CN111098299B - Method for compensating disturbance of space robot - Google Patents

Method for compensating disturbance of space robot Download PDF

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CN111098299B
CN111098299B CN201911241734.8A CN201911241734A CN111098299B CN 111098299 B CN111098299 B CN 111098299B CN 201911241734 A CN201911241734 A CN 201911241734A CN 111098299 B CN111098299 B CN 111098299B
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CN111098299A (en
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侯月阳
卢山
王奉文
张竞天
姜泽华
尹俊雄
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Shanghai Aerospace Control Technology Institute
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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
    • B25J9/1628—Programme controls characterised by the control loop
    • B25J9/1633—Programme controls characterised by the control loop compliant, force, torque control, e.g. combined with position control

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Abstract

The invention discloses a method for compensating disturbance of a space robot, which comprises the following steps: s1, establishing an overall dynamics model of the space robot based on Kennel dynamics; s2, establishing a rigid body dynamics model of the platform according to the space robot overall dynamics model, and calculating the disturbance moment of the mechanical arm to the platform posture; and S3, calculating the feedforward compensation amount of the platform attitude control from the angular momentum layer, and realizing the compensation of the disturbance torque of the platform attitude. The method is based on the Keynen dynamics principle to respectively establish the space robot overall dynamics model and the dynamics model of the space robot platform, so that the disturbance moment of the mechanical arm to the platform attitude is quickly and accurately calculated, the platform attitude disturbance moment is effectively compensated, the method has the characteristics of less calculation amount and accurate calculation result, and meanwhile, a new thought is provided for on-satellite control.

Description

Method for compensating disturbance of space robot
Technical Field
The invention relates to the field of space robots, in particular to a disturbance compensation method in a capture process of a space floating robot based on a Kennel dynamics principle.
Background
The spatial floating robot comprises a platform and mechanical arms, a large amount of research is conducted on mechanical arm modeling at home and abroad, various methods such as Lagrange, Newton-Euler, Kenn and the like are adopted, various factors are considered, however, for practical application, the mechanical arms are mostly used as disturbance to conduct anti-disturbance control on the platform, and integrated modeling is not conducted on the spatial floating robot to conduct disturbance compensation. And the international method for compensating the interference torque of the space floating robot is to establish a dynamic model of the space floating robot based on the Newton Euler principle, calculate the interference force/torque, and perform the compensation control of the interference torque by adopting a feedback mode, so that the calculation times are more, the simulation efficiency is very low, and the resource consumption of the controller is larger.
Disclosure of Invention
The invention provides a method for compensating disturbance of a space robot, which is characterized in that the space robot is integrally modeled based on the Kenn dynamics principle, the disturbance moment of a mechanical arm of the space robot on the platform attitude is calculated and obtained, and the disturbance moment of the platform attitude is subjected to feedforward compensation by utilizing an integrated dynamics model to calculate angular momentum.
In order to achieve the above object, the present invention provides a method for compensating disturbance of a space robot, comprising the following steps:
s1, establishing an overall dynamics model of the space robot based on Kennel dynamics;
s2, establishing a rigid body dynamics model of the platform according to the space robot overall dynamics model, and calculating the disturbance moment of the mechanical arm to the platform posture;
and S3, calculating the feedforward compensation amount of the platform attitude control from the angular momentum layer, and realizing the compensation of the disturbance torque of the platform attitude.
Preferably, the overall dynamic model of the space robot is as follows:
Figure GDA0003012304340000021
in the formula (I), the compound is shown in the specification,
Figure GDA0003012304340000022
Figure GDA0003012304340000023
in the formula, mjIs a single rigid body BjI is a mass unit matrix, Sj、JjIs a single rigid body BjOrigin O of coordinate systemjThe static moment and the inertia moment of the rotor,
Figure GDA0003012304340000024
and
Figure GDA0003012304340000025
respectively represent a single rigid body BjAcceleration and angular acceleration of, omegajRepresents a rigid body BjThe angular velocity of (a) of (b),
Figure GDA0003012304340000026
representing the first derivative of the control input quantity,pVjrepresenting a single rigid body BjThe speed of the deviation is controlled by the speed controller,pωjrepresenting a single rigid body BjThe speed of the deflection angle is set to be,
Figure GDA0003012304340000027
representing a single rigid body BjOrigin O of coordinate systemjIn the form of a cross-product of the static moments,
Figure GDA0003012304340000028
represents a rigid body BjForm of angular velocity cross product of fbAnd τbRespectively the main power and the main moment of the platform;
the driving moment of the platform is taken as the front 6 on the right side of the equal sign of the formula (11), and the disturbance moment of the robot arm to the platform attitude is taken as the right side of the equal sign of the formula (11) from the 7 th row.
