CN113001549A - Multi-mechanical-arm load distribution method based on generalized grasping inverse matrix - Google Patents

Multi-mechanical-arm load distribution method based on generalized grasping inverse matrix Download PDF

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CN113001549A
CN113001549A CN202110282277.8A CN202110282277A CN113001549A CN 113001549 A CN113001549 A CN 113001549A CN 202110282277 A CN202110282277 A CN 202110282277A CN 113001549 A CN113001549 A CN 113001549A
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virtual
tail end
mechanical arm
acceleration
mass
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李洋
耿琳
韩进喜
包阳
江涌
贾建光
盛经雨
李晶
王彤
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Chinese People's Liberation Army 32801
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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
    • 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
    • B25J9/1651—Programme controls characterised by the control loop acceleration, rate control

Abstract

The application discloses a multi-mechanical-arm load distribution method based on a generalized grasping inverse matrix, which comprises the following steps: step 1, calculating the dynamic operability of the tail end of each mechanical arm according to the tail end acceleration ellipsoids of the mechanical arms and the tail end acceleration linear equation of the mechanical arms, and determining the load distribution coefficient of each mechanical arm; step 2, calculating the object virtual mass, the virtual inertia and the virtual center of mass of the grabbed object according to the tail end virtual mass and the tail end virtual inertia of the mechanical arms and by combining a load distribution coefficient; and 3, constructing a generalized grasping inverse matrix according to the terminal virtual mass, the virtual inertia, the object virtual mass, the virtual inertia and the virtual center of mass, and determining the terminal load of each mechanical arm according to the total load of the mechanical arms. According to the technical scheme, the dynamic load distribution coefficient of the mechanical arm is determined, the generalized grasping inverse matrix is established by utilizing the virtual mass, the virtual inertia and the virtual mass center, and the dynamic load distribution of the tail ends of the multiple mechanical arms is realized.

Description

Multi-mechanical-arm load distribution method based on generalized grasping inverse matrix
Technical Field
The application relates to the technical field of mechanical arm control, in particular to a multi-mechanical arm load distribution method based on a generalized grasping inverse matrix.
Background
With the increasing demands of human beings on mechanical arms in the aspects of industrial production, intelligent service, educational medical treatment and the like, a single mechanical arm cannot be competent for certain tasks, and a multi-mechanical arm system is born from the birth and is widely applied. When a plurality of mechanical arms grip the same object, how to keep the stability of gripping is considered firstly, and when the object is gripped firmly, the mechanical arms are prevented from damaging the object by avoiding generating excessive internal force, so that the safety of operation is improved. Secondly, when an object with larger mass is grabbed, the load of the object needs to be reasonably distributed, and the load born by each mechanical arm is controlled to be far away from the load limit as far as possible, so that better motion performance and power characteristics are obtained. Finally, in the process of changing the position of the mechanical arm, the output capacity of the tail end force can be reduced in a certain direction, and if the load distribution mode is not adjusted in time, the overload accident of the mechanical arm can be caused, so that the reasonable dynamic load distribution of the multiple mechanical arms is very necessary.
In the prior art, most of loads of multiple mechanical arms are distributed by adopting a uniform load distribution method, the method has a good effect when the mechanical arms are in a static state, however, when a system of the multiple mechanical arms is in a motion state, the dynamic operability of the tail ends of the system is also dynamically changed, the output capacity of the tail end force of the mechanical arms is reduced, and if the load distribution mode of the system of the multiple mechanical arms is not adjusted in time, the joints of the mechanical arms are overloaded, and accidents are caused.
Disclosure of Invention
The purpose of this application lies in: the generalized grasping inverse matrix is established by constructing the acceleration ellipsoid at the tail end of the mechanical arm, dynamic load distribution is carried out according to the dynamic operability of the mechanical arm in the motion process, and the joint overload phenomenon caused by the dynamic operability of the mechanical arm is effectively avoided.
The technical scheme of the application is as follows: a multi-mechanical arm load distribution method based on a generalized grasping inverse matrix is provided, and the method comprises the following steps: step 1, calculating the dynamic operability of the tail end of each mechanical arm according to the tail end acceleration ellipsoids of the mechanical arms and the tail end acceleration linear equations of the mechanical arms, and determining the load distribution coefficient of each mechanical arm according to the dynamic operability of the tail end; step 2, calculating the object virtual mass, the object virtual inertia and the object virtual mass center of the grabbed object according to the tail end virtual mass and the tail end virtual inertia of the mechanical arms and by combining a load distribution coefficient; and 3, constructing a generalized grasping inverse matrix according to the tail end virtual mass, the tail end virtual inertia, the object virtual mass, the object virtual inertia and the object virtual center of mass, and determining the tail end load of each mechanical arm according to the total load of the mechanical arms.
