CN109623812B - Mechanical arm trajectory planning method considering spacecraft body attitude motion - Google Patents

Mechanical arm trajectory planning method considering spacecraft body attitude motion Download PDF

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CN109623812B
CN109623812B CN201811470615.5A CN201811470615A CN109623812B CN 109623812 B CN109623812 B CN 109623812B CN 201811470615 A CN201811470615 A CN 201811470615A CN 109623812 B CN109623812 B CN 109623812B
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mechanical arm
attitude
spacecraft
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planning
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CN109623812A (en
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藏悦
张尧
张景瑞
王典军
经姚翔
陈士明
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Beijing Institute of Technology BIT
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    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J9/00—Programme-controlled manipulators
    • B25J9/16—Programme controls
    • B25J9/1656—Programme controls characterised by programming, planning systems for manipulators
    • B25J9/1664—Programme controls characterised by programming, planning systems for manipulators characterised by motion, path, trajectory planning

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Abstract

The invention discloses a mechanical arm trajectory planning method considering spacecraft body attitude motion, and belongs to the field of multi-body system trajectory planning. The specific implementation method of the invention is as follows: firstly, determining the position of the tail end of a mechanical arm and the change track of attitude pointing by a quintic polynomial path planning method in the initial state of a spacecraft; according to the planning of the attitude motion of the central body of the spacecraft, the original expected position and the variation of the pointing direction of the central body in a coordinate system of the spacecraft body, which are generated due to the attitude motion of the central body, are obtained, so that the motion planning of the mechanical arm is compensated; correspondingly summing the original trajectory planning and the compensation planning of the tail end of the mechanical arm, recording as a final mechanical arm tail end point trajectory, and planning the motion trajectory of each joint angle of the mechanical arm through a kinematics pseudo-inverse algorithm so as to realize the mechanical arm trajectory planning considering the attitude motion of the spacecraft body; the method has the advantages of reducing the real-time calculation pressure of the satellite-borne computer, improving the track planning efficiency and the like.

Description

Mechanical arm trajectory planning method considering spacecraft body attitude motion
Technical Field
The invention relates to a mechanical arm trajectory planning method considering spacecraft attitude motion, and belongs to the field of multi-body system trajectory planning.
Background
In the process of executing on-orbit operation by a spacecraft system carrying the mechanical arm, a control target is usually the position and attitude pointing direction of an actuator at the tail end of the mechanical arm, and physical quantities which can be directly controlled in a model of the spacecraft system are the position and attitude of a central body of the spacecraft and the rotation angle of each section of mechanical arm joint. Therefore, in order to point the end effector at a desired position in space in a certain attitude, the motion of the robotic arm needs to be planned by a trajectory planning algorithm. In the related research of the trajectory planning of the mechanical arm, the position and the attitude orientation of the mechanical arm are usually described in a spacecraft central body coordinate system under the actual conditions of engineering measurement. However, in an actual task, a spacecraft central body may have a certain attitude motion, so that under the condition that the spatial position and the attitude orientation which are expected to be reached are not changed, the original expected position and the attitude orientation are also changed relative to the spacecraft central body. Therefore, under the condition that the spacecraft central body has attitude motion, the motion influence of the spacecraft central body needs to be considered and corresponding motion compensation needs to be added in the trajectory planning of the mechanical arm. However, in the existing related documents, most of researches only mention real-time motion compensation of the mechanical arm based on measurement of a target by a satellite-borne sensor, the method has a large calculation amount, and puts high requirements on the real-time calculation capability of a satellite-borne computer, and few documents perform open-loop planning on the motion compensation of the mechanical arm.
Disclosure of Invention
The invention discloses a mechanical arm trajectory planning method considering spacecraft body attitude motion, which aims to solve the problems that: when the expected position and the direction of the end actuator on the mechanical arm are fixed and unchanged in the inertial space, the trajectory planning of the end actuator of the mechanical arm is compensated according to the attitude motion information of the central body of the spacecraft, so that the end actuator of the mechanical arm can reach the original expected position and the direction in the inertial space under the condition that the central body of the spacecraft has attitude motion, the trajectory planning of the mechanical arm considering the attitude motion of the spacecraft body is realized, and the planning efficiency is high.
The purpose of the invention is realized by the following technical scheme.
The invention discloses a mechanical arm track planning method considering spacecraft body attitude motion. According to the planning of the attitude motion of the central body of the spacecraft, the original expected position and the variation of the pointing direction of the central body in the coordinate system of the spacecraft body, which are generated due to the attitude motion of the central body, are obtained, so that the motion planning of the mechanical arm is compensated. And correspondingly summing the original trajectory planning and the compensation planning at the tail end of the mechanical arm, recording the sum as a final mechanical arm tail end point trajectory, and obtaining the motion trajectory of each joint angle of the mechanical arm through a kinematic pseudo-inverse algorithm so as to realize the mechanical arm trajectory planning considering the spacecraft body attitude motion. The method has the advantages of reducing the real-time calculation pressure, improving the track planning efficiency and the like.
The invention discloses a mechanical arm trajectory planning method considering spacecraft body attitude motion, which comprises the following steps:
the method comprises the following steps: and determining the position and attitude pointing change track of the tail end actuator on the mechanical arm by a quintic polynomial path planning method in the initial state of the spacecraft.
Defining a central body coordinate system f of a service spacecraft at an initial moment in an initial state of the spacecraftb0And the system of inertia feCoincident, central body coordinate system fbMoves with the movement of the central body. Obtaining the initial position of the mechanical arm end actuator under the system according to the initial states of the service spacecraft central body and the mechanical arm
Figure GDA0002596077670000021
And initial attitude heading
Figure GDA0002596077670000022
Presetting the maximum value of the motion speed of the service spacecraft central body and the mechanical arm and the original expected position of the service spacecraft central body under a coordinate system
Figure GDA0002596077670000023
Pointing to the original expected attitude
Figure GDA0002596077670000024
Due to initial attitude pointing
Figure GDA0002596077670000025
Vector and original expected attitude pointing
Figure GDA0002596077670000027
Three incompletely independent components are respectively arranged in the vector, and the initial attitude points to
Figure GDA0002596077670000028
Vector and original expected attitude pointing
Figure GDA0002596077670000026
The vectors are all represented by directional cosines, the vectors beingThe first two components are selected as control quantities, but the corresponding third component has both positive and negative possibilities to avoid the uncertainty caused by the presence of both positive and negative possibilities, the orientation of the attitude represented by the direction cosine is translated into two azimuth angles α in spacenAnd αeThe first and second time derivatives of the attitude of the end effector are determined and converted to first and second time derivatives of the direction cosine, angle α is definednRepresenting attitude heading
Figure GDA0002596077670000029
And the main system XbObZbAngle between planes, αeRepresenting attitude heading
Figure GDA00025960776700000210
In the main system XbObZbProjection on plane and body system ObZbThe angle between the axes.
