CN115014363B - Attitude path planning method, system, equipment and medium based on rotation matrix topological structure - Google Patents
Attitude path planning method, system, equipment and medium based on rotation matrix topological structure Download PDFInfo
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Abstract
The invention provides a method, a system, equipment and a medium for planning an attitude path based on a rotation matrix topological structure. The method specifically comprises the following steps: step one, discretization of the posture and establishment of a graph structure: discretizing the processed object and establishing a graph structure on the processed object; establishing attitude limit; and thirdly, designing a cost function in the A-star algorithm so as to complete path planning. The invention can plan a path from the dangerous attitude maneuver to the safe attitude rapidly, and avoid the dangerous attitude in the maneuvering process.
Description
Technical Field
The invention belongs to the technical field of aerospace, and particularly relates to an attitude path planning method, an attitude path planning system, attitude path planning equipment and an attitude path planning medium based on a rotation matrix topological structure.
Background
In-orbit spacecraft usually encounter many limitations when performing attitude maneuvers, for example, in order to maintain communication, the antenna of the spacecraft needs to be kept in a certain direction; to avoid damage to the star sensor, the sensor needs to avoid the direction of sunlight. These pose constraints can be categorized into two types of pose limits: under an inertial system, included angles between some vectors fixedly connected with the spacecraft and known vectors are required to be smaller than or larger than a specific angle, the former corresponds to the pointing direction required to be kept in the spacecraft attitude maneuver process, and the latter corresponds to the pointing direction required to be avoided in the spacecraft attitude maneuver process. Common methods for solving such control problems are the potential function method and the path planning method. In the path planning method, a rotation trajectory meeting the constraint expectation is planned first and then controlled. The invention provides a method for planning a posture path by searching based on a topological structure of a rotation matrix, which aims at the problem of limited posture path planning.
Disclosure of Invention
The invention aims to solve the problems in the prior art and provides an attitude path planning method, an attitude path planning system, equipment and a medium based on a rotation matrix topological structure.
The invention is realized by the following technical scheme, and provides an attitude path planning method based on a rotating matrix topological structure, wherein the whole rotating matrix forms a three-dimensional special orthogonal group SO (3), the SO (3) is homomorphic and is positioned in a three-dimensional space to form a solid sphere with the same diameter and the radius of pi, any attitude of a spacecraft can be uniquely represented by one point in the solid sphere, the diameter identification means that any two points on the surface of the solid sphere on the same diameter represent the same rotating matrix, and the solid sphere with the same diameter is also called a three-dimensional real projective space
The method is in three-dimensional real projective space
Performing path planning by using an A algorithm; the method comprises the following specific steps:
step one, discretization of postures and establishment of a graph structure: discretizing the processed object and building a graph structure on the processed object;
step two, establishing attitude limit;
and thirdly, designing a cost function in the A-star algorithm so as to complete path planning.
Further, any given attitude R is according to the Euler's finite rotation theorem f Can all be moved from an initial attitude R 0 By an angle about an axis, as reflected in
Upper, initial attitude R 0 Is the center of the sphere O, given the attitude R f Is a certain point n = [ n ] in the ball 1 ,n 2 ,n 3 ] T The rotating shaft is
The corner is n 2 。
Further, any given attitude R f Is a 3 × 3 matrix, which may be composed of threeDimension vector n = [ n ] 1 ,n 2 ,n 3 ] T Generated using exponential mapping on SO (3), i.e.:
wherein I is an identity matrix [ ·] × Is a cross-product mapping:
further, for three-dimensional real projection space
The definition mode of any point n in the graph and the definition mode of adjacent points are as follows: taking 14 points on a sphere with a given sampling step size delta epsilon (0, pi) as a radius as adjacent points of n, and recording the adjacent points
The coordinates of the 14 points are respectively:
further, when n is close to a sphere with radius pi, the 14 adjacent points may have a mode length exceeding pi, and the points exceeding pi are discarded.