In any one of the above technical solutions, further, in step 1, calculating the dynamic operability of the end of each mechanical arm specifically includes: step 11, determining the joint acceleration of the mechanical arm according to the dynamic model of the mechanical arm, mapping the joint acceleration and the tail end of the mechanical arm, calculating the tail end acceleration of the mechanical arm, and constructing an acceleration ellipsoid of the mechanical arm; step 12, calculating the intersection point of the acceleration ellipsoid and a linear equation of the mechanical arm along the acceleration direction; and step 13, calculating the distance between the intersection point and the center of the acceleration ellipsoid, and recording the distance as the dynamic operability of the tail end.
In any of the above technical solutions, further, the terminal acceleration of the mechanical arm
Figure BDA0002979053100000021
The calculation formula of (2) is as follows:
Figure BDA0002979053100000022
wherein J (q) is a Jacobian matrix of robotic arms,
Figure BDA0002979053100000023
is the joint speed of the mechanical arm,
Figure BDA0002979053100000024
the joint acceleration q is the joint position of the mechanical arm;
the calculation formula of the acceleration ellipsoid is as follows:
(Va)TJ(q)-TQJ(q)-1(va)≤1
Figure BDA0002979053100000025
Q＝M(q)L-1L-1M(q)
in the formula, VaQ is an intermediate parameter, aHJ (q) is the jacobian matrix of the robot arm, m (q) is the inertial matrix of the robot arm, and L is the limit moment matrix of the robot arm.
In any of the above technical solutions, further, in step 1, the load distribution coefficient β of each robot armiThe corresponding calculation formula is:
Figure BDA0002979053100000031
Figure BDA0002979053100000032
in the formula (d)iIs a distance, i isSerial numbers of a plurality of robot arms, i ═ 1,2iIs the point of intersection, pxi、pyi、pziIs an intersection point PiThe coordinates of (a).
In any of the above technical solutions, further, the calculation formula of the generalized grasping inverse matrix is:
Figure BDA0002979053100000033
Figure BDA0002979053100000034
in the formula (I), the compound is shown in the specification,
Figure BDA0002979053100000035
in order to hold the inverse matrix in a broad sense,
Figure BDA0002979053100000036
for the end virtual mass, i is the serial number of the multiple robot arms, i is 1,2,., n,
Figure BDA0002979053100000037
as a virtual mass of the object, I3Is a three-dimensional unit matrix and is,
Figure BDA0002979053100000038
for terminal virtual inertia, S (-) is an antisymmetric matrix operation, riFor the holding position of the ith robot arm on the gripped object,
Figure BDA0002979053100000039
is the virtual inertia of the object, and o is the virtual center of mass of the object of the grabbed object.
In any of the above technical solutions, further, the virtual mass of the object
Figure BDA00029790531000000310
The calculation formula of (2) is as follows:
Figure BDA00029790531000000311
in the formula, betaiThe coefficients are distributed to the loads.
In any of the above technical solutions, further, the calculation formula of the virtual centroid of the object is:
Figure BDA00029790531000000312
where o is the virtual center of mass of the object, βiTo distribute the coefficient for the load, riIs the gripping position.
In any of the above technical solutions, further, the virtual inertia of the object
Figure BDA00029790531000000313
The calculation formula of (2) is as follows:
Figure BDA00029790531000000314
Figure BDA0002979053100000041
wherein o is the virtual object centroid of the grasped object.
The beneficial effect of this application is:
according to the technical scheme, the tail end dynamic operability of each mechanical arm is obtained by constructing the acceleration ellipsoid of the tail end of each mechanical arm and combining the tail end acceleration linear equation of the mechanical arms, the load distribution coefficient of each mechanical arm is determined, the load distribution coefficient of each mechanical arm is further combined, the tail end virtual mass and the tail end virtual inertia of the mechanical arms are calculated, the object virtual mass and the object virtual inertia of a grabbed object are calculated, a generalized grabbing inverse matrix is constructed, the dynamic distribution of tail end loads of the mechanical arms is realized according to the total load of the mechanical arms, the safety performance of the mechanical arms in the grabbing motion process is improved, the joint overload phenomenon of the mechanical arms is effectively avoided, and the output capacity of tail end force of the mechanical arms is optimized.