According to the azimuth angle αnAnd αeIs defined as
Figure GDA0002596077670000031
Wherein:
Figure GDA0002596077670000032
representing gestural pointing
Figure GDA0002596077670000033
The second component of (a).
In gesture-based pointing
Figure GDA0002596077670000034
Solving azimuth αeIn order to avoid singularity due to zero denominator, azimuth α is seteThe solution process of (2) is defined as:
Figure GDA0002596077670000035
wherein:
Figure GDA0002596077670000036
representing gestural pointing
Figure GDA0002596077670000037
The second component of (a) is,
Figure GDA0002596077670000038
representing gestural pointing
Figure GDA0002596077670000039
The third component.
Initial attitude pointing by end actuators
Figure GDA00025960776700000310
Obtaining an initial azimuth αn_0And αe_0Pointing by the end-effector to the desired attitude
Figure GDA00025960776700000311
Obtaining an original desired azimuth αn_r0And αe_r0. Bringing the end effector to the desired position
Figure GDA00025960776700000312
And original desired azimuth αn_r0And αe_r0And initial position
Figure GDA00025960776700000313
And initial azimuth αn_0And αe_0And performing difference to obtain the original position variation and the original azimuth angle variation of the end actuator.
In the method for planning the fifth-order polynomial, the coefficient to be determined of the fifth-order polynomial is solved according to the difference value of variables in the states of the start and the end of a task and the limitation of the change rate, and then the second-order smooth change process of the planning quantity with respect to time is obtained. The expected value of the planned quantity theta is recorded as thetarThe value of the initial state is recorded as theta0Defining the first derivative in the variation of the parameterHas a maximum value of
Figure GDA00025960776700000314
Maximum of the second derivative is
Figure GDA00025960776700000315
Then according to the fifth order polynomial, there are:
Figure GDA00025960776700000316
wherein,
Figure GDA00025960776700000317
the time coefficient tau is the current time t and the task duration tfThe ratio of (a) to (b).
According to the constraint conditions such as the limitation of the characteristic of the fifth-order polynomial and the change rate of the planning quantity, the task duration has the following constraint:
Figure GDA0002596077670000041
selecting the smallest one of the conditions simultaneously meeting the formula as the shortest time required by the task, thereby obtaining the shortest task time t meeting the motion constraint of each mechanical armf. On finding the task duration tfThen, based on the method of the fifth order polynomial, the planning quantity θ and its first and second time derivatives are:
Figure GDA0002596077670000042
in the process of planning the track of the mechanical arm, the planned quantity is the position of an actuator at the tail end of the mechanical arm
Figure GDA0002596077670000043
And attitude pointing
Figure GDA0002596077670000044
Solving the position of the mechanical arm end actuator by the method of the fifth-order polynomial
Figure GDA0002596077670000045
And azimuth angle
Figure GDA0002596077670000046
And
Figure GDA0002596077670000047
smooth continuous first and second time derivatives.
Due to the azimuth angle of the mechanical arm end actuator
Figure GDA0002596077670000048
And
Figure GDA0002596077670000049
is difficult to write into a form of showing the angular velocity of the mechanical arm joint, and the posture points to
Figure GDA00025960776700000410
The track can be written into a form of showing the angular velocity of the mechanical arm joint, and the planning of the mechanical arm joint track is facilitated. Therefore, before solving the joint angle motion law through the inverse kinematics relation of the mechanical arm, the azimuth angle of the end actuator on the mechanical arm is used
Figure GDA00025960776700000411
And
Figure GDA00025960776700000412
and its trajectory is converted into attitude pointing
Figure GDA00025960776700000413
The change trajectory of (2). According to the azimuth
Figure GDA00025960776700000414
And
Figure GDA00025960776700000415
pointing to the posture
Figure GDA00025960776700000416
The geometrical relationship between the two is as follows:
Figure GDA00025960776700000417
to the gesture direction
Figure GDA00025960776700000418
Calculating first and second time derivatives of
Figure GDA00025960776700000419
Wherein α is the azimuth angle
Figure GDA00025960776700000420
And
Figure GDA00025960776700000421
formed matrix of phi azimuth α matrix and attitude orientation
Figure GDA00025960776700000422
The conversion matrix between is specifically written as:
Figure GDA0002596077670000051
at this point, the lower position of the end effector in the Cartesian space is obtained through the programming of a quintic polynomial method
Figure GDA0002596077670000052
Pointing to the posture
Figure GDA0002596077670000053
Smoothing successive ideal first and second time derivative matrices
Figure GDA0002596077670000054
And
Figure GDA0002596077670000055
Figure GDA0002596077670000056
due to attitude pointing
Figure GDA0002596077670000057
The three components in the vector are not completely independent, so that
Figure GDA0002596077670000058
Representing gestural pointing
Figure GDA0002596077670000059
The first two components of the vector, denoted
Figure GDA00025960776700000510
Wherein:
Figure GDA00025960776700000511
position of mechanical arm end actuator obtained by formula
Figure GDA00025960776700000512
Pointing to the posture
Figure GDA00025960776700000513
Smoothing successive first and second time derivative matrices
Figure GDA00025960776700000514
And
Figure GDA00025960776700000515
namely, the mechanical arm end actuator obtained by the quintic polynomial programming method moves to the original expected position
Figure GDA00025960776700000516
Pointing to the original expected attitude
Figure GDA00025960776700000517
The trajectory of (2).