Preferably, the rigid body dynamics model of the platform is:
Figure GDA0003012304340000029
in the formula (I), the compound is shown in the specification,
Figure GDA00030123043400000210
respectively representing the projection change rate of the platform speed and the angular speed on the platform rigid body coordinate system, mbRepresenting platform quality, SbRepresenting the origin O of the platform coordinate systembThe static moment of (a) of (b),
Figure GDA00030123043400000211
representing the origin O of the platform coordinate systembCross multiplication form of the static moment of (J)bRepresenting the origin O of the platform coordinate systembThe inertia of the rotor is reduced to zero,
Figure GDA00030123043400000212
form of cross multiplication, V, representing the projection of a rigid body on a platform rigid body coordinate systembRepresenting the projection of the platform velocity on the platform rigid body coordinate system, frfAnd τrfThe difference between the main power and the disturbance power of the space robot platform and the difference between the main moment and the disturbance moment of the space robot platform are respectively; the right side of the equal sign of the formula (12) comprises the main moment of the platform and the disturbance moment of the mechanical arm to the attitude of the platform;
take "first 6 rows" of equation (11):
Figure GDA0003012304340000031
in the formula, MbAnd MbmRespectively an inertia matrix of the platform and an inertia matrix of the mechanical arm coupled with the platform,
Figure GDA0003012304340000032
is the angular acceleration of the joints of the mechanical arm,
Figure GDA0003012304340000033
is the generalized inertial force of the system;
subtracting the formula (13) from the formula (12) to obtain the disturbance torque of the mechanical arm to the platform attitude:
Figure GDA0003012304340000034
in the formula (I), the compound is shown in the specification,
Figure GDA0003012304340000035
preferably, the angular momentum feedforward compensation quantity for attitude control of the space robot platform is as follows:
Figure GDA0003012304340000036
in the formula IkIs the moment of inertia of the kth arm, phikIs an array formed by joint angles of a kth mechanical arm, KffIs a proportionality coefficient, and the value range is more than 0 and less than Kff＜1；
Increase arm angular momentum compensation circuit in platform attitude control system's control circuit, realize the compensation of arm to platform gesture disturbance moment, arm angular momentum compensation circuit is:
Figure GDA0003012304340000037
in the formula, hdTo command angular momentum, KmIs a symmetric positive definite matrix.
The invention has the following advantages:
the invention discloses a method for compensating the disturbance of a space robot, which is characterized in that an overall dynamics model of the space robot and a dynamics model of a space robot platform are respectively established based on the Kene dynamics principle, so that the disturbance torque of a mechanical arm to the platform attitude is rapidly and accurately calculated, feedforward supplementary control is established from the angular momentum level, and the feedforward compensation of the disturbance torque of the platform attitude is effectively realized. The invention has the characteristics of less calculation amount and accurate calculation result, and simultaneously provides a new idea for on-satellite control.
Drawings
FIG. 1 is a structural diagram of a space robot provided by the present invention;
fig. 2 is a flowchart of a method for compensating a disturbance torque of a space robot according to an embodiment of the present invention.
Detailed Description
The method for compensating the disturbance of the space robot provided by the invention is further described in detail by combining the figures and the specific embodiment. Advantages and features of the present invention will become apparent from the following description and from the claims. It is to be noted that the drawings are in a very simplified form and are all used in a non-precise ratio for the purpose of facilitating and distinctly aiding in the description of the embodiments of the invention.
As shown in fig. 1, the space robot includes a platform and a plurality of robot arms, and the robot arms may disturb the posture of the platform during movement to generate a disturbance torque.
