index function can be approximately expressed as
In this way, the optimal control problem of the continuous system is converted into a parameter optimization problem under a series of algebraic constraints, and a nonlinear programming method can be adopted for solving the problem.
First, the maximum allowable error is set to epsilon max Maximum allowable curvature ratio of r max The order of the initial interpolation polynomial is M. The algorithm optimization process comprises an error criterion, a curvature ratio criterion and a polynomial order criterion.
(1) Error criterion
Let the kth grid (K ∈ [ 1.,. K.,. K)]) The segment has L points which
The obtained state and the control amount are brought into the following formula
In the above formula, L is more than or equal to 1 and less than or equal to L, i is more than or equal to 1 and less than or equal to n, j is more than or equal to 1 and less than or equal to s, and for any i belongs to [1,2 ]]，j∈[1,2,...,s]And L is E [1,2]，
The error criterion is e max ≤ε max 。
(2) Criterion of curvature ratio
The state quantity estimated value of the kth section of the grid is recorded as
The curvature criterion is r k <r max 。
(3) Polynomial order criterion
N k Interpolating the order of a polynomial for a grid k, where the polynomial criterion is N k >M。
The invention provides an online autonomous flight path optimization control method for an unmanned aerial vehicle in a dynamic environment. Dividing the whole autonomous trajectory control interval of the unmanned aerial vehicle into a plurality of rolling optimization time windows by using a rolling time domain control strategy, and reasonably optimizing each section of trajectory; meanwhile, the flight time of the unmanned aerial vehicle reaching the target area and the threat probability are used as target functions, and a method capable of adaptively adjusting the weighting performance index and switching the sub-target functions is provided. And (3) continuously calculating on line by using a self-adaptive Radau pseudo spectrum method to realize the real-time control optimization of the online track of the unmanned aerial vehicle. The invention can carry out the ground penetration combat mission in the uncertain complex battlefield environment containing factors such as complex terrain obstacles, dynamic threat sources, time sensitive targets and the like, and greatly improves the timeliness, the accuracy and the degree of autonomy of the unmanned aerial vehicle penetration track control; meanwhile, the lower flight cost, the higher survival probability and the task completion probability of the unmanned aerial vehicle in the defense burst task are ensured, a new track can be readjusted according to new information, the algorithm has high convergence speed and high calculation precision, and the practical scene has strong practicability.
The invention relates to an online autonomous flight path optimization control method for an unmanned aerial vehicle in a dynamic environment.
The whole combat area is positioned in the horizontal plane for 30km multiplied by 30km, and the high-altitude range is 0,5000]And m is selected. The initial position of the unmanned plane is (0,0,500) m, the initial speed is 204m/s, the track inclination angle is theta =0 DEG, and the track drift angle is
Tangential overload limit of | n x (t) less than or equal to 2g, and normal overload limit is | n z (t) is less than or equal to 4g, and the limit of the roll angle is less than or equal to 50 degrees of gamma (t); when a weapon is thrown, the speed of the unmanned aerial vehicle is not less than 100m/s, and the track inclination angle is theta f =0 DEG, track deflection angle of
The battlefield known environment information is as follows: a cannon formation is arranged in the target area, and the position of the cannon formation is (5000,1000,0) m; two united warning radars are provided, the positions are (15000,5000,0) m and (15000,20000,0) m respectively, and the coverage range of all air defense units is 5km. In the process of defense penetration, the target can be maneuvered to a certain degree, and the final condition of the unmanned aerial vehicle attacking the target is that the distance between the unmanned aerial vehicle and the target is less than 500m, namely the whole track control optimization is stopped. The detection parameter of the early warning radar is c 1 ＝1.01，c 2 ＝1.25×10 -18 The RCS of the radar position and the target under the ideal condition is 1m 2 Has a maximum working distance of 30km. RCS model parameters were a =0.3172, b =0.1784 and c =1.003.
Case 1: considering that the target needs to perform a certain maneuver, the initial position of the target is set to be (25000,25000,0) m, and the target makes a uniform linear motion at a speed of 15 m/s.
Case 2: under the simulation conditions, the unmanned aerial vehicle needs to attack the ground target at 150s, assuming that the target motion speed is accelerated to 20m/s and the terminal time constraint is increased.
The simulation results are respectively shown in fig. 2 and fig. 3, and it can be seen from fig. 2 and fig. 3 that the unmanned aerial vehicle can perform autonomous trajectory control to complete a penetration task on the target under the condition of simple maneuvering on the target. The trajectory trend is substantially the same in both cases, whether for time-sensitive or non-time-sensitive targets. When unmanned aerial vehicle kept away from the target, unmanned aerial vehicle's overall movement can not receive the great influence of target motion. However, when the target approaches a certain distance, the influence of the change of the target position is enhanced, and the flight trajectory of the unmanned aerial vehicle needs to be continuously adjusted, which is reflected in trajectory fluctuation.
