CN115158705B - Sectional polynomial spacecraft attitude maneuver track planning method - Google Patents

Abstract

The invention discloses a method for planning a maneuvering trajectory of a segmented polynomial spacecraft attitude, and belongs to the field of spacecraft attitude planning. The implementation method of the invention comprises the following steps: establishing a spacecraft large-angle attitude maneuver model and a pointing constraint attitude ball map; the initial pointing and the target pointing of the spacecraft sensor are determined, the gesture track of the spacecraft is represented by a polynomial, the pointing constraint, the dynamics constraint and the bounded constraint are sequentially met in a layered mode through a spherical three-dimensional path planning, inverse dynamics and heuristic binary time distribution method, the shortest gesture maneuvering time gesture track and the fixed gesture maneuvering time gesture track can be obtained, the gesture track planning efficiency is high, and the complex pointing constraint processing capability is high. The planned track is used as the input of the gesture controller, the nominal track is tracked in real time through the output moment of the controller, the gesture maneuver for avoiding the complex tabu area is realized, and the real-time performance and the adaptability of the tracking control can be improved. The invention is more suitable for on-board autonomous attitude planning.

Description

Piecewise Polynomial Spacecraft Attitude Maneuver Trajectory Planning Method

Technical Field

The invention relates to a piecewise polynomial spacecraft attitude maneuver trajectory planning method, belonging to the field of spacecraft attitude planning.

Background technique

Spacecraft attitude maneuvers often face multiple pointing constraints in complex space environments. Pointing constraints can be divided into mandatory constraints and taboo constraints. Mandatory constraints mean that the spacecraft attitude must remain near a certain direction, and taboo constraints mean that the spacecraft attitude cannot be near a certain direction. Mandatory constraints include the camera needing to be aimed at the object being photographed and the antenna needing to be aimed at the signal transmitter, while taboo constraints include the camera needing to avoid strong light objects. In addition, spacecraft attitude maneuvers are also subject to bounded constraints, dynamic constraints, etc. These complex constraints limit the feasible space for attitude maneuvers.

Many scholars have conducted research on rapid attitude maneuver planning methods. Rapid attitude planning methods can plan feasible solutions for attitude maneuvers in a relatively short time. They can be roughly divided into random planning methods (Xu Rui, Wu Changqing, Zhu Shengying, et al. A rapid maneuver path planning method with complex sensor pointing constraints in the attitude space [J]. Information Systems Frontiers, 2017, 19 (4): 945-953.), geometric planning methods (Xu Rui, Wang Hui, Xu Wenming, et al. Rotational-path decomposition based recursive planning for spacecraft attitude reorientation [J]. Acta Astronautica, 2018, 143: 212-220.), and spatial discretization methods (Kjellberg, Lightsey. Discretized Quaternion Constrained Attitude Pathfinding [J]. Journal of Guidance, Control, and Dynamics, 2016, 39 (3): 713-718.). The random programming method has strong universality but has low planning efficiency in high-dimensional space, and there is uncertainty in the planning solution; the geometric programming method quickly generates attitude trajectories in a deterministic manner, but it is difficult to handle complex pointing constraints; the spatial discretization method can handle complex pointing constraints, but it requires the establishment of a spherical grid map in advance.

In addition, the existing feasible solution methods for attitude planning only focus on quickly giving feasible attitude trajectories, ignoring the attitude maneuvering time, such as the problem that the attitude maneuvering time is too long and the attitude maneuvering time cannot be determined.

Summary of the invention

In view of the problem that the existing attitude planning feasible solution search method has a weak ability to handle complex pointing constraints, the main purpose of the present invention is to provide a piecewise polynomial spacecraft attitude maneuver trajectory planning method, which can quickly plan the attitude maneuver feasible solution under complex pointing constraints, that is, obtain the attitude maneuver nominal trajectory. The method uses a polynomial to represent the attitude trajectory of the spacecraft, and hierarchically satisfies the pointing constraints, dynamic constraints and bounded constraints through spherical three-dimensional path planning, inverse dynamics and heuristic binary time allocation method, so as to obtain the shortest attitude maneuver time attitude trajectory and the fixed attitude maneuver time attitude trajectory, with high attitude trajectory planning efficiency, strong ability to handle complex pointing constraints, and the ability to avoid complex taboo areas, thereby improving the adaptability of the present invention.

