An end angle constraint guidance method using three-dimensional vector rotation

Abstract

The application discloses a terminal angle constraint guidance method adopting three-dimensional vector rotation, which can realize rotation track around an optimal space rotation shaft under the condition of meeting terminal angle constraint. The application innovatively proposes a mode of describing motion law by space vector and calculating the optimal space rotation shaft, instead of the strategy of realizing three-dimensional space guidance by adopting multi-direction decoupling in the traditional guidance method, so that the aircraft can attack the target according to the determined angle in the shortest rotation angle mode by space rotation of the vector rotation shaft and estimation of the remaining flight time. The application firstly determines the optimal rotation shaft according to the current relative position and velocity unit vector; secondly determines the expected rotation included angle and the rotation shaft according to the expected attack vector; and finally calculates the guidance law by estimating the remaining flight time, so as to realize the optimal space angle rotation to approach the target.

Description

Technical Field

[0001] This invention belongs to the field of guidance technology, specifically relating to an end-effector angle constraint guidance method using three-dimensional vector rotation. Background Technology

[0002] With the development of modern warfare, the requirements for guidance technology of aircraft such as missiles, drones, and loitering munitions are becoming increasingly higher. If the guidance law can achieve the purpose of striking the target in the preset attack direction by shaping the trajectory and making reasonable use of overload capacity, the capabilities of the aircraft will be maximized and the combat effectiveness will be improved.

[0003] Traditional guidance laws typically require decomposing the guidance law into two orthogonal directions, pitch and yaw, to complete guidance independently. However, this method can lead to ambiguity due to the gimbal lock problem of Euler angles when the angle exceeds 90° or 180°, affecting the adaptability of the guidance law. Secondly, a reasonable selection of the space axis can effectively shorten the guidance cycle, reduce the need for terminal overload, and facilitate approaching the desired direction. Summary of the Invention

[0004] To overcome the shortcomings of existing technologies, this invention provides a three-dimensional vector rotation-based end-effector angle constraint guidance method, which can achieve a rotation trajectory around an optimal spatial axis while satisfying end-effector angle constraints. This invention innovatively proposes using spatial vectors to describe the motion law and calculate the optimal spatial axis of rotation, replacing the traditional guidance method's strategy of multi-directional decoupling to achieve three-dimensional spatial guidance. By using vector axis spatial rotation and estimating the remaining flight time, the aircraft can smoothly attack the target at a predetermined angle with the shortest possible turn. This invention first determines the optimal axis of rotation based on the current relative position and velocity unit vector; secondly, it determines the desired rotation angle and axis of rotation based on the desired attack vector; finally, it calculates the guidance law by estimating the remaining flight time to achieve the optimal spatial angle rotation to approach the target.

[0005] The technical solution adopted by this invention to solve its technical problem is as follows:

[0006] Step 1: Set the unit vector direction;

[0007] Step 2: Calculate the rotation angle;

[0008] Step 3: Estimate the remaining flight time;

[0009] Step 4: Construct the guidance law expression;

[0010] Preferably, step 1 specifically comprises:

[0011] Let the velocity v and the target line length r be respectively:

[0012] v = ||v||, r = ||r|| (1)

[0013] For a given desired impact vector direction u d Calculate the unit velocity vector u v , Bullet line unit vector u r Line of sight rotation unit vector u ε and the expected impact rotation vector u δ As shown below:

[0014]

[0015] The rotational angular velocity of the target vector is:

[0016]

[0017] Preferably, step 2 specifically comprises:

[0018] Let ε represent the velocity vector u v and the target line vector u r The included angle; δ represents the target line vector u. r and the expected angle vector u d The angle between the two sides, according to the rules for calculating vector angles, is:

[0019]

[0020] The guidance law along the rotation axis u ε Rotate by an angle ε, while simultaneously rotating around the axis u δ The shortest guidance path is achieved by rotating the angle δ to approach the target.

[0021] Let γ be u ε ,u δ The included angle controls the twisting of the trajectory in space, and its expression is as follows:

[0022] γ=cos -1 (u ε ·u δ (5).