Furthermore, the terms "first", "second" and "first" are used for descriptive purposes only and are not to be construed as indicating or implying relative importance or implicitly indicating the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of the present invention, "a plurality" means two or more unless specifically defined otherwise.
While the present application has been described in connection with various embodiments, other variations to the disclosed embodiments can be understood and effected by those skilled in the art in practicing the claimed application, from a review of the drawings, the disclosure, and the appended claims. In the claims, the word "comprising" does not exclude other elements or steps, and the word "a" or "an" does not exclude a plurality.
The foregoing is a more detailed description of the invention in connection with specific preferred embodiments and it is not intended that the invention be limited to these specific details. For those skilled in the art to which the invention pertains, numerous simple deductions or substitutions may be made without departing from the spirit of the invention, which shall be deemed to belong to the scope of the invention.
Claims (8)
1. An online autonomous flight path optimization control method for an unmanned aerial vehicle in a dynamic environment is characterized by comprising the following steps:
step 1: establishing initial unmanned aerial vehicle kinematics and a kinetic equation according to flight parameters of the unmanned aerial vehicle in a dynamic environment;
step 2: adding conditional constraints to the kinematics and the dynamic equation of the initial unmanned aerial vehicle to obtain a nonlinear optimal control model;
the condition constraint comprises an initial constraint condition, a terminal condition constraint condition and a flight performance constraint condition, and the nonlinear optimal control model comprises the following steps: control variables and state variables;
and step 3: calculating the detection probability of the unmanned aerial vehicle detected by all the radars according to the correlation parameters between the current position of the unmanned aerial vehicle and the radars;
and 4, step 4: calculating a first performance index with minimum threat to the unmanned aerial vehicle according to the detection probability, and calculating a second performance index with minimum flight time of the unmanned aerial vehicle;
and 5: comprehensively weighting and optimizing the first performance index and the second performance index, and taking the optimized result as a target function;
step 6: optimizing the objective function by using the local planning control windows to convert the global minimum problem of the objective function into solving the objective function minimum problem in each local planning control window, obtain guide sub-objective functions of each local planning control window and establish unmanned aerial vehicle avoidance sub-objective functions;
and 7: mapping a time interval from the starting time to the ending time of the unmanned aerial vehicle to obtain a numerical value interval;
and 8: and in the numerical interval according to the time sequence, solving the control variable, the state variable, the constraint condition, the first performance index and the second performance index of the unmanned aerial vehicle of the next local planning control window by using an adaptive Radau pseudo-spectrum method under the guidance of the guidance subfunction and the avoidance subfunction according to the control variable, the state variable, the constraint condition, the first performance index and the second performance index of the unmanned aerial vehicle of the previous local planning control window, and generating the global track of the unmanned aerial vehicle.
2. The method for the online autonomous trajectory optimization control of the unmanned aerial vehicle in the dynamic environment according to claim 1, wherein the initial unmanned aerial vehicle kinematics and dynamics equations are as follows:
wherein (x, y, z) is the position coordinate of the unmanned aerial vehicle, V is the vacuum speed of the unmanned aerial vehicle, theta is the track inclination angle,
is a track deviation angle; n is a radical of an alkyl radical x For tangential overload, n z Normal overload and gamma roll angle.
3. The method for the online autonomous trajectory optimization control of the unmanned aerial vehicle in the dynamic environment according to claim 2,
the initial constraint conditions are as follows:
wherein, t 0 For the initial time of flight of the unmanned aerial vehicle, (x) 0 ,y 0 ,z 0 ) Is the coordinate of the initial position of the unmanned aerial vehicle, V 0 、θ 0 And
respectively the initial speed, initial track inclination angle and initial track deflection angle of the unmanned aerial vehicle, gamma 0 The initial roll angle;
the terminal constraints of the unmanned aerial vehicle are:
(x w ,y w ,z w ) For unmanned aerial vehicle weapon launch position coordinates, (x) f ,y f ,z f ) Terminal position coordinates for unmanned aerial vehicle trajectory control, t f For the time of flight terminal of the unmanned aerial vehicle, Δ x, Δ y and Δ z are allowable drop errors, V f 、θ f And
respectively the tail end speed, the tail end track inclination angle and the tail end track deflection angle of the unmanned aerial vehicle;
the flight performance constraint condition is
In the formula, t is the flight time of the unmanned aerial vehicle, z min And z max Minimum and maximum flying heights, V, of the unmanned aerial vehicle, respectively min And V max Minimum and maximum flight speeds, θ, respectively, of the drone min And theta max Respectively the minimum and maximum track inclination angles of the unmanned plane,
and
minimum and maximum flight path drift angles, gamma, respectively, for the drone min And gamma max Respectively the minimum and maximum roll angles of the drone,
is the maximum roll angle change rate of the unmanned plane, n xmax For maximum tangential overload of the drone, n zmax And the maximum normal overload of the unmanned aerial vehicle is realized.