Secondly, performing attitude motion planning according to the attitude motion requirement of the central body of the spacecraft, and simultaneously obtaining the original expected position of the system
Figure GDA00025960776700000518
Pointing to the posture
Figure GDA00025960776700000519
The changing trajectory due to the central body attitude motion compensates for the trajectory planning of the robotic arm.
At a desired position in the central body of the spacecraft
Figure GDA00025960776700000520
By the inertial space position vector in which it is located
Figure GDA00025960776700000521
The relative position with respect to an inertial space position vector R of the center of mass of the spacecraft centerbody is represented, and the transition from the inertial frame to the spacecraft frame is:
Figure GDA00025960776700000522
wherein: a. thebeA coordinate transformation matrix representing the inertial system to the spacecraft body system,
Figure GDA00025960776700000523
indicating a desired position in the central body of a spacecraft
Figure GDA00025960776700000524
Expressed under the inertial system.
Converting the coordinate into matrix A according to the rotation relationship of the coordinate systembeRate of change and angular velocity ω of rotation of the central body of the spacecraftbThe relationship between them is:
Figure GDA00025960776700000525
the first and second derivatives of the relative motion of the original desired point position are expressed as:
Figure GDA0002596077670000061
a certain attitude orientation e in inertial spacefeThe process of switching to the spacecraft system is as follows:
efb＝Abeefe(1.11)
according to the relation between the change rate of the coordinate transformation matrix and the rotation speed of the coordinate system, the attitude of the spacecraft system points to efbThe first and second time derivatives of (d) are:
Figure GDA0002596077670000062
wherein: a. thebeA coordinate transformation matrix representing the inertial system to the spacecraft body system,
Figure GDA0002596077670000063
representing angular velocity omega of rotation of the central body of a spacecraftbThe cross-multiplication matrix of (a) is specifically written as:
Figure GDA0002596077670000064
thereby obtaining a certain expected position of the central body of the spacecraft in the inertial space under the condition of attitude motion
Figure GDA0002596077670000065
And a certain attitude heading efbThe first and second time derivatives of the change in the spacecraft centerbody coordinate system are noted as:
Figure GDA0002596077670000066
wherein:
Figure GDA0002596077670000067
representing an attitude pointing vector efbThe first two components.
Obtained in the formula
Figure GDA0002596077670000068
And
Figure GDA0002596077670000069
and compensating the trajectory planning of the mechanical arm according to the change trajectory generated by the attitude motion of the spacecraft central body in the position and the attitude direction in the inertial space.
Step three: and correspondingly summing the motion tracks of the tail end points obtained in the first step and the second step, and solving the motion track of each joint angle by adopting a mechanical arm kinematics pseudo-inverse algorithm to realize mechanical arm track planning considering the attitude motion condition of the spacecraft body.
The track of the tail end point of the mechanical arm in the initial state of the spacecraft, which is obtained in the step one
Figure GDA00025960776700000610
And
Figure GDA00025960776700000611
the compensation quantity generated by the attitude motion of the spacecraft central body obtained in the step two
Figure GDA00025960776700000612
And
Figure GDA00025960776700000613
corresponding sums, recorded as end point trajectories
Figure GDA00025960776700000614
And
Figure GDA00025960776700000615
as input for the planning of the joint trajectory of the mechanical arm:
Figure GDA0002596077670000071
based on the kinematic relationship between the position and attitude orientation of the end actuator and the mechanical arm system, the motion of the mechanical arm in a Cartesian space is converted into the motion in a joint configuration space in a manner of pseudo-inverse solution of the Jacobian matrix.
The position and attitude orientation matrix of the end-effector in Cartesian space is recorded as
Figure GDA0002596077670000072
Recording the joint angle of each mechanical arm as η, the position and orientation matrix has the following relationship with the first derivative of the joint angle:
Figure GDA0002596077670000073
wherein J(η)Is the jacobian matrix of the joint angle of the mechanical arm.
According to the formula, the obtained end point track
Figure GDA0002596077670000074
And
Figure GDA0002596077670000075
and solving the motion trail of the joint angle of the mechanical arm in a reverse way according to the known kinematic relationship of the mechanical arm. And performing pseudo-inverse operation on the Jacobian matrix in the solving process, wherein the solved operation formula is as follows:
Figure GDA0002596077670000076
wherein
Figure GDA0002596077670000077
Obtaining ideal motion trail of each joint angle of the mechanical arm through a formula
Figure GDA0002596077670000078
And
Figure GDA0002596077670000079
the mechanical arm can reach the preset expected position and the posture pointing direction in the inertial space under the condition that the central body of the spacecraft carries out the posture motion, and then the mechanical arm trajectory planning considering the posture motion of the spacecraft body is realized.
The method also comprises the following four steps: the angular trajectory of each joint of the mechanical arm planned in the third step
Figure GDA00025960776700000710
And
Figure GDA00025960776700000711
the motion control to the mechanical arm is realized through the controller.
Preferably, in order to improve the condition that singularity is easy to occur in the pseudo-inverse operation process of the Jacobian matrix, a robust adjusting item is added in the operation, and singularity is avoided to a certain extent at the cost of sacrificing precision. The factor influencing the adjusting weight in the robust adjusting term is recorded as lambda, the larger the value of the lambda is, the larger the adjusting effect on the Jacobian matrix is, and the larger the error is brought. Adjusted pseudo-inverse operation expression
Figure GDA00025960776700000712
Comprises the following steps:
Figure GDA0002596077670000081
wherein In×nRepresenting an identity matrix, its dimensions and a planned end point trajectory matrix
Figure GDA0002596077670000082
And
Figure GDA0002596077670000083
the number of rows of (c) is the same.
Has the advantages that:
1. the invention discloses a mechanical arm trajectory planning method considering spacecraft body attitude motion, which is used for solving the change of an expected position and attitude direction of an original inertia space of a system while planning spacecraft central body attitude motion, and compensating motion planning of a mechanical arm, so that the mechanical arm can still reach the original expected position and attitude direction in the inertia space when the central body performs attitude motion.