Further, in step two, assuming that the spacecraft has p sensitive axes, l attitude constraints, each of which is defined by a pointing direction r j J =1, \ 8230;, l and angle θ j J =1, \8230, the l constitution, i.e. each sensitive axis w of the spacecraft during attitude maneuver k K =1, \8230;, p and r j J =1, \8230, the included angle alpha of l jk Are no less than theta j 。
Further, in step three, the a-algorithm calculates the priority of the node by the following function:
f(n)＝g(n)+h(n)
wherein f (n) represents the priority of the node n, the smaller the value is, the higher the priority is, and when the algorithm selects the next node to be traversed, the node with the highest priority is selected; g (n) is the cost from the origin to node n; h (n) is a heuristic item in the algorithm and is the estimated cost from the node n to the terminal;
the distance metric is a double translation invariant metric over SO (3), i.e.:
assuming that the parent node of node n is m, their corresponding rotation matrices generated by exponential mapping are R respectively n And R m Then the cost of node n is:
g(n)＝λ g [g(m)+d(R m ,R n )]
when the parent node is the starting point g (m) =0, the composition of the heuristic is:
h(n)＝λ 1 h 1 (n)+λ 2 h 2 (n)
h 2 (n)＝d(R n ,R f )
wherein h is 1 (n) measures attitude R n The degree of risk of the lower sensitive axis relative to the attitude-limiting zone; h is a total of 2 (n) is the attitude R n With the target attitude R f The shortest distance of (d); lambda g ，λ 1 And λ 2 Is a coefficient due to R f Is arbitrarily given when h 2 (n)＝d(R n ,R f ) And when the distance is less than or equal to delta, adding the terminal point into the path, finding a target posture, and stopping searching.
The invention provides an attitude path planning system based on a rotating matrix topological structure, wherein a three-dimensional special orthogonal group SO (3) is formed by the whole rotating matrix, the SO (3) is homomorphic with a solid sphere which is identical in diameter and has a radius of pi in a three-dimensional space, and any attitude of a spacecraft can be realizedIs uniquely represented by a point in the solid sphere, and the diameter identification means that any two points on the surface of the solid sphere on the same diameter represent the same rotation matrix, and the diameter identification solid sphere is also called a three-dimensional real projective space
The method is in three-dimensional real projective space
Performing path planning by using an A algorithm; the system comprises:
the discretization and graph structure building module comprises: and (3) discretization of the gesture and establishment of a graph structure: discretizing the processed object and establishing a graph structure on the processed object;
an attitude limiting module: for establishing pose limits;
a cost function design module: and the method is used for designing the cost function in the A-algorithm so as to complete path planning.
The invention further provides an electronic device, which includes a memory and a processor, where the memory stores a computer program, and the processor implements the steps of the method for planning the attitude path based on the rotation matrix topology when executing the computer program.
The invention proposes a computer readable storage medium for storing computer instructions which, when executed by a processor, implement the steps of the method for rotational matrix topology based pose path planning.
Drawings
FIG. 1 is a schematic diagram of a sampling scheme on a three-dimensional real projection space;
FIG. 2 is a schematic view of attitude constraints;
fig. 3 is a schematic diagram of simulation results.
Detailed Description
The technical solutions in the embodiments of the present invention will be described clearly and completely with reference to the accompanying drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The invention provides a gesture path planning method based on a rotating matrix topological structure, wherein the whole rotating matrix forms a three-dimensional special orthogonal group SO (3), the SO (3) is homomorphic in a three-dimensional space to form a solid sphere with the same diameter and the radius of pi, any gesture of a spacecraft can be uniquely represented by one point in the solid sphere, the identification of the diameter refers to that any two points on the surface of the solid sphere are positioned on the same diameter to represent the same rotating matrix, and the solid sphere with the same diameter is also called as a three-dimensional real projective space
The method is in three-dimensional real projective space
Performing path planning by using an A-algorithm; the method specifically comprises the following steps:
step one, discretization of the posture and establishment of a graph structure: discretizing the processed object and building a graph structure on the processed object; before the search algorithm is applied, the processed object needs to be discretized and a graph structure is built on the object, and the selection of the discretization mode directly influences the quality of a planning result.
Establishing attitude limit;
and thirdly, designing a cost function in the A-star algorithm so as to complete path planning.