[0023] Preferably, step 3 specifically comprises:

[0024] The arc length of a smooth spatial curve is related to the initial and final angles. According to the arc length formula for spatial curves, the remaining time t can be obtained using the curve integral expression of the second kind. go The expression is:

[0025]

[0026] Approximately expressed as:

[0027]

[0028] Preferably, step 4 specifically comprises:

[0029] The guidance law requires that ε→0 and δ→0 upon impact with the target; therefore, to simultaneously eliminate the two angular errors within a specified time, the expression for the acceleration vector is constructed as follows:

[0030]

[0031] Where K1 and K2 are guidance law design parameters; the first term on the right-hand side of the equation is -K1·ω r ×v indicates that the projectile-target line vector and velocity vector gradually converge, which is the guiding term generated by the proportional guidance law, aiming to guide the direction of motion towards the target; the second term Indicates the specified time t go The internal requirement is that the velocity direction of the landing point and the vector of the desired landing angle are collinear, which means that the direction of motion points towards the target in the set direction within a given time range;

[0032] Simplifying equation (8) yields the expression for the guidance law:

[0033]

[0034] A computer program that causes a computer to perform the aforementioned end-angle constraint guidance method.

[0035] An electronic device includes: a processor and a memory; the memory is used to store a computer program, and the processor is used to execute the computer program stored in the memory to cause the electronic device to perform the above-described end-angle constraint guidance method.

[0036] A computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the aforementioned end-angle constraint guidance method.

[0037] A chip includes a processor for calling and running a computer program from a memory, causing a device on which the chip is mounted to perform the aforementioned end-angle constraint guidance method.

[0038] A computer program product includes a computer storage medium storing a computer program, the computer program including instructions executable by at least one processor, which, when executed by the at least one processor, implement the aforementioned end-angle constraint guidance method.

[0039] The beneficial effects of this invention are as follows:

[0040] This invention has been successfully applied to the design and development of a certain type of aircraft. The designed guidance law can achieve the effect of striking in any direction under the condition that the capability allows. This method has a very broad application prospect and has great practical value for real-time terminal strikes at a specific angle of attack on vulnerable parts of the target. Attached Figure Description

[0041] Figure 1 This is a schematic diagram of spatial vectors and spatial angles in three-dimensional flight.

[0042] Figure 2 This is a schematic diagram for calculating the length of a space curve;

[0043] Figure 3 This is a schematic diagram of a three-dimensional ballistic curve;

[0044] Figure 4 This is a schematic diagram of the longitudinal, lateral, and resultant acceleration curves;

[0045] Figure 5 This is a schematic diagram of the angle during the guidance process;

[0046] Figure 6 This is a schematic diagram illustrating the remaining time estimation.

[0047] Figure 7 This is a schematic diagram of a three-dimensional ballistic trajectory from multiple angles.

[0048] Figure 8 A schematic diagram of longitudinal, lateral, and resultant acceleration curves from multiple angles;

[0049] Figure 9 This is a schematic diagram of the angles during the multi-angle guidance process;

[0050] Figure 10 This is a schematic diagram of multi-angle remaining time estimation. Detailed Implementation

[0051] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0052] To address the issue of non-singular three-dimensional ballistic guidance for aircraft when the terminal vector direction is given, this invention provides a method that uses spatial vectors to describe the optimal spatial axis of rotation and spatial angle. This avoids the problem of using Euler angles for pitch and yaw directions, which are singular. The direction of the force is calculated using spatial vectors to generate the guidance law, allowing the aircraft to reach the desired target vector with the shortest flight angle and the optimal axis of rotation, thus reducing the requirements for overload in the terminal phase.

[0053] A schematic diagram of the guidance law design scheme is shown below. Figure 1 As shown. Where the velocity vector v revolves around the vector axis u ε Approaching the target line vector r, while the target line r tends to revolve around u δ Approaching the desired landing angle vector ud ;u d Let ε represent the normal direction of the projection plane; ε represents the angle between the velocity vector and the target vector; δ represents the angle between the target vector and the desired angle of impact vector. The guidance problem is to solve for the expression of the acceleration vector a based on the above vectors and angles, and let a = ||a|| represent the magnitude of the acceleration.