2. According to the method for planning the trajectory of the mechanical arm in consideration of the attitude motion of the spacecraft body, disclosed by the invention, the influence of the attitude motion of the central body of the spacecraft is taken into consideration in the open-loop motion planning of the mechanical arm, the motion of the mechanical arm is planned in real time without depending on the measurement information of the expected position and the attitude direction, so that the calculation requirement of the trajectory planning of the mechanical arm is reduced under the condition of the requirement of the attitude motion of the spacecraft, the calculation pressure of the on-orbit real-time trajectory planning of the mechanical arm is reduced, and the.
3. The mechanical arm trajectory planning method considering the spacecraft body attitude motion disclosed by the invention is supplemented in two traditional solving methods. First, pointing at the passing attitude
Figure GDA0002596077670000084
Solving azimuth αeIn order to avoid singularity caused by denominator being zero, a judgment is added in the traditional azimuth angle solving method, and when the attitude points to
Figure GDA0002596077670000085
Where the first and third components are both 0 define azimuth αeIs 0. Secondly, in order to reduce the possibility of singularity occurrence in pseudo-inverse solution of the Jacobian matrix of the joint angle of the mechanical arm, a robust adjusting item is added in the pseudo-inverse solution process, and singularity is avoided to a certain extent at the cost of sacrificing precision.
Drawings
Fig. 1 is a schematic flow chart of a robot arm trajectory planning method considering spacecraft body attitude motion disclosed by the invention.
FIG. 2 is a schematic view of an end effector attitude heading vector and azimuth.
Fig. 3(a) is a graph showing the x-axis position tracking result.
Fig. 3(b) is a diagram showing the result of y-axis position tracking.
Fig. 3(c) is a graph showing the result of z-axis position tracking.
Fig. 4(a) is a difference diagram between the robot arm end point position and the desired position.
Fig. 4(b) is a difference diagram between the robot arm end point attitude heading and the desired attitude heading.
Fig. 5 is a comparison of whether determinant values of a jacobian matrix of joint angles of the mechanical arm supplement robust adjustment items in the mechanical arm trajectory planning process.
Detailed Description
For a better understanding of the objects and advantages of the present invention, reference should be made to the following detailed description taken in conjunction with the accompanying drawings and examples.
Example 1:
the embodiment discloses a track planning method for a mechanical arm composed of five sections of arm rods, and the track planning and simulation are carried out on the tail end position and the attitude direction of the mechanical arm aiming at the attitude motion task condition of a central body of a spacecraft. As shown in fig. 1, the method for planning the trajectory of the robot arm considering the attitude motion of the spacecraft body disclosed in this embodiment may be completed through the following steps:
the method comprises the following steps: and determining the position and attitude pointing change track of the tail end actuator on the mechanical arm by a quintic polynomial path planning method in the initial state of the spacecraft.
Initial values of relevant parameters of the spacecraft and the mechanical arm carried by the spacecraft are shown in table 1.
TABLE 1 spacecraft Central body and robot arm initial parameters
Figure GDA0002596077670000091
Defining azimuth αnRepresenting attitude heading
Figure GDA0002596077670000092
And the main system XbObZbAngle between planes, αeRepresenting attitude heading
Figure GDA0002596077670000093
In the main system XbObZbProjection on plane and body system ObZbAngle between axes according to azimuth αnAnd αeIs defined as
Figure GDA0002596077670000101
Wherein:
Figure GDA0002596077670000102
representing gestural pointing
Figure GDA0002596077670000103
The second component of (a).
In gesture-based pointing
Figure GDA0002596077670000104
Solving azimuth αeIn order to avoid singularity due to zero denominator, azimuth α is seteThe solution process of (2) is defined as:
Figure GDA0002596077670000105
wherein:
Figure GDA0002596077670000106
representing gestural pointing
Figure GDA0002596077670000107
The second component of (a) is,
Figure GDA0002596077670000108
representing gestural pointing
Figure GDA0002596077670000109
The third component.
According to the data shown in Table 1, the mechanical arm tail end is obtained through the spacecraft kinematics relationshipInitial position under spacecraft system
Figure GDA00025960776700001010
And azimuth angle
Figure GDA00025960776700001011
And
Figure GDA00025960776700001012
formed matrix azimuth matrix α0Comprises the following steps:
Figure GDA00025960776700001013
α0＝[14.94 95.14]Tdeg
the differences between the attitude of the central body, the end position of the robot arm and the attitude heading at the beginning and end states are shown in table 2.
TABLE 2 Start and end State parameter Differences
Figure GDA00025960776700001014
In the method for planning the fifth-order polynomial, the coefficient to be determined of the fifth-order polynomial is solved according to the difference value of variables in the states of the start and the end of a task and the limitation of the change rate, and then the second-order smooth change process of the planning quantity with respect to time is obtained. The expected value of the planned quantity theta is recorded as thetarThe value of the initial state is recorded as theta0Defining the maximum value of the first derivative in the parameter variation as
Figure GDA00025960776700001015
Maximum of the second derivative is
Figure GDA00025960776700001016
Then according to the fifth order polynomial, there are:
Figure GDA00025960776700001017
wherein,
Figure GDA0002596077670000111
the time coefficient tau is the current time t and the task duration tfThe ratio of (a) to (b).
According to the constraint conditions such as the change rate of the characteristics of the fifth-order polynomial and the variables in the initial and final states of the task, the task duration is constrained as follows:
Figure GDA0002596077670000112
substituting constraint conditions such as mechanical arm joint motion and the like to obtain the shortest task time t meeting the constraint of the spacecraft central body motion and each mechanical arm motion simultaneouslyfIt was 57.5 s.