In the application, in the process of constructing the generalized grasping inverse matrix, the load distribution coefficient is introduced to objectively reflect the output capacity of the mechanical arm force in the current state, the virtual mass and the virtual inertia of the object are confirmed by utilizing the load distribution coefficient, a basis is provided for realizing dynamic distribution of the mechanical arm load, and particularly when the load distribution coefficient of a certain mechanical arm is reduced, the load of the mechanical arm is reduced by the generalized grasping inverse matrix, so that the damage of the mechanical arm caused by overload of a joint is avoided.
Drawings
The advantages of the above and/or additional aspects of the present application will become apparent and readily appreciated from the following description of the embodiments, taken in conjunction with the accompanying drawings of which:
FIG. 1 is a schematic flow diagram of a multi-robot load sharing method based on a generalized grasping inverse matrix according to one embodiment of the present application;
FIG. 2 is a simulation diagram of a two-robot collaborative handling model according to an embodiment of the present application;
FIG. 3 is a simulation diagram of a motion trajectory according to one embodiment of the present application;
FIG. 4 is a simulation diagram of an acceleration trajectory according to an embodiment of the present application;
FIG. 5 is a simulation graph of load sharing coefficients according to one embodiment of the present application;
FIG. 6 is a simulated graph of end of arm force loading according to an embodiment of the present application;
FIG. 7 is a simulated view of moment loads at the end of a robotic arm according to an embodiment of the present application;
FIG. 8 is a simulated view of robot arm joint moments according to one embodiment of the present application.
Detailed Description
In order that the above objects, features and advantages of the present application can be more clearly understood, the present application will be described in further detail with reference to the accompanying drawings and detailed description. It should be noted that the embodiments and features of the embodiments of the present application may be combined with each other without conflict.
In the following description, numerous specific details are set forth in order to provide a thorough understanding of the present application, however, the present application may be practiced in other ways than those described herein, and therefore the scope of the present application is not limited by the specific embodiments disclosed below.
As shown in fig. 1 and fig. 2, in the present embodiment, a method for load distribution of multiple robots based on a generalized grasping inverse matrix is provided, and a two-robot cooperative handling system common in the industry is taken as an example, and the method for load distribution of multiple robots in the present embodiment is adopted to perform dynamic load distribution on the robots R1 and R2 in the system, so as to improve the operation safety. Two mechanical arms are respectively marked as R1 and R2, the performance parameters of the two mechanical arms are the same, and the holding positions are respectively R1＝[-0.1 0 0]T、r2＝[0.1 0 0]TThe mass m of the gripped object is 5kg, and the limit torque of each joint of the robot arm is L150120100805050]TN m, the movement time of the conveyed object is 3s, the control cycle of the double-mechanical-arm system is 10ms, and a rotic toolbox is matched and used in matlab to build a double-mechanical-arm cooperative conveying model.
As shown in fig. 3, for the two-robot collaborative handling model, a trajectory planning is performed by using a 3-time B-spline method to obtain a motion trajectory of an object:
Figure BDA0002979053100000051
Figure BDA0002979053100000052
Figure BDA0002979053100000061
in the formula, Trajx、TrajyAnd TrajzAre respectively provided withFor the x, y and z motion trajectories of the object in the working space, the acceleration a of the object can be obtained by performing a second derivation on the motion trajectories, as shown in fig. 4.
Thus, the system of this embodiment has a total load of multiple robotic arms
Figure BDA0002979053100000062
Comprises the following steps:
Figure BDA0002979053100000063
total load
Figure BDA0002979053100000064
Consists of 2 parts: firstly, the gravity of the gripped object; the second is the force required by the acceleration of the motion of the object being grasped. Total load
Figure BDA0002979053100000065
Dynamic load distribution during the movement of the gripped object, i.e. to the total load at each control cycle
Figure BDA0002979053100000066
And (6) distributing.
When T is 1s, a method for distributing loads of multiple robots in this embodiment is described by taking load distribution in the 100 th control cycle of the system as an example, where the method includes:
step 1, calculating the dynamic operability of the tail end of each mechanical arm according to the tail end acceleration ellipsoids of the mechanical arms and the tail end acceleration linear equations of the mechanical arms, and determining the load distribution coefficient of each mechanical arm according to the dynamic operability of the tail end.