As shown in fig. 2, the method for compensating for disturbance of a space robot disclosed by the present invention comprises the following steps:
s1, establishing an overall dynamics model of the space robot based on Kennel dynamics;
each rod piece of the space robot is equivalent to each single rigid body, and based on the Keen power principle, a single rigid body dynamic model is as follows:
Figure GDA0003012304340000041
in the formula, mjIs a single rigid body BjI is a mass unit matrix, Sj、JjIs a single rigid body BjOrigin O of coordinate systemjThe static moment and inertia of the physical quantity, the sign of the above physical quantity to indicate that the physical quantity and the following physical quantity carry out cross multiplication operation,
Figure GDA0003012304340000042
and
Figure GDA0003012304340000043
respectively represent a single rigid body BjAcceleration and angular acceleration of, omegajRepresents a rigid body BjAngular velocity of fjTo act on BjPrincipal vector of the force system of (1), τjTo act on BjForce system ofjPrincipal moment of (f)j，τjIncluding all actions on BjThe effect of the force of (c).
Formula (1) left-hand multiplying velocity and angular velocity partial derivatives
Figure GDA0003012304340000044
And single rigid body BjAcceleration and angular acceleration of
Figure GDA0003012304340000045
Substituting the compound into the formula (1),
Figure GDA0003012304340000046
wherein v isjRepresents a rigid body BjThe speed of (2).
Summing the dynamic models of all the single rigid bodies of the space robot, the following can be obtained:
Figure GDA0003012304340000051
order to
Figure GDA0003012304340000052
Figure GDA0003012304340000053
Then, formula (3) is:
Figure GDA0003012304340000054
order to
M＝∑Mj
Figure GDA0003012304340000055
Then
Equation (4) left side of equal sign can be simplified as:
Figure GDA0003012304340000056
due to the fact that
Figure GDA0003012304340000057
For active and/or constraining forces in the joints of the space robot and externally applied forces, namely:
Figure GDA0003012304340000058
when formula (6) is substituted into formula (4), the right side of the equal sign of formula (4) is:
Figure GDA0003012304340000059
the second term of the formula (7) is the contact force between the platform and the tail end of the mechanical arm (external force applied to the platform);
the first term of the formula (7) is active and/or constraint force in a space robot joint, the space robot joint refers to a part which can generate relative motion between two rod pieces of the space robot, and the first term of the formula (7) is expanded according to the joint:
Figure GDA0003012304340000061
due to the fact that
Figure GDA0003012304340000062
Figure GDA0003012304340000063
Figure GDA0003012304340000064
Then, the first term of equation (7) is simplified to:
Figure GDA0003012304340000065
wherein the content of the first and second substances,
Figure GDA0003012304340000066
is a generalized main force.
The generalized main moment acting on the mechanical arm joint is TjthjWherein, TjIs the yaw rate, thjIs the joint active moment, then:
Figure GDA0003012304340000067
thjreduced to tjJ is 1,.. N, the main power of the robot arm is
Figure GDA0003012304340000068
Defining a virtual joint, wherein the virtual joint represents that six degrees of freedom exist between a platform and an inertia system of the space robot, namely displacement in three directions and rotation around the three directions, and the virtual joint has no force action, namely the space robot is not stressed except the platform, then:
Figure GDA0003012304340000069
for the virtual joint, there are
Figure GDA0003012304340000071
Known as v ═pvbU, then
pvb＝[I 0…0]
pωb＝[0 I 0…0]
Therefore, the main system power for introducing the virtual joint is
Figure GDA0003012304340000072
By combining the joint (equation (8)) and virtual joint (equation (9)) functions of the space robot, it is possible to obtain:
Figure GDA0003012304340000073
combining the formula (5) and the formula (10), the space robot overall dynamics model is established based on kahn dynamics:
Figure GDA0003012304340000074
because the disturbance force and the disturbance torque of the space robot are 6 dimensions in total, the main moment of the front 6 behavior platform on the right side of the equation (11) with the same sign is the disturbance force torque of the robot arm to the platform attitude on the right side of the equation (11) with the same sign from the 7 th row.