Adopting a method of a fifth-order polynomial to adjust the tail end position of the mechanical arm
Figure GDA0002596077670000113
And azimuth angle αn、αeAnd spacecraft central body attitude motion, the planning quantity and the first and second derivatives thereof are expressed as:
Figure GDA0002596077670000114
according to azimuth αnAnd αePointing to the posture
Figure GDA0002596077670000115
The geometrical relationship between the two is as follows:
Figure GDA0002596077670000116
to the gesture direction
Figure GDA0002596077670000117
Calculating first and second time derivatives of
Figure GDA0002596077670000118
Figure GDA0002596077670000119
Wherein phi is an azimuth α matrix and an attitude heading
Figure GDA00025960776700001110
The conversion matrix between is specifically written as:
Figure GDA00025960776700001111
at this point, the lower position of the end effector in the Cartesian space is obtained through the programming of a quintic polynomial method
Figure GDA00025960776700001112
Pointing to the posture
Figure GDA00025960776700001113
Smoothing successive ideal first and second time derivative matrices
Figure GDA00025960776700001114
And
Figure GDA0002596077670000121
Figure GDA0002596077670000122
due to attitude pointing
Figure GDA0002596077670000123
The three components in the vector are not completely independent, so that
Figure GDA0002596077670000124
Representing gestural pointing
Figure GDA0002596077670000125
The first two components of the vector, denoted
Figure GDA0002596077670000126
Wherein:
Figure GDA0002596077670000127
derived mechanical arm end actuator position
Figure GDA0002596077670000128
Pointing to the posture
Figure GDA0002596077670000129
Smoothing successive first and second time derivative matrices
Figure GDA00025960776700001210
And
Figure GDA00025960776700001211
namely, the mechanical arm end actuator obtained by the quintic polynomial programming method moves to the original expected position
Figure GDA00025960776700001212
Pointing to the original expected attitude
Figure GDA00025960776700001213
The trajectory of (2). The solid line illustrated as "p 1" in fig. 3 is the result of performing only the original spatial fixation position without compensating for the tracking situation.
Step two: carrying out attitude motion planning according to the attitude motion requirement of the central body of the spacecraft, and simultaneously obtaining the original expected position of the system
Figure GDA00025960776700001214
Pointing to the posture
Figure GDA00025960776700001215
The changing trajectory due to the central body attitude motion compensates for the trajectory planning of the robotic arm.
A desired position in the central body of the spacecraftDevice for placing
Figure GDA00025960776700001216
By the inertial space position vector in which it is located
Figure GDA00025960776700001217
The relative position with respect to an inertial space position vector R of the center of mass of the spacecraft centerbody is represented, and the transition from the inertial frame to the spacecraft frame is:
Figure GDA00025960776700001218
wherein: a. thebeA coordinate transformation matrix representing the inertial system to the spacecraft body system,
Figure GDA00025960776700001219
indicating a desired position in the central body of a spacecraft
Figure GDA00025960776700001220
Expressed under the inertial system.
Converting the coordinate into matrix A according to the rotation relationship of the coordinate systembeRate of change and angular velocity ω of rotation of the central body of the spacecraftbThe relationship between them is:
Figure GDA00025960776700001221
the first and second derivatives of the relative motion of the original desired point position are expressed as:
Figure GDA00025960776700001222
Figure GDA00025960776700001223
a certain attitude orientation e in inertial spacefeThe process of switching to the spacecraft system is as follows:
efb＝Abeefe
according to the relation between the change rate of the coordinate transformation matrix and the rotation speed of the coordinate system, the attitude of the spacecraft system points to efbThe first and second time derivatives of (d) are:
Figure GDA0002596077670000131
Figure GDA0002596077670000132
wherein: a. thebeCoordinate transformation matrix, omega, representing the inertial system to the spacecraft body systembRepresenting the rotating angular speed of the central body of the spacecraft, the wave number above the central body is marked by a cross-multiplication matrix,
Figure GDA00025960776700001317
the specific writing is as follows:
Figure GDA0002596077670000133
thereby obtaining a certain expected position of the central body of the spacecraft in the inertial space under the condition of attitude motion
Figure GDA0002596077670000134
And a certain attitude heading efbThe first and second time derivatives of the change in the spacecraft centerbody coordinate system are noted as:
Figure GDA0002596077670000135
wherein:
Figure GDA0002596077670000136
representing an attitude pointing vector efbThe first two components.
Figure GDA0002596077670000137
And
Figure GDA0002596077670000138
and compensating the trajectory planning of the mechanical arm according to the change trajectory generated by the attitude motion of the spacecraft central body in the position and the attitude direction in the inertial space.
Step three: and correspondingly summing the motion tracks of the tail end points obtained in the first step and the second step, and solving the motion track of each joint angle by adopting a mechanical arm kinematics pseudo-inverse algorithm to realize mechanical arm track planning considering the attitude motion condition of the spacecraft body.
The track of the tail end point of the mechanical arm in the initial state of the spacecraft, which is obtained in the step one
Figure GDA0002596077670000139
And
Figure GDA00025960776700001310
the compensation quantity generated by the attitude motion of the spacecraft central body obtained in the step two
Figure GDA00025960776700001311
And
Figure GDA00025960776700001312
corresponding sums, recorded as end point trajectories
Figure GDA00025960776700001313
And
Figure GDA00025960776700001314
as input for the planning of the joint trajectory of the mechanical arm:
Figure GDA00025960776700001315
Figure GDA00025960776700001316
based on end-effectorsThe kinematic relationship between the position and attitude orientation and the mechanical arm system converts the motion of the mechanical arm in a Cartesian space into the motion in a joint configuration space in a mode of pseudo-inverse solution of the Jacobian matrix. The position and attitude orientation matrix of the end-effector in Cartesian space is recorded as
Figure GDA0002596077670000141
The joint angle of each mechanical arm is recorded as
Figure GDA00025960776700001411
The pose matrix and the first derivative of the joint angle have the following relationship:
Figure GDA0002596077670000142
wherein J(η)Jacobian matrix for the arm joint angle:
Figure GDA0002596077670000143
in the formula AbjIs a coordinate transformation matrix from the j section mechanical arm coordinate system to the main system,jis a j section mechanical arm rotating shaft direction matrix, ejtIs the attitude pointing vector r between the jth section of mechanical arm and the tail end actuatorjtIs the vector from the center of mass of the jth arm to the center of mass of the end effector.
In order to enable the number of the degrees of freedom of the mechanical arm to meet the planning requirements of position and posture pointing, the tail end joint of the mechanical arm has three degrees of freedom. In order to determine the attitude orientation of the end actuator, the relation between the rotation angular speed of the end actuator relative to the last mechanical arm and the joint angle of the end actuator is defined to be the same as the relation between the angular speed and the attitude angle in the 3-1-2 rotation mode in the spacecraft attitude kinematics. End effector coordinate system f5Coordinate system f of the previous section of mechanical arm4A conversion matrix of45＝(Ay(θ(2))Ax(θ(1))Az(θ(3)))TAnd θ (k) represents the kth component of the attitude angle θ.
