Fixed-wing Target Tracking Method Based on Quadratic Optimization of Bessel Curve

Abstract

The present invention discloses a fixed-wing target tracking method based on quadratic optimization of Bessel curves. The position of the observed target and its timestamp obtained through real-time observation on the fixed wing are stored as data. A loss function is established based on the Bessel curve, and then the constraints of the loss function are established. The initial predicted tracking trajectory of the Bessel curve is determined by solving the minimization target. The predicted target position at the next moment is determined on the initial predicted tracking trajectory. Between the real-time observed target position and the predicted target position, the final preset trajectory is established through the Dubins curve to achieve target tracking. Tracking the target by the predicted trajectory in the present invention can improve the pursuit speed of the fixed wing. At the same time, when the target is lost, it can continue to move forward according to the predicted trajectory to search for the target again, greatly reducing the target tracking speed and increasing the possibility of reducing target loss.

Description

Technical Field

[0001] The present invention relates to a planning and control method for a fixed-wing to track a target in the field of unmanned aerial vehicle technology, in particular to a method for generating a predicted motion trajectory when a fixed-wing unmanned aerial vehicle tracks a target and then realizing target tracking, mainly involving the secondary optimization of a Bezier curve and the generation of the motion trajectory of the fixed-wing unmanned aerial vehicle. Background Art

[0002] When the flight speed of a fixed-wing is relatively fast, it is difficult to achieve fast tracking and problems such as target loss are likely to occur. It is necessary to predict the trajectory and generate a trajectory that conforms to the motion of the fixed-wing for faster target tracking and reducing the loss probability. Since there is relatively little research on fixed-wing target pursuit currently, no relevant research data has been found.

[0003] Domestically, there is an application that constrains the Bezier curve based on a safety corridor and optimizes the trajectory to find a collision-free path. However, it is mainly used for quadrotors and does not involve the trajectory optimization of fixed-wings. There is relatively little research on optimizing the motion trajectory of a fixed-wing when it quickly tracks a target. Summary of the Invention

[0004] In order to solve the problems in the background art, the present invention proposes a fixed-wing target tracking method based on the secondary optimization of the Bezier curve, which solves the technical problems that the fixed-wing has a fast flight speed and is subject to dynamic constraints and is prone to losing the target when tracking the target.

[0005] To achieve the above object, the technical solution of the present invention includes the following steps:

[0006] S1. The current position of the target is observed in real time on the fixed-wing as the observed target position, and the observed target position and its corresponding timestamp information are formed into data for storage; the timestamp is the moment.

[0007] S2. A loss function is established according to the Bezier curve, and then the constraints of the loss function are established.

[0008] S3. The observed target positions and their corresponding timestamp data at all historical moments obtained in S1 are input into the loss function, and the optimal parameters of the Bezier curve are obtained by solving with the goal of minimizing the loss function, and then the optimal Bezier curve is determined as the preliminary predicted tracking trajectory.

[0009] S4. Then, the point at the next moment is determined as the predicted target position as the target point in chronological order on the preliminary predicted tracking trajectory. Between the observed target position obtained in real time and the predicted target position, the final preset trajectory of the fixed-wing is established through the Dubins curve with the minimum turning radius of the fixed-wing as the constraint, and then the fixed-wing flight is controlled to track the target.

[0010] A gimbal is installed on the fixed-wing, and a camera is installed on the gimbal. The camera captures images of the target, and after image analysis and processing, the position of the target is obtained.

[0011] Based on the observed target position, the present invention establishes and obtains a trajectory through Bessel curve fitting, and then substitutes the time to obtain the predicted target position.

[0012] The specific loss function is as follows:

[0013]

[0014] where J pre represents the loss value between the predicted target and the actual target position, represents the square of the second norm, B(t i ) is the predicted target position at the i-th moment t i , is the observed target position at the i-th moment t i , is the weight at the i-th moment t i , ω p is the weight of the second-order orthogonal term, used to avoid overfitting; t1 represents the initial first moment, t L represents the current moment, L is the time length up to the current moment, and i represents the serial number of the moment; is the Bessel curve coefficient at the moment t, c u is the position coordinate of the u-th control point of the Bessel curve, u represents the serial number of the control point of the Bessel curve, and n represents the total number of control points of the Bessel curve; is the Bessel curve coefficient at the i-th moment t i , B(t) is the predicted target position at the moment t; B (2) (t) represents the second derivative of the predicted target position B(t), where is the quadratic orthogonal term.