Any given attitude R according to the Euler's theorem of finite rotation f Can all be moved from an initial attitude R 0 By an angle about an axis, as reflected in
Upper, initial attitude R 0 Is the center of the sphere O, given the attitude R f Is a certain point in the ball n = [ ] 1 ,n 2 ,n 3 ] T The rotating shaft is
The corner is | | n | | non-conducting phosphor 2 。
At any given attitude R f Is a 3 × 3 matrix, can be represented by a corresponding three-dimensional vector n = [ n ] 1 ,n 2 ,n 3 ] T Generated using exponential mapping on SO (3), i.e.:
wherein I is an identity matrix [ ·] × Is a cross-product mapping:
for three-dimensional real projection space
The definition mode of any point n in the graph and the definition mode of adjacent points are as follows: taking 14 points on a sphere with a given sampling step size delta epsilon (0, pi) as a radius as adjacent points of n, and recording the adjacent points
The coordinates of the 14 points are respectively:
when n is close to a sphere with radius pi, it is possible that the 14 neighboring points may exceed pi in mode length, and are discarded for points exceeding pi.
In step two, the spacecraft is assumed to have p sensitive axes and l attitude limits, and each attitude limit is pointed by a pointing direction r j J =1, \8230, l and angle theta j J =1, \8230, the l constitution, i.e. each sensitive axis w of the spacecraft during attitude maneuver k K =1, \ 8230;, p and r j J =1, \ 8230;, the angle α of l jk Are not less than theta j 。
In step three, the a-algorithm is a heuristic search algorithm, and calculates the priority of the node by the following function:
f(n)＝g(n)+h(n)
wherein f (n) represents the priority of the node n, the smaller the value is, the higher the priority is, and when the algorithm selects the next node to be traversed, the node with the highest priority is selected; g (n) is the cost from the starting point to node n; h (n) is a heuristic item in the algorithm and is the estimated cost from the node n to the terminal;
the distance metric is a double translation invariant metric over SO (3), i.e.:
assuming that the parent node of node n is m, their corresponding rotation matrices generated by exponential mapping are R respectively n And R m Then the cost of node n is:
g(n)＝λ g [g(m)+d(R m ,R n )]
when g (m) =0 when the parent node is the start point, the composition of the heuristic is:
h(n)＝λ 1 h 1 (n)+λ 2 h 2 (n)
h 2 (n)＝d(R n ,R f )
wherein h is 1 (n) measures the attitude R n The degree of risk of the lower sensitive axis relative to the attitude-limiting zone; h is 2 (n) is the attitude R n With the target attitude R f The shortest distance of (d); lambda [ alpha ] g ，λ 1 And λ 2 Is a coefficient due to R f Is arbitrarily given, when h 2 (n)＝d(R n ,R f ) And when the distance is less than or equal to delta, adding the terminal point into the path, finding a target posture, and stopping searching.
The invention provides aThe attitude path planning system based on the rotating matrix topological structure is characterized in that a three-dimensional special orthogonal group SO (3) is formed by the whole rotating matrix, the SO (3) is homomorphic in a three-dimensional space to form a diametrically-identified solid sphere with the radius of pi, any attitude of a spacecraft can be uniquely represented by one point in the solid sphere, diametrically-identified points on the surface of the solid sphere mean the same rotating matrix, and the diametrically-identified solid sphere is also called a three-dimensional real projective space
The method is in three-dimensional real projective space
Performing path planning by using an A-algorithm; the system comprises:
the discretization and graph structure building module comprises: and (3) discretization of the gesture and establishment of a graph structure: discretizing the processed object and building a graph structure on the processed object;
an attitude limiting module: for establishing attitude constraints;
a cost function design module: and the method is used for designing the cost function in the A-algorithm so as to complete path planning.