The purpose of the present invention is achieved through the following technical solutions.

The present invention discloses a piecewise polynomial spacecraft attitude maneuver trajectory planning method, which establishes a spacecraft large-angle attitude maneuver model and a pointing constraint attitude sphere map; determines the initial pointing and target pointing of a spacecraft sensor, performs three-dimensional spherical path planning to obtain a three-dimensional pointing path node set, and converts the three-dimensional pointing nodes into attitude quaternion nodes; adopts time average allocation, performs minimum acceleration trajectory planning on the attitude quaternion nodes and performs inverse dynamics processing to obtain the initial attitude trajectory of the spacecraft; and satisfies bounded constraints through a heuristic binary time allocation optimization method to obtain a shortest attitude maneuver time attitude trajectory that satisfies complex constraints.

The present invention discloses a piecewise polynomial spacecraft attitude maneuver trajectory planning method, comprising the following steps:

Step 1: Based on the attitude quaternion, the dynamic equations and kinematic equations of the rigid spacecraft are established, and the bounded constraints and pointing constraints are given, that is, a large-angle attitude maneuvering model of the spacecraft is established, and the initial attitude and target attitude of the spacecraft attitude maneuver are given.

Based on the attitude quaternion, the dynamic equation and kinematic equation of the rigid spacecraft are established as follows:

Where: q = [q ₀ ,q ₁ ,q ₂ ,q ₃ ] ^T is the attitude quaternion, which represents the rotation from the body coordinate system to the inertial coordinate system, ω = [ω ₁ ,ω ₂ ,ω ₃ ] ^T represents the satellite angular velocity in the body coordinate system, J = diag (J ₁ ,J ₂ ,J ₃ ) represents the inertia matrix of the satellite relative to the body system, ω ^× is the cross product matrix form of ω, u = [u ₁ ,u ₂ ,u ₃ ] ^T is the control torque of the satellite in the body system, and

The bounded torque and bounded angular velocity constraints are expressed as follows:

u _i ≤u _max i＝1,2,3 (4)

ω _i ≤ω _max i＝1,2,3 (5)

Directional constraints include taboo constraints and mandatory constraints, which are expressed as follows:

Where: r _b is the direction vector of the laser axis in the inertial system, r _s and r _v are the forbidden cone axis and forced cone axis in the inertial system, respectively, θ _s and θ _v are the forbidden cone half-angle and forced cone half-angle in the inertial system, respectively.

Step 2: After establishing the large-angle attitude maneuver model of the spacecraft, the initial orientation of the spacecraft sensor r ₀ and the target orientation r _f are given. Three-dimensional spherical path planning is performed, and the path planning state space is the attitude sphere surface composed of unit vectors. The way to expand new nodes is to perform Euler rotation from the current node to the random node with a step length of δ° to obtain a three-dimensional pointing node, and the three-dimensional pointing node is converted into an attitude quaternion node.

In order to obtain the shortest attitude maneuvering path with fewer nodes and improve the ability to handle complex pointing constraints, it is preferred to use the RRT*-SMART algorithm for three-dimensional spherical path planning, which can avoid complex taboo areas and improve the adaptability of the present invention.

Step 3: Use polynomials to represent the attitude quaternion components, use time averaging to plan the minimum acceleration trajectory of the attitude quaternion nodes and perform inverse dynamics processing to obtain the initial attitude trajectory of the spacecraft.

In order to save computing resources as much as possible while satisfying obstacle avoidance performance, as a preferred method, the quaternion trajectories of adjacent attitude quaternion nodes are represented by a fifth-order polynomial.

The quaternion trajectory of adjacent attitude quaternion nodes is expressed by a 5th-order polynomial

Among them, q _i (t), i = 0, 1, 2, 3 are the four components of the attitude quaternion.

Complex posture trajectories are represented by piecewise polynomials

Among them, there are n+1 attitude quaternion nodes, and there are n segments of complex attitude trajectories. _qi ,i＝1,2,…,n is a matrix composed of polynomial coefficients. qi _is obtained by closed-form solution of minimum acceleration trajectory planning to obtain a continuous and smooth complex attitude trajectory.