Specifically, the lagrange method is adopted, and the rigid body kinetic equation of the mechanical arm is constructed as follows:
Figure BDA0002979053100000067
in the formula, τIn the present embodiment, the robot arms R1 and R2 are respectively configured to include 6 joints in a matrix form, so that the joint torque τ is calculated for the robot arm R11＝[τ1,...,τ6]M (q) is an inertia matrix of the robot arm, which is a positive definite symmetric matrix,
Figure BDA0002979053100000068
is a combination item of a matrix of the Coriolis force, the centrifugal force and the gravity, q is the joint position of the mechanical arm,
Figure BDA0002979053100000069
is the joint speed of the mechanical arm,
Figure BDA00029790531000000610
is the joint acceleration of the mechanical arm.
When T is 1s, the inertia matrix M of the robot arm R11(q) is:
Figure BDA00029790531000000611
note that, since the items are merged
Figure BDA00029790531000000612
The dynamic operability of the tail end of the mechanical arm is not influenced, and the calculation can not be carried out.
Therefore, the dynamic operability of the tail end of each mechanical arm can be calculated by derivation based on the kinetic equation, and the process specifically comprises the following steps:
step 11, determining the joint acceleration of the mechanical arm according to the dynamic model of the mechanical arm, mapping the joint acceleration and the tail end of the mechanical arm, calculating the tail end acceleration of the mechanical arm, and constructing an acceleration ellipsoid of the mechanical arm;
further, the joint velocity of the robot arm can be known from the jacobian matrix
Figure BDA0002979053100000071
And the mapping relation between the tail end speed V of the mechanical arm is as follows:
Figure BDA0002979053100000072
wherein J (q) is a Jacobian matrix of the robot arm, and the Jacobian matrix J is exemplified by the robot arm R11(q) is:
Figure BDA0002979053100000073
by deriving the above formula, the terminal acceleration of the mechanical arm can be obtained
Figure BDA0002979053100000074
The calculation formula of (2) is as follows:
Figure BDA0002979053100000075
namely:
Figure BDA0002979053100000076
Figure BDA0002979053100000077
in the formula, aHIs the spatial acceleration caused by centrifugal, coriolis and gravity forces.
In this embodiment, in order to construct an acceleration ellipsoid, the joint moment τ of the mechanical arm is also normalized:
Figure BDA0002979053100000078
Figure BDA0002979053100000079
in the formula (I), the compound is shown in the specification,
Figure BDA00029790531000000710
the ultimate moment of the gamma-th joint in the mechanical arm. After standardization, the standardized joint torque can be used
Figure BDA00029790531000000711
Acceleration of leading end
Figure BDA00029790531000000712
The calculation formula (2) is operated.
Based on calculated tip acceleration
Figure BDA00029790531000000713
And constructing an acceleration ellipsoid of the mechanical arm by combining the definition of the speed operability ellipsoid, wherein the calculation formula of the acceleration ellipsoid is as follows:
(Va)TJ(q)-TQJ(q)-1(Va)≤1
Figure BDA0002979053100000081
Q＝M(q)L-1L-1M(q)
in the formula, VaQ is an intermediate parameter, aHJ (q) is a space acceleration, j (q) is a jacobian matrix of the manipulator, m (q) is an inertia matrix of the manipulator, and is a positive definite matrix, and L is a limit moment matrix of the manipulator.
Since the inertia matrix M (q) is a positive definite matrix, L-1L-1Being positive definite matrices, so the intermediate matrix J (q)-TQJ(q)-1Is also positive, therefore, the acceleration ellipsoid constructed in this embodiment is a 6-dimensional ellipsoid, in which the middle matrix J (q)-TQJ(q)-1Determines the shape and size of the ellipsoid.
By making an aim atThe 6-dimensional ellipsoids constructed in the examples were analyzed for the intermediate matrix J (q)-TQJ(q)-1Dividing into:
Figure BDA0002979053100000082
in the formula, A3×3The moving acceleration capacity of the tail end of the mechanical arm in the three-dimensional working space is described, and meanwhile, the force output capacity of the tail end of the mechanical arm in each direction in the three-dimensional working space is also described; d3×3The rotation acceleration capability of the tail end of the mechanical arm in the three-dimensional working space is described, and the moment output capability of the tail end of the mechanical arm in all directions in the three-dimensional working space is also described.
Intermediate matrix J (q)-TQJ(q)-1The shape of the acceleration ellipsoid at the tail end of the mechanical arm can be changed continuously in the motion process of the mechanical arm, which means that the acceleration capacity of the tail end of the mechanical arm in moving and rotating in a working space is changed continuously, so that the acceleration ellipsoid needs to be calculated once in each control period to realize dynamic load distribution.