When describing the attitude maneuver of the spacecraft, the attitude parameters such as a rotation matrix, a quaternion, an Euler angle and the like are needed, however, except the rotation matrix, other various attitude parameters cannot globally and uniquely describe the attitude of the spacecraft, which can cause singular problems or an 'unwinding' phenomenon in the control process. The rotation matrix can globally and uniquely describe the attitude of the spacecraft, and the overall rotation matrix forms a three-dimensional special orthogonal group SO (3), the SO (3) is both a lie group and a differential manifold, and the topological property of the rotation matrix is very useful in the planning/control problem. The SO (3) is homomorphic in a solid sphere with diameter being equal to pi in a three-dimensional space, that is, any posture of the spacecraft can be uniquely represented by one point in the solid sphere, and the diameter-equal meaning that any two points on the surface of the solid sphere on the same diameter represent the same rotationTurning to the matrix, this pair of diametrically identified solid spheres is also referred to as three-dimensional real projective space
Any given attitude R according to the Euler's law of finite rotation f Can all be moved from an initial attitude R 0 By an angle about an axis, as reflected in
Upper, initial attitude R 0 Is the center of the sphere O, given the attitude R f Is a certain point n = [ n ] in the ball 1 ,n 2 ,n 3 ] T The rotating shaft is
The corner is | | n | | non-conducting phosphor 2 . At any given attitude R f Is a 3 × 3 matrix, can be represented by a corresponding three-dimensional vector n = [ n ] 1 ,n 2 ,n 3 ] T Generated using exponential mapping on SO (3), i.e.:
wherein I is an identity matrix [ ·] × Cross-product mapping:
the invention is in
The path planning is performed by using the a-algorithm.
The effect of the invention is illustrated in a set of simulations. Assuming that the system of the spacecraft is coincident with the inertial system at the initial moment, and the initial attitude I and the target attitude R of the spacecraft are f The method comprises the following steps:
in that
The corresponding points above are respectively:
n 0 ＝[0,0,0] T ,n f ＝[1.1561,0.0181,-2.5667] T
in the inertial system, the sensitive axes of the spacecraft are:
w 1 ＝[0.5590,0.1816,0.8090] T ,w 2 ＝[-0.1394,0.8800,0.4540] T ,w 3 ＝[0.6725,0.6725,0.3090] T
attitude constraints for the spacecraft are shown in table 1. The avoidance type refers to the need of the spacecraft to keep the sensitive axis out of this area during maneuvering.
TABLE 1 attitude limiting parameters of spacecraft
The coefficients chosen in the simulation were:
λ g ＝2,λ 1 ＝0.5,λ 2 ＝3
as shown in fig. 3, in the initial posture, one of the three sensitive axes is in the posture forbidden region CZ4, and the target posture is a safe posture in which none of the three axes is in the posture forbidden region. The invention can plan a path from the dangerous attitude maneuver to the safe attitude rapidly, and avoid the dangerous attitude in the maneuvering process.
The invention further provides an electronic device, which includes a memory and a processor, where the memory stores a computer program, and the processor implements the steps of the method for planning the attitude path based on the rotation matrix topology when executing the computer program.
The invention proposes a computer readable storage medium for storing computer instructions which, when executed by a processor, implement the steps of the method for rotational matrix topology based pose path planning.
The memory in the embodiments of the present application may be either volatile memory or nonvolatile memory, or may include both volatile and nonvolatile memory. The non-volatile memory may be a Read Only Memory (ROM), a Programmable ROM (PROM), an Erasable PROM (EPROM), an electrically Erasable EPROM (EEPROM), or a flash memory. Volatile memory can be Random Access Memory (RAM), which acts as external cache memory. By way of example, and not limitation, many forms of RAM are available, such as Static Random Access Memory (SRAM), dynamic random access memory (dynamic RAM, DRAM), synchronous Dynamic Random Access Memory (SDRAM), double data rate SDRAM (DDR SDRAM), enhanced SDRAM (ESDRAM), SLDRAM (synchronous DRAM), and direct rambus RAM (DR RAM). It should be noted that the memories of the methods described herein are intended to comprise, without being limited to, these and any other suitable types of memories.
In the above embodiments, the implementation may be wholly or partially realized by software, hardware, firmware, or any combination thereof. When implemented in software, it may be implemented in whole or in part in the form of a computer program product. The computer program product includes one or more computer instructions. When loaded and executed on a computer, cause the processes or functions described in accordance with the embodiments of the application to occur, in whole or in part. The computer may be a general purpose computer, a special purpose computer, a network of computers, or other programmable device. The computer instructions may be stored in a computer readable storage medium or transmitted from one computer readable storage medium to another computer readable storage medium, for example, the computer instructions may be transmitted from one website, computer, server, or data center to another website, computer, server, or data center via wire (e.g., coaxial cable, fiber optic, digital Subscriber Line (DSL)) or wireless (e.g., infrared, wireless, microwave, etc.). The computer-readable storage medium can be any available medium that can be accessed by a computer or a data storage device, such as a server, a data center, etc., that includes one or more available media. The usable medium may be a magnetic medium (e.g., a floppy disk, a hard disk, a magnetic tape), an optical medium (e.g., a Digital Video Disc (DVD)), or a semiconductor medium (e.g., a Solid State Disc (SSD)), among others.