According to equations (1) and (2), the torque trajectory and angular velocity trajectory of the spacecraft can be expressed by the first and second derivatives of the quaternion. The first and second derivatives of the quaternion are expressed as follows:

The average time allocation is used for initial time allocation, and the complex attitude trajectory represented by equation (10) is subjected to inverse dynamics processing represented by equations (1), (2), (11) and (12) to obtain the initial attitude trajectory of the spacecraft.

Step 4: Use the initial attitude trajectory obtained in step 3 as heuristic information to perform deterministic optimization on the time allocation ratio. Given the attitude maneuvering time interval, use the binary search method to perform piecewise polynomial attitude trajectory planning multiple times, so that the angular velocity or control torque gradually approaches the corresponding maximum value until the attitude trajectory with the shortest attitude maneuvering time is obtained.

The initial posture trajectory is used as heuristic information, including the maximum angular velocity ω _m , the initial angular velocity ω ₀ , the terminal angular velocity ω _f , and the distance between adjacent nodes, that is, the posture quaternion angle d _s . The acceleration distance and deceleration distance are calculated by the following formula

Where t ₁ and t ₂ are acceleration time and deceleration time, respectively, d ₁ and d ₂ are acceleration distance and deceleration distance, respectively. If d ₁ + d ₂ < d _s , the time interval ti between adjacent nodes _is updated as follows:

Where t _m is the maximum acceleration time. If d ₁ +d ₂ ≥ _{d s} , the time interval t _i between adjacent nodes is updated as follows:

t _i = t ₁ + t ₂ (15)

After the above deterministic optimization of the time allocation ratio, given the attitude maneuvering time interval [T _min ,T _max ], the bisection method is used to perform piecewise polynomial attitude trajectory planning multiple times, so that the angular velocity or control torque gradually approaches the corresponding maximum value until the attitude trajectory with the shortest attitude maneuvering time is obtained.

The method also includes step five: using the trajectory obtained in step four as the nominal trajectory as the input of the attitude controller, and tracking the nominal trajectory in real time through the controller output torque to achieve attitude maneuvers to avoid complex taboo areas, and can improve the real-time and adaptability of tracking control.

Beneficial effects:

1. The piecewise polynomial spacecraft attitude maneuver trajectory planning method disclosed in the present invention uses a polynomial to represent the attitude trajectory of the spacecraft. Through spherical three-dimensional path planning, inverse dynamics and heuristic binary time allocation method, the pointing constraint, dynamic constraint and bounded constraint are successively satisfied in layers, and the attitude trajectory with the shortest attitude maneuvering time and the attitude trajectory with fixed attitude maneuvering time can be obtained. The attitude trajectory planning efficiency is high, the real-time performance of tracking control is improved, and it is more suitable for autonomous attitude planning on board.

2. The piecewise polynomial spacecraft attitude maneuver trajectory planning method disclosed in the present invention adopts spherical path planning to satisfy pointing constraints, adopts inverse dynamics to satisfy dynamic constraints, and adopts a heuristic binary time allocation method to satisfy bounded constraints, thereby achieving hierarchical and orderly satisfaction of pointing constraints, dynamic constraints and bounded constraints, and thus has strong processing capabilities for complex pointing constraints, can avoid complex taboo areas, and improve the adaptability of the present invention.

3. The piecewise polynomial spacecraft attitude maneuver trajectory planning method disclosed in the present invention uses polynomials to represent the attitude quaternion components of the spacecraft and normalizes the attitude quaternion. After solving the attitude trajectory with the shortest attitude maneuvering time, it can quickly solve the attitude trajectory of any fixed attitude maneuvering time (greater than the shortest attitude maneuvering time), and is still applicable to tasks that have requirements for attitude maneuvering time.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG1 is a flow chart of a piecewise polynomial spacecraft attitude maneuver trajectory planning method disclosed in the present invention.

Figure 2 shows the torque trajectory during the spacecraft attitude maneuver.