[0054] The design steps are described below:

[0055] Step 1: Set the direction of the unit vector;

[0056] Let the velocity v and the target line length r be respectively:

[0057] v = ||v||, r = ||r|| (10)

[0058] For a given desired impact vector direction u d like Figure 1 As shown. Calculate the unit velocity vector u. v , Bullet line unit vector u r Line of sight rotation unit vector u ε and the expected impact rotation vector u δ As shown below:

[0059]

[0060] The rotational angular velocity of the target vector is:

[0061]

[0062] Step 2: Calculate the rotation angle;

[0063] Let ε represent the velocity vector u v and the target line vector u r The included angle; δ represents the target line vector u. r and the expected angle vector u d The angle between the two sides, according to the rules for calculating vector angles, is:

[0064] ε=cos -1 (u v ·u r ), δ=cos -1 (u r ·u d (13)

[0065] Clearly, the guidance law is along the rotation axis u ε Rotate by an angle ε, while simultaneously rotating around the axis u δ The rotation angle δ approaches the target to find the shortest guidance path. Let γ be u. ε ,u δThe included angle, usually a small angle, controls the twisting of the trajectory in space, and is expressed as follows:

[0066] γ=cos -1 (u ε ·u δ (14)

[0067] Step 3: Estimate the remaining flight time;

[0068] like Figure 2 As shown, the arc length of a smooth spatial curve is related to the initial and final angles. According to the arc length formula for spatial curves, using the curve integral expression of the second kind, the remaining time t is... go The expression is:

[0069]

[0070] This integral can be approximated as:

[0071]

[0072] Step 4: Construct the guidance law expression;

[0073] The guidance law requires that ε→0 and δ→0 upon impact with the target. Therefore, to simultaneously eliminate the two angular errors within a specified time, the expression for the acceleration vector is constructed as follows:

[0074]

[0075] Where K1 and K2 are the guidance law design parameters. The first term in the equation on the right-hand side is -K1·ω. r ×v indicates that the projectile-target line vector and velocity vector gradually converge, which is the guiding term generated by the proportional guidance law, aiming to guide the direction of motion towards the target; the second term Indicates the specified time t go The internal requirement is that the velocity direction at the point of impact and the vector of the desired angle of impact are collinear, meaning that the direction of motion points towards the target in the set direction within a given time range. Simplifying the above equation yields the expression for the guidance law:

[0076]

[0077] From the above expression, we can see that t go The accuracy of the estimation affects the performance of the guidance law, when t go When the estimate is too large, the overload pressure gradually increases; when t go When the estimation is small, the overload pressure gradually decreases, but it is prone to causing a large detour. Therefore, the estimation accuracy is higher when both ε and γ are small angles.

[0078] Example:

[0079] This technology is further described using a scenario involving a directional angle attack by an aircraft. Assume the aircraft completes initial guidance, and the start of terminal guidance is the initial moment of the simulation. At this moment, the target's position in the launch coordinate system is [5000 0 0]. T The coordinates of the spacecraft relative to the launch system are [2000 300 50]. T The velocity v, trajectory inclination angle, and trajectory deviation angle are 300 m / s, 10°, and 10° respectively, and the desired landing angle vector u is... d = [-0.5 -0.85 -0.17] T This means the impact angle is 120° longitudinally and 10° laterally. This impact angle is typical of a reverse-slope attack method with an additional lateral attack angle. Assume the basic parameters of the aircraft are as follows:

[0080] Step 1: Calculate the direction of the unit vector;

[0081] Assume an initial time of 0, a velocity v = 300, and a target line of reference r = 3015.4. Calculate the unit vectors in the target frame:

[0082] Velocity vector:

[0083] Bullet line vector:

[0084] Direction of the rotation axis of the bullet target line:

[0085] Desired impact rotation axis vector direction:

[0086] Step 2: Calculate the rotation angle;

[0087] velocity vector u v and the target line vector u r The included angle:

[0088] ε=cos -1 (u v ·u r )=cos -1 ([0.970.17-0.17]·[0.990.1-0.02])=0.3151rad

[0089] Projectile line vector u r and the expected angle vector u d The included angle:

[0090] δ=cos -1 (u r ·u d )=cos -1([0.990.1-0.02]·[-0.5-0.85-0.17])=1.9847rad

[0091] u ε ,u δ The resulting ballistic twist angle:

[0092] γ=cos -1 (u ε ·u δ )=cos -1 ([0.060.50.86]·[-0.003-0.20.98])=0.7329rad

[0093] Step 3: Estimate remaining flight time;

[0094]

[0095] Step four: Calculate the guidance law;

[0096] Given guidance parameters K1 = 4 and K2 = 2, the guidance law calculation results are as follows:

[0097]

[0098] Overload under velocity system in Let be the rotation matrix from the target frame to the velocity frame.