In implementation, the steps of the above method may be performed by integrated logic circuits of hardware in a processor or instructions in the form of software. The steps of a method disclosed in connection with the embodiments of the present application may be directly implemented by a hardware processor, or may be implemented by a combination of hardware and software modules in a processor. The software module may be located in ram, flash memory, rom, prom, or eprom, registers, etc. storage media as is well known in the art. The storage medium is located in a memory, and a processor reads information in the memory and completes the steps of the method in combination with hardware of the processor. To avoid repetition, it is not described in detail here.
It should be noted that the processor in the embodiments of the present application may be an integrated circuit chip having signal processing capability. In implementation, the steps of the above method embodiments may be performed by integrated logic circuits of hardware in a processor or instructions in the form of software. The processor described above may be a general purpose processor, a Digital Signal Processor (DSP), an Application Specific Integrated Circuit (ASIC), a Field Programmable Gate Array (FPGA) or other programmable logic device, discrete gate or transistor logic, discrete hardware components. The various methods, steps, and logic blocks disclosed in the embodiments of the present application may be implemented or performed. A general purpose processor may be a microprocessor or the processor may be any conventional processor or the like. The steps of the method disclosed in connection with the embodiments of the present application may be directly implemented by a hardware decoding processor, or implemented by a combination of hardware and software modules in the decoding processor. The software module may be located in ram, flash memory, rom, prom, or eprom, registers, etc. storage media as is well known in the art. The storage medium is located in a memory, and a processor reads information in the memory and completes the steps of the method in combination with hardware of the processor.
The method, the system, the equipment and the medium for posture path planning based on the rotating matrix topological structure are introduced in detail, the principle and the implementation mode of the invention are explained by applying specific examples, and the description of the embodiments is only used for helping to understand the method and the core idea of the invention; meanwhile, for a person skilled in the art, according to the idea of the present invention, the specific embodiments and the application range may be changed, and in summary, the content of the present specification should not be construed as a limitation to the present invention.
Claims (10)
1. A gesture path planning method based on a rotation matrix topological structure is characterized in that a three-dimensional special orthogonal group SO (3) is formed by the whole rotation matrix, the SO (3) is homomorphic in a three-dimensional space to form a solid sphere which is identical in diameter and pi in radius, any gesture of a spacecraft can be uniquely represented by one point in the solid sphere, the diameter identification means that any two points on the surface of the solid sphere are on the same diameter to represent the same rotation matrix, and the solid sphere identical in diameter is also called a three-dimensional real projective space
The method is in three-dimensional real projective space
Performing path planning by using an A-algorithm; the method specifically comprises the following steps:
step one, discretization of postures and establishment of a graph structure: discretizing the processed object and building a graph structure on the processed object;
establishing attitude limit;
and thirdly, designing a cost function in the A-star algorithm so as to complete path planning.