According to the obtained tail end point track
Figure GDA0002596077670000144
And
Figure GDA0002596077670000145
and solving the motion trail of the joint angle of the mechanical arm in a reverse way according to the known kinematic relationship of the mechanical arm. And performing pseudo-inverse operation on the Jacobian matrix in the solving process, wherein the solved operation formula is as follows:
Figure GDA0002596077670000146
Figure GDA0002596077670000147
wherein
Figure GDA0002596077670000148
The obtained ideal motion track of each joint angle of the mechanical arm
Figure GDA0002596077670000149
And
Figure GDA00025960776700001410
the planning method can realize the planning of the mechanical arm track considering the attitude motion of the spacecraft body, so that the mechanical arm can reach the preset expected position and the attitude direction in the inertial space under the condition that the spacecraft central body carries out the attitude motion. As shown in fig. 3(a), fig. 3(b) and fig. 3(c) by the dashed line labeled "p 12", the result of the mechanical arm motion compensation based on the central body attitude motion substantially reduces the difference between the target and the target when no compensation planning is performed, and improves the planning accuracy. As shown in fig. 4(a) and 4(b), the difference between the planned trajectory of the robot arm considering the attitude motion of the spacecraft body and the desired position and attitude heading is finally converged to zero, which indicates that the desired value can be reached.
The method also comprises the following four steps: machine for planning three middle stepsAngular orbit of each joint of mechanical arm
Figure GDA0002596077670000151
And
Figure GDA0002596077670000152
the motion control to the mechanical arm is realized through the controller.
Preferably, in order to improve the condition that singularity is easy to occur in the pseudo-inverse operation process of the Jacobian matrix, a robust adjusting item is added in the operation, and singularity is avoided to a certain extent at the cost of sacrificing precision. The factor influencing the adjusting weight in the robust adjusting term is recorded as lambda, the larger the value of the lambda is, the larger the adjusting effect on the Jacobian matrix is, and the larger the error is brought. In the modified pseudo-inverse operation expression
Figure GDA0002596077670000153
Comprises the following steps:
Figure GDA0002596077670000154
in the formula I5×5Representing a five-dimensional identity matrix.
In this embodiment, the adjustment factor λ is 10-3. As shown in fig. 5, whether to add a robust adjustment term has an effect on the jacobian matrix determinant values, the closer to zero the more likely it is to generate singularities.
Under the trajectory planning method of the mechanical arm, the tail end of the mechanical arm can reach a certain fixed expected position and attitude direction in an inertial space under the condition that the central body of the spacecraft carries out certain attitude motion, the motion of the mechanical arm is planned in real time without depending on measurement information of the expected position and the attitude direction, the calculation pressure of the on-orbit real-time trajectory planning of the mechanical arm is reduced, and the planning efficiency is improved.
The above detailed description is intended to illustrate the objects, aspects and advantages of the present invention, and it should be understood that the above detailed description is only exemplary of the present invention and is not intended to limit the scope of the present invention, and any modifications, equivalents, improvements and the like within the spirit and principle of the present invention should be included in the scope of the present invention.

Claims (5)

1. The mechanical arm trajectory planning method considering spacecraft body attitude motion is characterized by comprising the following steps of: comprises the following steps of (a) carrying out,
the method comprises the following steps: determining the position of a mechanical arm end actuator and the change track of the attitude pointing direction by a quintic polynomial path planning method in the initial state of the spacecraft;
secondly, performing attitude motion planning according to the attitude motion requirement of the central body of the spacecraft, and simultaneously obtaining the original expected position of the system
Figure FDA0002596077660000011
Pointing to the posture
Figure FDA0002596077660000012
Compensating the trajectory planning of the mechanical arm due to the changing trajectory generated by the attitude motion of the central body;
step three: correspondingly summing the motion tracks of the tail end points obtained in the first step and the second step, solving the motion track of each joint angle by adopting a mechanical arm kinematics pseudo-inverse algorithm, and realizing mechanical arm track planning considering the attitude motion condition of the spacecraft body;
the specific implementation method of the step one is that,
defining a central body coordinate system f of a service spacecraft at an initial moment in an initial state of the spacecraftb0And the system of inertia feCoincident, central body coordinate system fbMove with the movement of the central body; obtaining the initial position of the tail end of the mechanical arm under the system according to the initial states of the central body and the mechanical arm of the service spacecraft
Figure FDA0002596077660000013
And initial attitude heading
Figure FDA0002596077660000014
Presetting the maximum value of the motion speed of the service spacecraft central body and the mechanical arm and the original expected position of the service spacecraft central body under a coordinate system
Figure FDA0002596077660000015
Pointing to the original expected attitude
Figure FDA0002596077660000016
Due to initial attitude pointing
Figure FDA0002596077660000017
Vector and original expected attitude pointing
Figure FDA0002596077660000018
All vectors are expressed by direction cosine and the moduli of the vectors are all 1, so that the initial attitude points to
Figure FDA0002596077660000019
Vector and original expected attitude pointing
Figure FDA00025960776600000110
Respectively having three components which are not completely independent, so that the first two components are respectively selected as variables, but the corresponding third component has positive and negative possibilities, and in order to avoid uncertainty caused by the positive and negative possibilities, the attitude direction represented by direction cosine is converted into two azimuth angles α in spacenAnd αeThe first and second time derivatives of the attitude of the end effector are obtained and converted into the first and second time derivatives of the direction cosine, the azimuth is defined αnRepresenting attitude heading