Step 12, calculating the intersection point of the acceleration ellipsoid and a linear equation of the mechanical arm along the acceleration direction;
specifically, the direction coordinate of the acceleration in any direction of the center of the over-acceleration ellipsoid is set as [ a ]x ay az]＝[-0.02 0.51 1.19]Therefore, the equation of a straight line of the robot arm in the acceleration direction is obtained as:
Figure BDA0002979053100000083
namely:
Figure BDA0002979053100000091
correspondingly, in the acceleration ellipsoid, for a three-dimensional symmetric matrix A3×3Move and moveThe dynamic acceleration ellipsoid equation has the following form:
[x y z]·A3×3·[x y z]T＝1
namely:
Figure BDA0002979053100000092
therefore, the intersection point P of the acceleration ellipsoid and the linear equation can be calculated1＝(px1，py1，pz1)＝(-0.01，0.14，0.33)。
And step 13, calculating the distance between the intersection point and the center of the acceleration ellipsoid, and recording the distance as the dynamic operability of the tail end.
According to the intersection point Pi＝(pxi，pyi，pzi) The distance d between the acceleration ellipsoid and the center of the acceleration ellipsoid can be calculatedi：
Figure BDA0002979053100000093
In the formula (d)iFor the distance, i is a serial number of the plurality of robot arms, and i is 1, 2.
The distance describes the force output capacity of the tail end of the mechanical arm in a certain direction in a working space at a certain moment, the distance is dynamically changed due to the fact that the acceleration ellipsoid of the tail end of the mechanical arm and the acceleration direction of an object are continuously changed, the distance is used as the tail end dynamic operability degree of the mechanical arm, the tail end dynamic operability degree of each mechanical arm can be further obtained, the force load distribution coefficient and the load distribution coefficient beta of each mechanical arm at a certain moment are determined through the ratio of the tail end dynamic operability degrees of the mechanical armsiThe corresponding calculation formula is:
Figure BDA0002979053100000094
Figure BDA0002979053100000095
in the formula (d)iFor the distance, i is a serial number of the plurality of robot arms, i is 1,2iIs the intersection point, pxi、pyi、pziIs the intersection point PiThe coordinates of (a).
In the present embodiment, the load distribution coefficient β is introducediTo objectively reflect the output capability of the mechanical arm in the current state and utilize the load distribution coefficient betaiConfirming the virtual mass and the virtual inertia of the object to further influence the constructed generalized grasping inverse matrix so as to realize the dynamic distribution of the load of the mechanical arm, particularly when the load distribution coefficient beta of a certain mechanical armiWhen descending, the load of the mechanical arm is reduced by holding the inverse matrix in a generalized manner, so that the damage of the mechanical arm caused by overload of the joint is avoided.
In the present embodiment, as shown in fig. 5, the load distribution coefficient βiThe ratio which dominates the virtual mass of each mechanical arm is a dynamically changing parameter, so that a calculation is required to be performed in each control period.
Will intersect point P1Substituting (-0.01, 0.14, 0.33) into the above calculation procedure, the distance d can be obtained1The above process is repeated for 0.36 to obtain the distance d corresponding to the arm R220.44, corresponding load sharing factor β1＝0.45，β2＝0.55。
Step 2, calculating the object virtual mass, the object virtual inertia and the object virtual mass center of the grabbed object according to the tail end virtual mass and the tail end virtual inertia of the mechanical arms and by combining a load distribution coefficient;
in this embodiment, the virtual mass and the virtual inertia of the grasped object at a certain time are respectively used
Figure BDA0002979053100000101
The virtual mass and the virtual inertia of the tail end of the ith mechanical arm are respectively expressed as
Figure BDA0002979053100000102
Due to virtual mass of object
Figure BDA0002979053100000103
By a load distribution coefficient betaiAnd determining that the corresponding calculation formula is as follows:
Figure BDA0002979053100000104
accordingly, the virtual inertia of the object
Figure BDA0002979053100000105
The calculation formula of (2) is as follows:
Figure BDA0002979053100000106
Figure BDA0002979053100000107
where o is the virtual center of mass of the object, r, of the grasped objectiFor the holding position of the i-th robot arm on the gripped object, S (r)i-o) is (r)i-o) and S (-) is an inverse symmetric matrix operation.