2. The method of claim 1, wherein any given pose R is according to the euler's finite rotation theorem f Can all be moved from an initial attitude R 0 By an angle about an axis, as reflected in
Upper, initial attitude R 0 Is the center of the sphere O, given the attitude R f Is a certain point n = [ n ] in the ball 1 ,n 2 ,n 3 ] T The rotating shaft is
The corner is | | n | | non-conducting phosphor 2 。
3. The method of claim 2, wherein any given pose R f Is a 3 × 3 matrix, can be represented by a corresponding three-dimensional vector n = [ n ] 1 ,n 2 ,n 3 ] T Generated using exponential mapping on SO (3), namely:
wherein I is an identity matrix [ ·] × Is a cross-product mapping:
4. the method of claim 3, wherein the shadowgraph space is defined for three dimensions
The definition mode of any point n in the graph and the definition mode of adjacent points are as follows: taking 14 points on a sphere with a given sampling step size delta epsilon (0, pi) as a radius as adjacent points of n, and recording the adjacent points
The coordinates of the 14 points are respectively:
[n 1 +Δ',n 2 +Δ',n 3 +Δ'] T ,[n 1 +Δ',n 2 +Δ',n 3 -Δ'] T ,[n 1 +Δ',n 2 -Δ',n 3 +Δ'] T ,[n 1 +Δ',n 2 -Δ',n 3 -Δ'] T ,[n 1 -Δ',n 2 +Δ',n 3 +Δ'] T ,[n 1 -Δ',n 2 +Δ',n 3 -Δ'] T ,[n 1 -Δ',n 2 -Δ',n 3 +Δ'] T ,[n 1 -Δ',n 2 -Δ',n 3 -Δ'] T ,[n 1 +Δ,n 2 ,n 3 ] T ,[n 1 -Δ,n 2 ,n 3 ] T ,[n 1 ，n 2 +Δ，n 3 ] T ，[n 1 ，n 2 -Δ，n 3 ] T ，[n 1 ，n 2 ，n 3 +Δ] T ，[n 1 ，n 2 ，n 3 -Δ] T 。
5. the method of claim 4, wherein when n is close to a sphere of radius π, said 14 neighboring points have a possible mode length exceeding π, and discarding points exceeding π.
6. The method according to claim 5, characterized in that in step two, it is assumed that the spacecraft has p sensitive axes, l attitude constraints, each attitude constraint being defined by a pointing direction r j J =1, \ 8230;, l and angle θ j J =1, \ 8230;, i.e. each sensitive axis w of the spacecraft during attitude maneuver k K =1, \8230;, p and r j ,j＝1, \ 8230, angle alpha of l jk Are no less than theta j 。
7. The method of claim 6, wherein in step three, the A-algorithm calculates the priority of the nodes by the following function:
f(n)＝g(n)+h(n)
wherein f (n) represents the priority of the node n, the smaller the value is, the higher the priority is, and when the algorithm selects the next node to be traversed, the node with the highest priority is selected; g (n) is the cost from the starting point to node n; h (n) is a heuristic item in the algorithm and is the estimated cost from the node n to the terminal;
the distance metric is a double translation invariant metric over SO (3), i.e.:
assuming that the parent node of node n is m, their corresponding rotation matrices generated by exponential mapping are R respectively n And R m Then the cost of node n is:
g(n)＝λ g [g(m)+d(R m ,R n )]
when g (m) =0 when the parent node is the start point, the composition of the heuristic is:
h(n)＝λ 1 h 1 (n)+λ 2 h 2 (n)
h 2 (n)＝d(R n ,R f )
wherein h is 1 (n) measures the attitude R n The degree of risk of the lower sensitive axis relative to the attitude-limiting zone; h is 2 (n) is the attitude R n With the target attitude R f The shortest distance of (d); lambda [ alpha ] g ，λ 1 And λ 2 Is a coefficient due to R f Is arbitrarily given when h 2 (n)＝d(R n ,R f ) And when the distance is less than or equal to delta, adding the terminal point into the path, finding a target posture, and stopping searching.
8. A posture path planning system based on a rotation matrix topological structure is characterized in that a three-dimensional special orthogonal group SO (3) is formed by the whole rotation matrix, the SO (3) is homomorphic in a three-dimensional space to form a solid sphere which is identical in diameter and pi in radius, any posture of a spacecraft can be uniquely represented by one point in the solid sphere, the diameter identification means that any two points on the surface of the solid sphere are on the same diameter to represent the same rotation matrix, and the solid sphere identical in diameter is also called a three-dimensional real projective space
The system is in a three-dimensional real projective space
Performing path planning by using an A algorithm; the system comprises:
the discretization and graph structure building module comprises: and (3) discretization of the gesture and establishment of a graph structure: discretizing the processed object and building a graph structure on the processed object;
an attitude limiting module: for establishing attitude constraints;
a cost function design module: and the method is used for designing the cost function in the A-algorithm so as to complete path planning.
9. An electronic device comprising a memory and a processor, the memory storing a computer program, wherein the processor, when executing the computer program, performs the steps of the method according to any of claims 1-7.
10. A computer-readable storage medium storing computer instructions, which when executed by a processor, perform the steps of the method of any one of claims 1 to 7.
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