Figure FDA00025960776600000111
And the main system XbObZbAngle between planes, αeRepresenting attitude heading
Figure FDA00025960776600000112
In the main system XbObZbProjection on plane and body system ObZbThe included angle between the axes;
according to the azimuth angle αnAnd αeIs defined as
Figure FDA00025960776600000113
Wherein:
Figure FDA00025960776600000114
representing gestural pointing
Figure FDA00025960776600000115
The second component of (a);
in gesture-based pointing
Figure FDA00025960776600000116
Solving azimuth αeIn order to avoid singularity due to zero denominator, azimuth α is seteThe solution process of (2) is defined as:
Figure FDA0002596077660000021
wherein:
Figure FDA0002596077660000022
representing gestural pointing
Figure FDA0002596077660000023
The second component of (a) is,
Figure FDA0002596077660000024
representing gestural pointing
Figure FDA0002596077660000025
The third component;
through powderEnd actuator initial attitude pointing
Figure FDA0002596077660000026
Obtaining an initial azimuth αn_0And αe_0Pointing by the end-effector to the desired attitude
Figure FDA0002596077660000027
Obtaining an original desired azimuth αn_r0And αe_r0(ii) a Bringing the end effector to the desired position
Figure FDA0002596077660000028
And original desired azimuth αn_r0And αe_r0And initial position
Figure FDA0002596077660000029
And initial azimuth αn_0And αe_0Making a difference to obtain the original position variation and the original azimuth variation of the tail end actuator;
in the quintic polynomial planning method, a coefficient to be determined of a quintic polynomial is solved according to a difference value of a variable in a task starting state and a task ending state and a change rate limit, and a second-order smooth change process of a planning quantity with respect to time is further obtained; the expected value of the planned quantity theta is recorded as thetarThe value of the initial state is recorded as theta0Defining the maximum value of the first derivative in the parameter variation as
Figure FDA00025960776600000210
Maximum of the second derivative is
Figure FDA00025960776600000211
Then according to the fifth order polynomial, there are:
Figure FDA00025960776600000212
wherein,
Figure FDA00025960776600000213
the time coefficient tau is the current time t and the task duration tfThe ratio of (A) to (B);
according to the constraint conditions such as the limitation of the characteristic of the fifth-order polynomial and the change rate of the planning quantity, the task duration has the following constraint:
Figure FDA00025960776600000214
selecting the smallest one of the conditions simultaneously meeting the formula as the shortest time required by the task, thereby obtaining the shortest task time t meeting the motion constraint of each mechanical armf(ii) a On finding the task duration tfThen, based on the method of the fifth order polynomial, the planning quantity θ and its first and second time derivatives are:
Figure FDA0002596077660000031
in the process of planning the track of the mechanical arm, the planned quantity is the position of an actuator at the tail end of the mechanical arm
Figure FDA0002596077660000032
And attitude pointing
Figure FDA0002596077660000033
Solving the position of the mechanical arm end actuator by the method of the fifth-order polynomial
Figure FDA0002596077660000034
And azimuth angle
Figure FDA0002596077660000035
And
Figure FDA0002596077660000036
smooth continuous first and second time derivatives;
due to the azimuth angle of the mechanical arm end actuator
Figure FDA0002596077660000037
And
Figure FDA0002596077660000038
is difficult to write into a form of showing the angular velocity of the mechanical arm joint, and the posture points to
Figure FDA0002596077660000039
The track can be written into a form of showing the angular velocity of the mechanical arm joint, which is beneficial to planning the mechanical arm joint track; therefore, before solving the joint angle motion law through the inverse kinematics relation of the mechanical arm, the azimuth angle of the end actuator on the mechanical arm is used
Figure FDA00025960776600000310
And
Figure FDA00025960776600000311
and its trajectory is converted into attitude pointing
Figure FDA00025960776600000312
The change trajectory of (2); according to the azimuth
Figure FDA00025960776600000313
And
Figure FDA00025960776600000314
pointing to the posture
Figure FDA00025960776600000315
The geometrical relationship between the two is as follows:
Figure FDA00025960776600000316
to the gesture direction
Figure FDA00025960776600000317
Calculating first and second time derivatives of
Figure FDA00025960776600000318
Wherein α is the azimuth angle
Figure FDA00025960776600000319
And
Figure FDA00025960776600000320
formed matrix of phi azimuth α matrix and attitude orientation
Figure FDA00025960776600000321
The conversion matrix between is specifically written as:
Figure FDA00025960776600000322
at this point, the lower position of the end effector in the Cartesian space is obtained through the programming of a quintic polynomial method
Figure FDA00025960776600000323
Pointing to the posture
Figure FDA00025960776600000324
Smoothing successive ideal first and second time derivative matrices
Figure FDA00025960776600000325
And
Figure FDA00025960776600000326
Figure FDA00025960776600000327
due to attitude pointing
Figure FDA00025960776600000328
The three components in the vector are not completely independent, so that
Figure FDA00025960776600000329
Representing gestural pointing
Figure FDA00025960776600000330
The first two components of the vector, denoted
Figure FDA00025960776600000331
Wherein:
Figure FDA0002596077660000041
position of mechanical arm end actuator obtained by formula
Figure FDA0002596077660000042
Pointing to the posture
Figure FDA0002596077660000043
Smoothing successive first and second time derivative matrices
Figure FDA0002596077660000044
And
Figure FDA0002596077660000045
namely, the mechanical arm end actuator obtained by the quintic polynomial programming method moves to the original expected position
Figure FDA0002596077660000046
Pointing to the original expected attitude
Figure FDA0002596077660000047
The trajectory of (2).
2. As claimed inSolving 1 the mechanical arm trajectory planning method considering spacecraft body attitude motion is characterized in that: step four, the angular trajectory of each joint of the mechanical arm planned in the step three is further included
Figure FDA0002596077660000048
And
Figure FDA0002596077660000049
the motion control to the mechanical arm is realized through the controller.