Figure 3 shows the angular velocity trajectory during the spacecraft attitude maneuver.

Figure 4 shows the quaternion trajectory during the spacecraft attitude maneuver.

Figure 5 shows the three-dimensional pointing path of the sensitive element during the spacecraft attitude maneuver.

Detailed ways

The present invention will be further explained below in conjunction with the accompanying drawings and embodiments.

Example 1

As shown in FIG. (1), the piecewise polynomial spacecraft attitude maneuver trajectory planning method disclosed in this embodiment has the following specific implementation steps:

Step 1: Use equations (1) and (2) to establish a large-angle attitude maneuver model for the spacecraft, where the spacecraft body moment of inertia is diag(100,100,100)kg·m ² , and consider bounded torque and bounded angular velocity constraints, with maximum torque u _max =1N·m and maximum angular velocity ω _max =0.1rad/s.

In order to demonstrate the ability of the piecewise polynomial spacecraft attitude maneuver trajectory planning method to handle complex pointing constraints, 15 taboo cone constraints are considered. The specific parameters are shown in Table 1.

Table 1 Pointing constraint parameters

Step 2: Given the initial pointing r _start = [0.8867, -0.4603, 0.0440] ^T and the target pointing r _goal = [-0.7922, -0.6099, 0.0225] ^T , perform three-dimensional spherical path planning. The path planning algorithm selects the RRT*-SMART algorithm, the step size is selected as 1° when expanding new nodes, and the path planning state space is the attitude sphere surface composed of unit vectors. The planning results are shown in Table 2. A total of 7 attitude nodes divide the attitude maneuver path into 6 segments.

Table 2 Three-dimensional spherical path planning

Step 3: Use equations (7), (8) and (9) to represent the attitude quaternion trajectory of adjacent nodes with a fifth-order polynomial, use equation (10) to represent the complex attitude trajectory with a piecewise polynomial, and use equations (11) and (12) to represent the torque trajectory and angular velocity trajectory of the spacecraft with the first and second derivatives of the quaternion.

The initial time allocation adopts the average time allocation. The complex posture trajectory represented by equation (10) is processed by inverse dynamics represented by equations (1), (2), (11) and (12) to obtain the initial posture trajectory. Its coefficients are shown in Table 3.

Table 3 Initial polynomial attitude trajectory coefficients

Step 4: Use the initial attitude trajectory as heuristic information to perform deterministic optimization on the time allocation ratio. Given an attitude maneuvering time interval of [10,100]s, use the bisection method to perform piecewise polynomial attitude trajectory planning multiple times to obtain the attitude trajectory with the shortest attitude maneuvering time. The attitude trajectory consists of the torque trajectory, angular velocity trajectory, and attitude quaternion trajectory, as shown in Figures (2), (3), and (4), respectively. The pointing path of the sensitive element is shown in Figure (5), where the red area represents the taboo constraint area and the black curve represents the pointing path of the sensor. The polynomial attitude trajectory coefficient corresponding to the shortest attitude maneuvering time is

Table 4. Shortest attitude maneuver time polynomial attitude trajectory coefficients

The specific description above further illustrates the purpose, technical solutions and beneficial effects of the invention in detail. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims (2)

1. The method for planning the attitude maneuver trajectories of the segmented polynomial spacecraft is characterized by comprising the following steps of: comprises the following steps of the method,

Firstly, establishing a dynamic equation and a kinematic equation of a rigid spacecraft based on a gesture quaternion, and giving a bounded constraint and a pointing constraint, namely establishing a spacecraft large-angle gesture maneuver model and giving a spacecraft gesture maneuver initial gesture and a target gesture;

the first implementation method of the step is that,

Based on the attitude quaternion, a dynamic equation and a kinematic equation of the rigid spacecraft are established as follows:

Wherein: q= [ q ₀,q₁,q₂,q₃]^T ] is a posture quaternion representing rotation from the body coordinate system to the inertial coordinate system, ω= [ ω ₁,ω₂,ω₃]^T ] represents the satellite angular velocity in the body coordinate system, j=diag (J ₁,J₂,J₃) represents the inertia matrix of the satellite with respect to the body system, ω ^× is a cross-multiplied matrix form of ω, u= [ u ₁,u₂,u₃]^T is a control moment in the satellite body system, and