S2, establishing a rigid body dynamics model of the platform according to the space robot overall dynamics model, and calculating the disturbance moment of the mechanical arm to the platform posture;
acceleration of the platform
Figure GDA0003012304340000075
Substituting into formula (1), a rigid body dynamics model of the platform can be obtained:
Figure GDA0003012304340000081
in the formula (I), the compound is shown in the specification,
Figure GDA0003012304340000082
respectively representing the change rate of the platform speed and the angular speed projected in the platform rigid coordinate system,
Figure GDA0003012304340000083
and the acceleration of the platform is different,
Figure GDA0003012304340000084
as with the angular acceleration of the space robot,namely:
Figure GDA0003012304340000085
Figure GDA0003012304340000086
the device comprises an active moment of the platform and a disturbance moment of the mechanical arm to the attitude of the platform.
The "first 6 rows" of equation (11) may be written as:
Figure GDA0003012304340000087
subtracting the formula (13) from the formula (12) to obtain the disturbance torque of the mechanical arm to the platform attitude:
Figure GDA0003012304340000088
in the formula (I), the compound is shown in the specification,
Figure GDA0003012304340000089
and S3, calculating the feedforward compensation amount of the platform attitude control from the angular momentum layer, and realizing the compensation of the disturbance torque of the platform attitude.
In order to compensate the disturbance of the motion of the mechanical arm to the platform attitude, feedforward compensation control is established through the coordination relation of the angular momentum layer.
When the initial angular momentum of the space robot is zero and no external moment acts on the space robot, the angular momentum of the space robot is always zero:
Figure GDA00030123043400000810
in the formula, L0Angular momentum of the space robot to the platform centroid, I0Is the moment of inertia of the platform, omega0As angular velocity of the platform, IkIs the moment of inertia of the kth arm, phikFormed by joint angles of kth armAnd (3) an array.
Variation of angular momentum of space robot and platform control torque tau0And disturbance torque taudThe relationship of (1) is:
Figure GDA00030123043400000811
in order to derive the angular momentum of the platform disturbance torque to be compensated, if the platform keeps the attitude unchanged in the motion process of the mechanical arm and the initial angular momentum is zero, the following steps are provided:
Figure GDA0003012304340000091
equation (17) gives the compensation amount for the platform attitude control angular momentum feedforward compensation. In practice, the attitude of the platform cannot be completely kept still, and the attitude cannot be completely performed according to equation (17) during compensation, but should be properly reduced, so that the final feedforward compensation amount is:
Figure GDA0003012304340000092
in the formula, KffIs a proportionality coefficient, and the value range is more than 0 and less than Kff＜1。
In order to enable a platform attitude control system in a space robot to receive an angular momentum instruction, a mechanical arm angular momentum compensation loop is added in a control loop of the platform attitude control system, so that compensation of a mechanical arm on a platform attitude disturbance torque is realized, and the mechanical arm angular momentum compensation loop is as follows:
Figure GDA0003012304340000093
in the formula, hdTo command angular momentum, KmIs a symmetric positive definite matrix.
The conventional method for calculating the disturbance torque of the space robot platform comprises the following steps: a dynamic model of the space robot is established based on a Newton Euler method, and the interference torque is calculated according to the Newton Euler dynamic model. Compared with the conventional method, the calculation method of the attitude disturbance torque of the space robot platform provided by the invention has the advantages that the calculation result is the same, the calculation amount is different, the method provided by the invention adopts 6 times of addition and 8 times of multiplication, and the conventional calculation method adopts 27 times of addition and 27 times of multiplication, so that the calculation method of the disturbance torque of the attitude of the robot platform provided by the invention has the characteristic of less calculation amount.
The invention discloses a method for disturbance compensation of a space robot, which is characterized in that an overall dynamics model of the space robot is established based on the Kenn dynamics principle, and a mechanical arm and a platform are described by adopting the same dynamics model, so that the disturbance torque of the mechanical arm on the attitude of the platform is quickly and accurately calculated, feedforward supplementary control is established from the aspect of angular momentum, and the feedforward compensation of the disturbance torque of the attitude of the platform is effectively realized. The invention has the characteristics of less calculation amount and accurate calculation result, and simultaneously provides a new idea for on-satellite control.
While the present invention has been described in detail with reference to the preferred embodiments, it should be understood that the above description should not be taken as limiting the invention. Various modifications and alterations to this invention will become apparent to those skilled in the art upon reading the foregoing description. Accordingly, the scope of the invention should be determined from the following claims.