In the present embodiment, the end virtual mass of the robot arm R1 is set at the time t ═ 1s
Figure BDA0002979053100000111
According to the load distribution coefficient beta1And beta2The end virtual mass m of the mechanical arm R2 can be obtained by scaling21.22, the tip virtual inertia of the robot arm R1 and the robot arm R2 is set
Figure BDA0002979053100000112
Is a three-dimensional identity matrix, the virtual mass of the object
Figure BDA0002979053100000113
Comprises the following steps:
Figure BDA0002979053100000114
the calculated virtual centroid of the object is:
Figure BDA0002979053100000115
virtual inertia of object
Figure BDA0002979053100000116
Comprises the following steps:
Figure BDA0002979053100000117
and 3, constructing a generalized grasping inverse matrix according to the tail end virtual mass, the tail end virtual inertia, the object virtual mass, the object virtual inertia and the object virtual center of mass, and determining the tail end load of each mechanical arm according to the total load of the mechanical arms.
The embodiment is based on the acceleration ellipsoid of the mechanical arm and J (q)-TQJ(q)-1In order to realize dynamic distribution of the load of each mechanical arm, a generalized grasping inverse matrix is constructed according to the end virtual mass, the end virtual inertia, the object virtual mass and the object virtual inertia, and the calculation formula of the generalized grasping inverse matrix is as follows:
Figure BDA0002979053100000118
Figure BDA0002979053100000119
in the formula (I), the compound is shown in the specification,
Figure BDA00029790531000001110
for the said generalized inverse of the grasping matrix,
Figure BDA00029790531000001111
i is a serial number of the plurality of robot arms, i is 1, 2.. times.n,
Figure BDA00029790531000001112
for the virtual mass of the object, I3Is a three-dimensional unit matrix and is,
Figure BDA0002979053100000121
in order to compensate for the inertia,
Figure BDA0002979053100000122
for the terminal virtual inertia, S (-) is an antisymmetric matrix operation, riFor the holding position of the i-th robot arm on the gripped object,
Figure BDA0002979053100000123
and o is the virtual object inertia and the virtual object center of mass of the grabbed object.
For the two-robot cooperative transportation system in this embodiment, the generalized grasping inverse matrix is constructed by:
Figure BDA0002979053100000124
in the formula (I), the compound is shown in the specification,
Figure BDA0002979053100000125
is an item of distribution of force, wherein,
Figure BDA0002979053100000126
to distribute the amount of force to the end of the 1 st robot arm,
Figure BDA0002979053100000127
for the magnitude of the force distributed to the 2 nd end of the arm, the distribution of the force
Figure BDA0002979053100000128
Is defined by the virtual mass of the end of the arm
Figure BDA0002979053100000129
Determining, and end of virtual quality
Figure BDA00029790531000001210
Is given by the corresponding load distribution factor betaiTherefore, the term can be used for load distribution according to the output capacity of each mechanical arm force at different moments, and joint overload can be avoided.
Figure BDA00029790531000001211
The adjustment items of the proportion of the force and the moment can be distributed by adjusting the tail end virtual mass of the mechanical arm
Figure BDA00029790531000001212
And virtual inertia of object
Figure BDA00029790531000001213
The pure force output by a part of the tail end of the mechanical arm can be converted into the moment, so that the effect of increasing the output of the tail end force of the mechanical arm and reducing the output of the moment is achieved. When the torque output capacity of the mechanical arm is insufficient, the virtual mass of the tail end of the mechanical arm is increased, and a part of pure force can be converted into torque, so that the gripping performance of the mechanical arm is further optimized.
Figure BDA00029790531000001214
Is a torque compensation term in which, among other things,
Figure BDA00029790531000001215
Figure BDA00029790531000001222
for counteracting disturbance torque produced by non-uniform grip, and by compensating for inertia
Figure BDA00029790531000001216
And virtual mass of object
Figure BDA00029790531000001217
Is distributed to the end of the ith mechanical arm to ensure the stable holding of the objects by the multiple mechanical arms.
Figure BDA00029790531000001218
The item is a moment distribution item, the moment output of the mechanical arm can be adjusted to be the moment distributed to the tail end of the ith mechanical arm, and the magnitude of the moment is determined by the virtual inertia of the tail end
Figure BDA00029790531000001219
And (6) determining.
After the generalized inverse grasping matrix is constructed, the generalized inverse grasping matrix and the total loads of the plurality of mechanical arms of the system are calculated
Figure BDA00029790531000001220
Load distribution is carried out on the mechanical arms R1 and R2, and the distribution mode is as follows:
Figure BDA00029790531000001221
in the formula, h1For distributed load of arm R1, h2Distributing the load for the robot arm R1.