The moment bounded and angular velocity bounded constraints are expressed in the form:

u_i≤u_max i＝1,2,3 (4)

ω_i≤ω_max i＝1,2,3 (5)

pointing constraints include tabu constraints and mandatory constraints, expressed in the form:

Wherein: r _b is the direction vector of the laser main shaft under the inertial system, r _s and r _v are the tabu cone main shaft and the forced cone main shaft under the inertial system respectively, and theta _s and theta _v are the tabu cone half angle and the forced cone half angle under the inertial system respectively;

carrying out three-dimensional spherical path planning by adopting an RRT-SMART algorithm;

Step two, after a spacecraft large-angle attitude maneuver model is established, giving an initial pointing direction r ₀ and a target pointing direction r _f of a spacecraft sensor; carrying out three-dimensional spherical path planning, wherein the path planning state space is a gesture sphere surface formed by unit vectors, and the new node is expanded in such a way that Euler rotation with the step length delta degrees is carried out from the current node to the random node, so as to obtain a three-dimensional pointing node, and the three-dimensional pointing node is converted into a gesture quaternion node;

Step three, expressing gesture quaternion components by using polynomials, adopting time average allocation, planning minimum acceleration track of gesture quaternion nodes, and carrying out inverse dynamics processing to obtain an initial gesture track of the spacecraft;

Step four, taking the initial gesture track obtained in the step three as heuristic information, carrying out deterministic optimization on the time allocation proportion, giving a gesture maneuvering time interval, and carrying out piecewise polynomial gesture track planning for a plurality of times by adopting a dichotomy to enable the angular speed or the control moment to approach the corresponding maximum value gradually until the shortest gesture maneuvering time gesture track is obtained;

The realization method of the fourth step is that,

Taking the initial gesture track as heuristic information, wherein the heuristic information comprises a maximum angular speed omega _m, an initial angular speed omega ₀ and a terminal angular speed omega _f, and the distance between adjacent nodes is a gesture quaternion included angle d _s; the acceleration distance and the deceleration distance are calculated by

Wherein t ₁ and t ₂ are acceleration time and deceleration time, respectively, and d ₁ and d ₂ are acceleration distance and deceleration distance, respectively; if d ₁+d₂＜d_s, then the neighbor node time interval t _i is updated as follows

Wherein t _m is the maximum acceleration time; if d ₁+d₂≥d_s, then the neighbor node time interval t _i is updated as follows

t_i＝t₁+t₂ (15)

After the deterministic optimization is carried out on the time distribution proportion, a gesture maneuvering time interval [ T _min,T_max ] is given, and a dichotomy is adopted to carry out piecewise polynomial gesture track planning for many times, so that the angular speed or the control moment gradually approaches the corresponding maximum value until the shortest gesture maneuvering time gesture track is obtained;

the quaternion track of the quaternion nodes of adjacent gestures is represented by a 5 th order polynomial

Wherein q _i (t), i=0, 1,2,3 are 4 components of the gesture quaternion;

Complex gesture trajectory is represented by a piecewise polynomial

Wherein, the number of gesture quaternion nodes is n+1, the complex gesture track is n sections, q _i, i=1, 2, …, n is a matrix formed by polynomial coefficients, q _i is obtained by closed solving of minimum acceleration track planning, and continuous and smooth complex gesture tracks are obtained;

the moment and angular velocity trajectories of the spacecraft according to equations (1) and (2) can be represented by the first and second derivatives of the quaternion, which are represented as follows

And (3) carrying out initial time distribution by adopting average time distribution, and carrying out inverse dynamics processing on the complex gesture tracks represented by the formula (10) represented by the formulas (1), (2), (11) and (12) to obtain initial gesture tracks of the spacecraft.

2. A segmented polynomial spacecraft attitude maneuver trajectory planning method as claimed in claim 1, wherein: and step five, taking the track obtained in the step four as the input of a gesture controller, tracking the nominal track in real time through the output moment of the controller, realizing gesture maneuver for avoiding complex tabu areas, and improving the real-time performance and adaptability of tracking control.