3. The method for planning a trajectory of a robotic arm taking into account attitude motion of a spacecraft of claim 1, wherein: the concrete implementation method of the second step is that,
at a desired position in the central body of the spacecraft
Figure FDA00025960776600000410
By the inertial space position vector in which it is located
Figure FDA00025960776600000411
The relative position with respect to an inertial space position vector R of the center of mass of the spacecraft centerbody is represented, and the transition from the inertial frame to the spacecraft frame is:
Figure FDA00025960776600000412
wherein: a. thebeA coordinate transformation matrix representing the inertial system to the spacecraft body system,
Figure FDA00025960776600000413
indicating a desired position in the central body of a spacecraft
Figure FDA00025960776600000414
Expressed in the inertial system;
coordinate transformation based on coordinate system rotation relationshipMatrix AbeRate of change and angular velocity ω of rotation of the central body of the spacecraftbThe relationship between them is:
Figure FDA00025960776600000415
the first and second derivatives of the relative motion of the original desired point position are expressed as:
Figure FDA00025960776600000416
a certain attitude orientation e in inertial spacefeThe process of switching to the spacecraft system is as follows:
efb＝Abeefe(0.11)
according to the relation between the change rate of the coordinate transformation matrix and the rotation speed of the coordinate system, the attitude of the spacecraft system points to efbThe first and second time derivatives of (d) are:
Figure FDA00025960776600000417
wherein: a. thebeA coordinate transformation matrix representing the inertial system to the spacecraft body system,
Figure FDA00025960776600000418
representing angular velocity omega of rotation of the central body of a spacecraftbThe cross-multiplication matrix of (1) is specifically written as:
Figure FDA0002596077660000051
thereby obtaining a certain expected position of the central body of the spacecraft in the inertial space under the condition of attitude motion
Figure FDA0002596077660000052
And a certain attitude heading efbFirst and second order times of change in spacecraft centerbody coordinate systemThe intermediate derivative, which is noted as:
Figure FDA0002596077660000053
wherein:
Figure FDA0002596077660000054
representing an attitude pointing vector efbThe first two components;
obtained in the formula
Figure FDA0002596077660000055
And
Figure FDA0002596077660000056
and compensating the trajectory planning of the mechanical arm according to the change trajectory generated by the attitude motion of the spacecraft central body in the position and the attitude direction in the inertial space.
4. The method for planning a trajectory of a robotic arm taking into account the attitude motion of a spacecraft of claim 3, wherein: the third step is realized by the concrete method that,
the track of the tail end point of the mechanical arm in the initial state of the spacecraft, which is obtained in the step one
Figure FDA0002596077660000057
And
Figure FDA0002596077660000058
the compensation quantity generated by the attitude motion of the spacecraft central body obtained in the step two
Figure FDA0002596077660000059
And
Figure FDA00025960776600000510
corresponding sums, recorded as end point trajectories
Figure FDA00025960776600000511
And
Figure FDA00025960776600000512
as input for the planning of the joint trajectory of the mechanical arm:
Figure FDA00025960776600000513
based on the kinematic relationship between the position and attitude orientation of the tail end actuator and the mechanical arm system, converting the motion of the mechanical arm in a Cartesian space into the motion in a joint configuration space by a pseudo-inverse solution mode of a Jacobian matrix;
the position and attitude orientation matrix of the end-effector in Cartesian space is recorded as
Figure FDA00025960776600000514
Recording the joint angle of each mechanical arm as η, the position and orientation matrix has the following relationship with the first derivative of the joint angle:
Figure FDA00025960776600000515
wherein J(η)A jacobian matrix of the joint angle of the mechanical arm;
according to the formula, the obtained end point track
Figure FDA00025960776600000516
And
Figure FDA00025960776600000517
solving the motion trail of the joint angle of the mechanical arm in a reverse way according to the known kinematic relationship of the mechanical arm; and performing pseudo-inverse operation on the Jacobian matrix in the solving process, wherein the solved operation formula is as follows:
Figure FDA0002596077660000061
wherein
Figure FDA0002596077660000062
Obtaining ideal motion trail of each joint angle of the mechanical arm through a formula
Figure FDA0002596077660000063
And
Figure FDA0002596077660000064
the mechanical arm can reach the preset expected position and the posture pointing direction in the inertial space under the condition that the central body of the spacecraft carries out the posture motion, and then the mechanical arm trajectory planning considering the posture motion of the spacecraft body is realized.
5. The method for planning a trajectory of a robotic arm taking into account the attitude motion of a spacecraft of claim 4, wherein: in order to improve the condition that singularity is easy to occur in the pseudo-inverse operation process of the Jacobian matrix, a robust adjusting item is added in the operation, and singularity is avoided to a certain extent at the cost of sacrificing precision; the factor influencing the adjusting weight in the robust adjusting item is recorded as lambda, the larger the value of the lambda is, the larger the adjusting effect on the Jacobian matrix is, and meanwhile, the larger the error is brought; adjusted pseudo-inverse operation expression
Figure FDA0002596077660000065
Comprises the following steps:
Figure FDA0002596077660000066
wherein In×nRepresenting an identity matrix, its dimensions and a planned end point trajectory matrix
Figure FDA0002596077660000067
And
Figure FDA0002596077660000068
the number of rows of (c) is the same.
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Citations (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN103235597A (en) * 2013-04-09 2013-08-07 北京理工大学 Rapid stable joint control method for attitude maneuver of spacecraft
CN106891335A (en) * 2017-03-23 2017-06-27 北京空间飞行器总体设计部 A kind of submissive and control method for coordinating of the in-orbit capture process of robot for space
CN108132601A (en) * 2017-12-06 2018-06-08 西北工业大学 A kind of method for inhibiting spacecraft pedestal attitude disturbance using mechanical arm
CN108214519A (en) * 2017-12-18 2018-06-29 北京航空航天大学 A kind of aerial any attitude extremely lands the self-adjusting quadruped robot of posture
EP3351355A1 (en) * 2015-09-18 2018-07-25 Kawasaki Jukogyo Kabushiki Kaisha Device and method for positioning processing tool
CN108621162A (en) * 2018-05-09 2018-10-09 广西科技大学 A kind of manipulator motion planning method

Patent Citations (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN103235597A (en) * 2013-04-09 2013-08-07 北京理工大学 Rapid stable joint control method for attitude maneuver of spacecraft
EP3351355A1 (en) * 2015-09-18 2018-07-25 Kawasaki Jukogyo Kabushiki Kaisha Device and method for positioning processing tool
CN106891335A (en) * 2017-03-23 2017-06-27 北京空间飞行器总体设计部 A kind of submissive and control method for coordinating of the in-orbit capture process of robot for space
CN108132601A (en) * 2017-12-06 2018-06-08 西北工业大学 A kind of method for inhibiting spacecraft pedestal attitude disturbance using mechanical arm
CN108214519A (en) * 2017-12-18 2018-06-29 北京航空航天大学 A kind of aerial any attitude extremely lands the self-adjusting quadruped robot of posture
CN108621162A (en) * 2018-05-09 2018-10-09 广西科技大学 A kind of manipulator motion planning method

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