[0015] In this embodiment, a fifth-order Bessel curve is adopted, n is 5, and the schematic diagram of the fifth-order Bessel curve is as shown in Figure 2 .

[0016] The weight i at the i-th moment t in the loss function is specifically set as:

[0017]

[0018] where t L is the current moment, t i is the historical i-th moment, k t represents the preset time weight coefficient. As can be seen from the above formula, as time goes by, tL -t i The value of is getting larger, and the weight of the corresponding moment

[0019] is getting lower. The present invention uses a double tangent curve to design the weight in the objective function, so that the weight decreases with time. The earlier the observed moment is, the lower the weight is in the loss function, thereby optimizing the confidence of the observed target position between different moments and achieving accurate target tracking.

[0020] The present invention adds a designed second-order orthogonal term to the loss function, which can avoid overfitting and minimize the difference between the target trajectory and the observed distance.

[0021] The present invention establishes a loss function based on the weight designed by the double tangent curve and the difference between the observed target position and the predicted target position generated by the Bezier curve, and adds a second-order orthogonal term to avoid overfitting, which can track the target better and achieve accurate tracking.

[0022] The constraints in the loss function include predicted velocity and acceleration constraints [-v mp , v mp , [-a mp , a mp . Inequality constraints are established from the predicted velocity and acceleration constraints:

[0023] -v mp ≤n·(c u -c u-1 )≤v mp

[0024] -a mp ≤n·(n - 1)·(c u -2c u-1 +c u-2 ) / s t ≤a mp

[0025] where n is the order of the Bezier curve, s t is the time scale parameter, c u is the position coordinate of the u-th control point of the Bezier curve, c u-1 is the position coordinate of the (u - 1)-th control point of the Bezier curve, c u-2 is the position coordinate of the (u - 2)-th control point of the Bezier curve, v mp represents the predicted velocity constraint of the target, and a mp represents the predicted acceleration constraint of the target.

[0026] The Bezier curve is enclosed in the convex hull formed by connecting its control points. The present invention utilizes the convex hull property of the Bezier curve to constrain the positions of the control points. By differentiating the Bezier curve, it remains a Bezier curve. The present invention linearly represents the control points with the control points of a lower-order Bezier curve using the derivative property of the Bezier curve.

[0027] The present invention adds inequality constraints for predicting velocity and acceleration constraints based on the convex hull property and derivative property of the Bezier curve to make the target trajectory feasible.

[0028] In the step S3, the second norm of the Bezier curve is positive definite. Regarding the loss function and its constraints as a quadratic optimization problem with constraints, the open-source OOQP solver is used to solve the loss function and its constraints, obtaining each control point in the Bezier curve and getting the optimal preliminary predicted tracking trajectory.

[0029] Since the second norm of the Bezier curve is positive definite, the present invention performs quadratic optimization on the loss function, calculates the optimal solution that minimizes the difference between the observed target position and the predicted target position, and obtains the preliminary predicted tracking trajectory.

[0030] In the step S4, specifically, by setting up a Dubins path calculation module, the shortest fixed-wing motion trajectory to reach the target is generated as the final preset trajectory according to the turning radius interval [RMIN, RMAX] of the fixed wing and the predicted target position.

[0031] The beneficial effects of the present invention are as follows:

[0032] The present invention can improve the pursuit speed of the fixed wing from the trajectory tracking target. At the same time, when the target is lost, it can continue to move forward according to the predicted trajectory, re-search for the target, greatly reducing the target tracking speed and increasing the speed of the fixed wing tracking the target and reducing the possibility of target loss. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] The drawings forming a part of this application are used to provide a further understanding of the present invention. The schematic embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute an improper limitation of the present invention.

[0034] Figure 1 is a schematic diagram of the architecture of the present invention;

[0035] Figure 2 is a schematic diagram of a Bezier curve;

[0036] Figure 3 is a schematic diagram of a predicted trajectory;

[0037] Figure 4 is a ROS simulation effect diagram. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0038] To make the objectives, technical solutions, and advantages of the present invention more clear and understandable, the present invention will be further described in detail below in conjunction with the embodiments and the drawings. Herein, the illustrative embodiments of the present invention and their descriptions are used to explain the present invention, but do not limit the present invention.