In the present embodiment, the change curves of the mechanical arms R1 and R2 in the system, including the force load and the moment load, are plotted by plot function of MATLAB, as shown in fig. 6 and 6,
wherein f is1x、f1y、f1zForce load component, f, of the mechanical arm R1 along three coordinate axes of xyz2x、f2y、f2zForce load components of the mechanical arm R2 along the directions of three coordinate axes of xyz;
t1x、t1y、t1zthree in xyz for the end of the mechanical arm R1Moment load component in the direction of the coordinate axes, t2x、t2y、t2zMoment load components of the end of the mechanical arm R2 in the directions of the three coordinate axes xyz.
As can be seen from the figure, the total load is generated during the movement of the two mechanical arms
Figure BDA0002979053100000131
Reasonably distributed to the tail end of each mechanical arm, when the double-mechanical-arm system runs for 2.8 seconds, as can be seen from fig. 4, the load distribution coefficient beta of the mechanical arm R11When the value is 0.255, the dynamic operability of the end portion decreases, and the force output capability also decreases, and at this time, the load borne by the robot arm R1 decreases, and the force load component f decreases1x、f1y、f1z0.92N, 0.53N and 5.6N respectively.
Accordingly, as can be seen from fig. 4, the load distribution coefficient β of the robot arm R220.745, its dynamic operability at the end is increased, meaning the force output capability is increased, and therefore, it bears a large load to avoid the problem of joint overload, the force load component f of the arm R22x、f2y、f2z7.366N, 4.2554N, 44.962N, respectively.
By calculating the joint moments of the mechanical arms R1 and R2 through inverse dynamics, the change curves of the joint moments of the mechanical arms R1 and R2 along with time can be obtained, as shown in (a) and (b) of fig. 8, wherein tau is shown in the graph1To tau6The joint moment of each joint in each mechanical arm.
As can be seen from FIG. 8, the moments of the joints of the mechanical arms R1 and R2 are respectively controlled between 10-50 N.m and 40-80 N.m, the moment of the joints changes smoothly without sudden change and the phenomenon of joint overload caused by the reduction of the dynamic operability of the tail end is further proved that the total load is further proved
Figure BDA0002979053100000132
The load distribution method is reasonably distributed to the tail end of each mechanical arm, and the rationality of the load distribution method in the embodiment is verified.
The technical scheme of the application is described in detail above with reference to the accompanying drawings, and the application provides a multi-manipulator load distribution method based on a generalized grasping inverse matrix, which comprises the following steps: step 1, calculating the dynamic operability of the tail end of each mechanical arm according to the tail end acceleration ellipsoids of the mechanical arms and the tail end acceleration linear equations of the mechanical arms, and determining the load distribution coefficient of each mechanical arm according to the dynamic operability of the tail end; step 2, calculating the object virtual mass, the object virtual inertia and the object virtual mass center of the grabbed object according to the tail end virtual mass and the tail end virtual inertia of the mechanical arms and by combining a load distribution coefficient; and 3, constructing a generalized grasping inverse matrix according to the tail end virtual mass, the tail end virtual inertia, the object virtual mass, the object virtual inertia and the object virtual center of mass, and determining the tail end load of each mechanical arm according to the total load of the mechanical arms. According to the technical scheme, the dynamic load distribution coefficient of the mechanical arm is determined, the generalized grasping inverse matrix is established by utilizing the virtual mass, the virtual inertia and the virtual mass, and the dynamic load distribution of the tail ends of the multiple mechanical arms is realized.
The steps in the present application may be sequentially adjusted, combined, and subtracted according to actual requirements.
The units in the device can be merged, divided and deleted according to actual requirements.
Although the present application has been disclosed in detail with reference to the accompanying drawings, it is to be understood that such description is merely illustrative and not restrictive of the application of the present application. The scope of the present application is defined by the appended claims and may include various modifications, adaptations, and equivalents of the invention without departing from the scope and spirit of the application.

Claims (8)

1. A multi-mechanical arm load distribution method based on a generalized grasping inverse matrix is characterized by comprising the following steps:
step 1, calculating the dynamic operability of the tail end of each mechanical arm according to the tail end acceleration ellipsoids of the mechanical arms and the tail end acceleration linear equations of the mechanical arms, and determining the load distribution coefficient of each mechanical arm according to the dynamic operability of the tail end;
step 2, calculating the object virtual mass, the object virtual inertia and the object virtual center of mass of the grabbed object according to the tail end virtual mass and the tail end virtual inertia of the mechanical arms and by combining the load distribution coefficient;
and 3, constructing a generalized grasping inverse matrix according to the tail end virtual mass, the tail end virtual inertia, the object virtual mass, the object virtual inertia and the object virtual center of mass, and determining the tail end load of each mechanical arm according to the total load of the mechanical arms.