[0099] Guidance law expressions in the target coordinate system were designed in three directions following the steps described above. The results of these guidance laws were then substituted into the flight dynamics equations to complete closed-loop simulation verification. The mass is assumed to be 20 kg, and the reference area is 0.02 m². 2 Aerodynamic drag coefficient: C D (Ma,χ)=0.5-2Ma+3Ma+0.004χ 2 Lift and lateral force coefficients: C L (Ma,α)=0.2α,C Z (Ma,β)=-0.2β. Where Ma is the flight Mach number, α is the angle of attack, β is the sideslip angle, and χ=cos -1 (cosα·cosβ) is the combined angle of attack.

[0100] To verify the guidance capability of the algorithm, the aircraft was controlled using STT (Side-Trip Time) mode, limiting the maximum angle of attack and maximum sideslip angle to no more than 14° and 6° respectively. This angle limit restricts the upper limit of usable overload capacity, making the simulation results more practically relevant. The simulation results are as follows: Figures 3-6 As shown. Figure 3 The flight trajectory in a three-dimensional space scene is shown, and the guidance law enables the aircraft to hit the target in a predetermined direction. Figure 4The values ​​from top to bottom represent the pitch acceleration, yaw acceleration, and resultant acceleration, respectively. All overload signals meet the available overload limits. Figure 5 The angles from top to bottom represent the angle between velocity and target line, the angle between current target line and desired vector, and the angle between current axis of rotation and desired axis of rotation, respectively. The simulation shows the process of the three angles gradually converging to 0. Figure 6 The remaining flight time is estimated, and simulations show that the remaining time estimate becomes increasingly accurate as the missile-target distance decreases.

[0101] To verify the adaptability of the guidance law, additional simulations were performed for longitudinal impact angles of 60°, 70°, 80°, 90°, 100°, 110°, 120°, 130°, 140°, 150°, and 160°, yielding guidance results. Figures 7-10 As shown in the figure. The simulation results show that within the range of the guidance law, the flight trajectory achieves the trajectory in three-dimensional space with the minimum turning angle, without any singularities, and achieves all-angle guidance within the usable overload capacity range.

Claims

1. A method for end-effector angle constraint guidance employing three-dimensional vector rotation, characterized in that, Includes the following steps: Step 1: Set the unit vector direction; Set speed and bullet eye line length They are respectively: For a given desired impact vector direction Calculate the unit velocity vector Bullet line unit vector Line of sight rotation unit vector and expected impact rotation vector As shown below: The rotational angular velocity of the target vector is: Step 2: Calculate the rotation angle; set up Represents velocity vector and bullet target line vector The included angle; Represents the target line vector and expected landing angle vector The angle between the two sides, according to the rules for calculating vector angles, is: Guidance law along the axis of rotation Rotation angle Simultaneously around the axis of rotation Rotation angle Approaching the target is the shortest guidance path; set up for The included angle controls the twisting of the trajectory in space, and its expression is as follows: Step 3: Estimate the remaining flight time; The arc length of a smooth spatial curve is related to the initial and final angles. Based on the arc length formula for spatial curves, the remaining time can be obtained using the curve integral expression of the second kind. The expression is: Approximately expressed as: Step 4: Construct the guidance law expression; The guidance law requires that upon impact with the target, it must satisfy... Therefore, to simultaneously eliminate the two angular errors within a specified time, the expression for the acceleration vector is constructed as follows: in For guidance law design parameters; the first term on the right side of the equation The first term indicates that the projectile-target line vector and velocity vector are gradually converging, representing the guidance term generated by the proportional guidance law, intended to guide the direction of motion towards the target; the second term... Indicates at the specified time The internal requirement is that the velocity direction of the landing point and the vector of the desired landing angle are collinear, which means that the direction of motion points towards the target in the set direction within a given time range; Simplifying equation (8) yields the expression for the guidance law:

2. An electronic device, characterized in that, include: Processor and memory; The memory is used to store a computer program, and the processor is used to execute the computer program stored in the memory to cause the electronic device to perform the method as described in claim 1.

3. 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 method as described in claim 1.

4. A chip, characterized in that, include: A processor for retrieving and running a computer program from memory, causing a device on which the chip is mounted to perform the method as described in claim 1.

5. A computer program product, characterized in that, The computer program product includes a computer storage medium storing a computer program, the computer program including instructions executable by at least one processor, which, when executed by the at least one processor, implement the method as described in claim 1.

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