[0039] As Figure 1 shown, the embodiments of the present invention and their implementation processes are as follows:

[0040] S1. The current position of the observation target is observed in real time on the fixed wing as the observation target position, and the observation target position and its corresponding timestamp information are formed into data for storage; the timestamp is the moment.

[0041] A pan-tilt is installed on the fixed wing, and a camera is installed on the pan-tilt. The camera captures an image of the target and then obtains the target position through image analysis and processing.

[0042] S2. A loss function is established based on the Bessel curve, and then constraints of the loss function are established.

[0043] The loss function is specifically as follows:

[0044]

[0045] Where J pre represents the loss value between the predicted target position and the actual target position, represents the square of the second norm, B(t i ) is the predicted target position at the i-th moment t i , is the observed target position at the i-th moment t i , is the weight at the i-th moment t i , ω p is the weight of the second-order orthogonal term, which is used to avoid overfitting; t1 represents the initial first moment, t L represents the current moment, L is the time length up to the current moment, and i represents the serial number of the moment; is the Bessel curve coefficient at the moment t, c u is the coordinate of the u-th control point position of the Bessel curve, u represents the serial number of the control point of the Bessel curve, and n represents the total number of control points of the Bessel curve; is the Bessel curve coefficient at the i-th moment t i , B(t) is the predicted target position at the moment t; B (2) (t) represents the second derivative of the predicted target position B(t), where is the quadratic orthogonal term.

[0046] In this embodiment, a fifth-order Bessel curve is adopted, n is 5, and the schematic diagram of the fifth-order Bessel curve is as Figure 2As shown

[0047] The weight at the \(i\)-th moment \(t\) in the loss function i is Specifically set as:

[0048]

[0049] where \(t\) L is the current moment, \(t\) i is the \(i\)-th historical moment, and \(k\) t represents a preset time weight coefficient. From the above formula, as time \(t\) L - \(t\) i increases, the weight of the corresponding moment becomes lower and lower.

[0050] The constraints in the loss function include prediction speed and acceleration constraints \([-v\) mp , \(v\) mp , \([-a\) mp , \(a\) mp . Inequality constraints are established from the prediction speed and acceleration constraints:

[0051] - \(v\) mp ≤ \(n\cdot(c\) u - \(c\) u-1 ) ≤ \(v\) mp

[0052] - \(a\) mp ≤ \(n\cdot(n - 1)\cdot(c\) u - 2\(c\) u-1 +\(c\) u-2 ) / \(s\) t ≤ \(a\) mp

[0053] where \(n\) is the order of the Bezier curve, \(s\) t is the time scale parameter, \(c\) u is the position coordinate of the \(u\)-th control point of the Bezier curve, \(c\) u-1 is the position coordinate of the \((u - 1)\)-th control point of the Bezier curve, \(c\) u-2 is the position coordinate of the \((u - 2)\)-th control point of the Bezier curve, \(v\) mp represents the prediction speed constraint of the target, and \(a\) mp represents the prediction acceleration constraint of the target.

[0054] S3. Input the observed target positions and their corresponding moment data at all historical moments obtained in S1 into the loss function, and solve with the goal of minimizing the loss function to obtain the parameters of the optimal Bezier curve, and then determine the optimal Bezier curve as the preliminary prediction tracking trajectory;

[0055] The second norm of the Bezier curve is positive definite. Regarding the loss function and its constraints as a quadratic optimization problem with constraints, the open-source solver OOQP is used to solve the loss function and its constraints, obtaining each control point in the Bezier curve and getting the optimal preliminary predicted tracking trajectory.

[0056] S4. Then, on the preliminary predicted tracking trajectory, the point at the next moment is determined in chronological order as the predicted target position, which is the target point. Between the real-time obtained observed target position and the predicted target position, with the minimum turning radius of the fixed-wing as the constraint, the final preset trajectory of the fixed-wing is established through the Dubins curve, and then the fixed-wing flight is controlled to track the target.

[0057] The specific implementation is to set up a Dubins path calculation module, and generate the shortest fixed-wing motion trajectory to reach the target as the final preset trajectory according to the turning radius interval [RMIN, RMAX] of the fixed-wing and the predicted target position.

[0058] As Figure 3 shown, the solid line part is the target position curve of past observations, and the dashed line part is the predicted target position curve.