2. The generalized grasping inverse matrix-based multi-robot load distribution method according to claim 1, wherein the step 1 of calculating the dynamic operability of the end of each robot arm specifically comprises:
step 11, determining the joint acceleration of the mechanical arm according to the dynamic model of the mechanical arm, mapping the joint acceleration and the tail end of the mechanical arm, calculating the tail end acceleration of the mechanical arm, and constructing an acceleration ellipsoid of the mechanical arm;
step 12, calculating the intersection point of the acceleration ellipsoid and a linear equation of the mechanical arm along the acceleration direction;
and step 13, calculating the distance between the intersection point and the center of the acceleration ellipsoid, and recording the distance as the dynamic operability of the tail end.
3. The generalized grasping inverse matrix-based multi-robot load sharing method of claim 2, wherein the terminal acceleration of the robot
Figure FDA0002979053090000011
The calculation formula of (2) is as follows:
Figure FDA0002979053090000012
wherein, J (q)Is a jacobian matrix of the robotic arms,
Figure FDA0002979053090000013
is the joint speed of the mechanical arm,
Figure FDA0002979053090000014
the joint acceleration q is the joint position of the mechanical arm;
the calculation formula of the acceleration ellipsoid is as follows:
(Va)TJ(q)-TQJ(q)-1(Va)≤1
Figure FDA0002979053090000021
Q＝M(q)L-1L-1M(q)
in the formula, VaQ is an intermediate parameter, aHJ (q) is a jacobian matrix of the robot arm, m (q) is an inertia matrix of the robot arm, and L is a limit moment matrix of the robot arm.
4. The generalized grasping inverse matrix-based multi-robot load distribution method according to claim 2, wherein in the step 1, the load distribution coefficient β of each robot isiThe corresponding calculation formula is:
Figure FDA0002979053090000022
Figure FDA0002979053090000023
in the formula (d)iFor the distance, i is the serial number of the plurality of robot arms, i is 1,2, …, n, PiIs the intersection point, pxi、pyi、pziIs the intersection point PiThe coordinates of (a).
5. The generalized grasping inverse matrix-based multi-robot load distribution method according to claim 1, wherein the generalized grasping inverse matrix is calculated by the formula:
Figure FDA0002979053090000024
Figure FDA0002979053090000025
in the formula (I), the compound is shown in the specification,
Figure FDA0002979053090000026
for the said generalized inverse of the grasping matrix,
Figure FDA0002979053090000027
for the end virtual mass, i is a serial number of the plurality of robot arms, i is 1,2, …, n,
Figure FDA0002979053090000028
for the virtual mass of the object, I3Is a three-dimensional unit matrix and is,
Figure FDA0002979053090000029
for the terminal virtual inertia, S (-) is an antisymmetric matrix operation, riFor the holding position of the i-th robot arm on the gripped object,
Figure FDA00029790530900000210
and o is the virtual inertia of the object and the virtual mass center of the object.
6. The generalized grasping inverse matrix-based multi-robot load sharing method of claim 5, wherein the object isVirtual mass
Figure FDA00029790530900000211
The calculation formula of (2) is as follows:
Figure FDA0002979053090000031
in the formula, betaiAnd distributing coefficients for the load.
7. The generalized grasping inverse matrix-based multi-robot load sharing method according to claim 5, wherein the calculation formula of the virtual center of mass of the object is:
Figure FDA0002979053090000032
wherein o is the virtual center of mass of the object, βiTo distribute the load factor, riIs the gripping position.
8. The generalized grasping inverse matrix-based multi-robot load sharing method of claim 5, wherein the object virtual inertia
Figure FDA0002979053090000033
The calculation formula of (2) is as follows:
Figure FDA0002979053090000034
Figure FDA0002979053090000035
wherein o is the virtual centroid of the object.
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Publication number Priority date Publication date Assignee Title
CN117171914A (en) * 2023-09-05 2023-12-05 三河市皓智精密机械制造有限公司 High-precision spindle performance test method and system

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN117171914A (en) * 2023-09-05 2023-12-05 三河市皓智精密机械制造有限公司 High-precision spindle performance test method and system
CN117171914B (en) * 2023-09-05 2024-03-12 三河市皓智精密机械制造有限公司 High-precision spindle performance test method and system

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