4. The method for the online autonomous trajectory optimization control of the unmanned aerial vehicle in the dynamic environment according to claim 3, wherein the step 3 comprises:
step 31: establishing a radar threat model according to the correlation parameters of the unmanned aerial vehicle and the air defense radar;
step 32: establishing an unmanned aerial vehicle circumferential RCS model under the radar threat model;
step 33: and calculating the detection probability of the unmanned aerial vehicle detected by the thunder according to the circumferential RCS model of the unmanned aerial vehicle.
5. The method for the online autonomous trajectory optimization control of the unmanned aerial vehicle in the dynamic environment according to claim 4, wherein the radar threat model is expressed as:
in the formula (x) r ,y r ,z r ) The position coordinates of the enemy air defense radar are obtained, and r is the relative distance between the unmanned aerial vehicle and the enemy air defense radar;
the unmanned aerial vehicle circumferential RCS model is as follows:
wherein sigma is the scattering cross section area of the unmanned aerial vehicle radar, a, b and c are the characteristic parameters of the radar,
the probability of the instantaneous capture of the drone at a time is
In the formula, c 1 、c 2 Configuring parameters, R, for the radar itself t The relative distance between the unmanned aerial vehicle and the radar at the moment is, and sigma is the radar scattering sectional area of the unmanned aerial vehicle at the moment;
when n air defense radar sites of enemies form the combined air defense system, the detection probability of the air defense system to the unmanned aerial vehicle is
Wherein i represents the serial number of the air defense radars, n represents the total number of the air defense radars, and P T (i) Representing the probability that each air defense radar is instantaneously captured.
6. The method for the online autonomous trajectory optimization control of the unmanned aerial vehicle in the dynamic environment according to claim 5,
the first performance index is J time ＝t f -t 0 The second performance index is
The integrated weighting of the first performance index and the second performance index is as follows:
in the formula, ω 1 、ω 2 As a weighting coefficient, P (X (t)) is the probability of being captured by all radars in the current time state of the drone;
the objective function is
In the formula, r (t) is the distance between the position of the unmanned aerial vehicle at the current moment and the attack target reference point, and v (t) is the approaching speed of the unmanned aerial vehicle and the attack target reference point at the moment.
7. The method for optimizing and controlling the unmanned aerial vehicle online autonomous flight path under the dynamic environment according to claim 6, wherein solving the objective function minimization problem in each local planning control window is represented as:
where g is a non-linear function to be optimized in relation to the parameters in brackets, in relation to the entire control process,
heuristic functions for residual cost, C k In order to be able to update the environmental constraints,
state feedback obtained for sensor sampling;
the guide sub-targeting function is:
in the formula, r (kT) c +T p ) Optimizing the distance, v, between the position of the drone and the target position for the kth rolling window terminal moment c (kT c +T p ) Therefore, the approaching speed of the unmanned aerial vehicle and the target position at the moment;
unmanned plane avoidance sub-objective function of
Wherein (x (t), y (t), z (t)) is the position coordinate of the drone at the current time, (x) threat ,y threat ,z threat ) Position coordinates, x, for sudden threats a 、y b And z c The safe distances from the sudden threat in the three coordinate directions are respectively.
8. The method for the online autonomous trajectory optimization control of the unmanned aerial vehicle in the dynamic environment according to claim 7, wherein step 8 comprises:
step 81: grid division is carried out on each local planning control window by adopting an interval division network, and discretization is carried out on a control variable, a state variable, a constraint condition, a first performance index and a second performance index by adopting a fixed M-order interpolation polynomial;
step 82: according to the divided grids, under the guidance of the guide sub-function and the avoidance sub-target function, solving the optimal control problem of the control variable, the state variable, the constraint condition, the first performance index and the second performance index of the unmanned aerial vehicle of the next local planning control window, converting the optimal control problem into an NLP problem, and solving the NLP problem by adopting a sequence quadratic programming method;
step 83: taking a sign =1, if the grid k meets the error criterion, making k = k +1, and repeating the step 83; if K = K and sign =1, the algorithm is completed to obtain the calculated track; if K = K and sign =0, jumping to step 82, otherwise let sign =0;
step 84: if r k ≥r max Or N k >M, dividing a sub-network for the network K, enabling K = K +1, jumping to the Step 83, and jumping to Step2 if K = K;
and step 85: increasing the order of the interpolation polynomial of the kth sub-network, jumping to Step2 if K = K, otherwise jumping to Step 83;
step 86: and repeating the steps 81 to 85 to obtain the global track of the unmanned aerial vehicle.
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| GB2628013A (en) * | 2023-02-28 | 2024-09-11 | Beijing Institute Tech | Method and system for unmanned aerial vehicle (UAV) path planning and tracking control and electronic device |
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