[0059] As Figure 4 shown is the simulation effect diagram in the ROS operating system. The car is the target to be tracked, the fixed-wing aircraft is the fixed-wing UAV used for tracking in the present invention, the thick curve is the predicted target motion curve, and the thin curve is the fixed-wing predicted motion trajectory generated based on the predicted target position.

[0060] Aiming at the disadvantage that the fixed-wing UAV is not flexible in target tracking due to dynamic constraints, the present invention designs a target tracking method based on quadratic optimization of the Bezier curve, obtains the preliminary predicted tracking trajectory of the target in the future for a period of time, determines the predicted target position at the next moment on the preliminary predicted tracking trajectory, and between the real-time observed target position and the predicted target position, establishes the final preset trajectory through the Dubins curve. The fixed-wing UAV obtains the motion trajectory in advance, improves the tracking speed, and greatly reduces the probability of target loss during the target tracking of the fixed-wing UAV.

Claims

1. A fixed-wing target tracking method based on quadratic optimization of Bezier curves, characterized in that The method includes the following steps: S1. The current position of the observed target is observed in real time on the fixed wing as the observed target position, and the observed target position and its corresponding timestamp information are formed into data for storage; S2. A loss function is established according to the Bezier curve, and then the constraints of the loss function are established; S3. The observed target positions and their corresponding time data at all historical moments obtained in S1 are input into the loss function, and the parameters of the optimal Bezier curve are obtained by solving with the goal of minimizing the loss function, and then the optimal Bezier curve is determined as the preliminary prediction tracking trajectory; S4. Then, the point at the next moment is determined as the predicted target position in chronological order on the preliminary prediction tracking trajectory. Between the observed target position obtained in real time and the predicted target position, the final preset trajectory of the fixed wing is established through the Dubins curve with the minimum turning radius of the fixed wing as the constraint, and then the fixed wing flight is controlled to track the target; The specific form of the loss function is as follows: Among them, J pre represents the loss value between the predicted target and the actual target position, represents the square of the second norm, B(t i ) is the predicted target position at the i-th moment t i , is the observed target position at the i-th moment t i , is the weight at the i-th moment t i , ω p is the weight of the second-order orthogonal term; t1 represents the initial first moment, t L represents the current moment, L is the time length up to the current moment, and i represents the serial number of the moment; is the Bezier curve coefficient at time t, c u is the position coordinate of the u-th control point of the Bezier curve, u represents the serial number of the control point of the Bezier curve, and n represents the total number of control points of the Bezier curve; is the Bezier curve coefficient at the i-th moment t i , B(t) is the predicted target position at time t; B (2) (t) represents the second derivative of the predicted target position B(t); The weight of the $i$-th moment $t$ in the loss function i is specifically set as follows: Among them, t L is the current moment, t i is the i-th moment, k t represents the time weight coefficient.

2. The fixed-wing target tracking method based on quadratic optimization of Bezier curves according to claim 1, characterized in that: The constraints in the loss function include predicted velocity and acceleration constraints [-v mp , v mp , [-a mp , a mp . Inequality constraints are established from the predicted velocity and acceleration constraints: -v mp ≤n·(c u -c u-1 )≤v mp -a mp ≤n·(n - 1)·(c u -2c u-1 +c u-2 ) / s t ≤a mp where n is the order of the Bézier curve, s t is the time scale parameter, c u is the position coordinate of the u-th control point of the Bézier curve, c u-1 is the position coordinate of the (u-1)-th control point of the Bézier curve, c u-2 is the position coordinate of the (u-2)-th control point of the Bézier curve, v mp represents the predicted velocity constraint of the target, a mp represents the predicted acceleration constraint of the target.

3. The fixed-wing target tracking method based on quadratic optimization of Bezier curves according to claim 1, characterized in that: In step S3, the loss function and its constraints are regarded as a quadratic optimization problem with constraints, and the OOQP open-source solver is used to solve the loss function and its constraints to obtain each control point in the Bezier curve, and the optimal preliminary prediction tracking trajectory is obtained.

4. The fixed-wing target tracking method based on quadratic optimization of Bezier curves according to claim 1, characterized in that: In step S4, specifically, by setting a Dubins path calculation module, the shortest fixed wing motion trajectory to reach the target is generated according to the turning radius interval [RMIN, RMAX] of the fixed wing and the predicted target position as the final preset trajectory.

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