Claims (3)

1. A method for compensating disturbance of a space robot is characterized by comprising the following steps:
s1, establishing an overall dynamics model of the space robot based on Kennel dynamics;
s2, establishing a rigid body dynamics model of the platform according to the space robot overall dynamics model, and calculating the disturbance moment of the mechanical arm to the platform posture;
s3, calculating a feedforward compensation quantity of the platform attitude control from the angular momentum layer to realize the compensation of the disturbance moment of the platform attitude;
the calculation formula of the feedforward compensation quantity of the platform attitude control is as follows:
Figure FDA0003012304330000011
in the formula IkIs the moment of inertia of the kth arm, phikIs an array formed by joint angles of a kth mechanical arm, KffIs proportional coefficient, t is time, and the value range is more than 0 and less than Kff＜1；
Increase arm angular momentum compensation circuit in platform attitude control system's control circuit, realize the compensation of arm to platform gesture disturbance moment, arm angular momentum compensation circuit is:
Figure FDA0003012304330000012
in the formula, hdTo command angular momentum, KmIs a symmetric positive definite matrix.
2. The method of claim 1, wherein the global dynamics model of the space robot is:
Figure FDA0003012304330000013
in the formula (I), the compound is shown in the specification,
Figure FDA0003012304330000014
Figure FDA0003012304330000015
in the formula, mjIs a single rigid body BjI is a mass unit matrix, Sj、JjIs a single rigid body BjOrigin O of coordinate systemjThe static moment and the inertia moment of the rotor,
Figure FDA0003012304330000021
and
Figure FDA0003012304330000022
respectively represent a single rigid body BjAcceleration and angular acceleration of, omegajRepresents a rigid body BjThe angular velocity of (a) of (b),
Figure FDA0003012304330000023
representing the first derivative of the control input quantity,pVjrepresenting a single rigid body BjThe speed of the deviation is controlled by the speed controller,pωjrepresenting a single rigid body BjThe speed of the deflection angle is set to be,
Figure FDA0003012304330000024
representing a single rigid body BjOrigin O of coordinate systemjIn the form of a cross-product of the static moments,
Figure FDA0003012304330000025
represents a rigid body BjForm of angular velocity cross product of fbAnd τbRespectively the main power and the main moment of the platform;
the driving moment of the platform is taken as the front 6 on the right side of the equal sign of the formula (11), and the disturbance moment of the robot arm to the platform attitude is taken as the right side of the equal sign of the formula (11) from the 7 th row.
3. The method of claim 2, wherein the rigid body dynamics model of the platform is:
Figure FDA00030123043300000213
in the formula (I), the compound is shown in the specification,
Figure FDA0003012304330000026
respectively representing platform speedsRate of change of degree and angular velocity projected in platform rigid coordinate system, mbRepresenting platform quality, SbRepresenting the origin O of the platform coordinate systembThe static moment of (a) of (b),
Figure FDA0003012304330000027
representing the origin O of the platform coordinate systembCross multiplication form of the static moment of (J)bRepresenting the origin O of the platform coordinate systembThe inertia of the rotor is reduced to zero,
Figure FDA0003012304330000028
form of cross multiplication, V, representing the projection of a rigid body on a platform rigid body coordinate systembRepresenting the projection of the platform velocity on the platform rigid body coordinate system, frfAnd τrfThe difference between the main power and the disturbance power of the space robot platform and the difference between the main moment and the disturbance moment of the space robot platform are respectively;
the right side of the equal sign of the formula (12) comprises the main moment of the space robot platform and the disturbance moment of the mechanical arm to the platform attitude;
take "first 6 rows" of equation (11):
Figure FDA0003012304330000029
in the formula, MbAnd MbmRespectively an inertia matrix of the platform and an inertia matrix of the mechanical arm coupled with the platform,
Figure FDA00030123043300000210
is the angular acceleration of the joints of the mechanical arm,
Figure FDA00030123043300000211
is the generalized inertial force of the system;
subtracting the formula (13) from the formula (12) to obtain the disturbance torque of the mechanical arm to the platform attitude:
Figure FDA00030123043300000212
in the formula (I), the compound is shown in the specification,
Figure FDA0003012304330000031
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