A multi-arm load distribution method based on generalized grasp inverse matrix

Abstract

The application discloses a multi-robot arm load distribution method based on a generalized grasping inverse matrix, which comprises the following steps: 1. calculating the end dynamic operability of each robot arm and determining the load distribution coefficient of each robot arm according to the end acceleration ellipsoid of the robot arms and the end acceleration linear equation of the robot arms; 2. calculating the object virtual mass, virtual inertia and virtual centroid of the grasped object according to the end virtual mass and end virtual inertia of the robot arms and in combination with the load distribution coefficient; and 3. constructing the generalized grasping inverse matrix according to the end virtual mass, virtual inertia, object virtual mass, virtual inertia and virtual centroid and determining the end load of each robot arm according to the total load of the robot arms. Through the technical scheme, the dynamic load distribution coefficient of the robot arm is determined, the generalized grasping inverse matrix is established by using the virtual mass, virtual inertia and virtual centroid, and the end dynamic load distribution of the multi-robot arm is realized.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of robot arm control, and in particular, relates to a multi-robot arm load distribution method based on a generalized grasp inverse matrix. BACKGROUND

[0002] With the increasing demand of human beings for robot arms in industrial production, intelligent services, education and medical treatment, etc., a single robot arm cannot complete some tasks, and a multi-robot arm system is thus born and has been widely applied. When multiple robot arms grasp the same object, the first consideration is how to maintain the stability of grasping, and in the process of firmly grasping the object, it is also necessary to avoid generating excessive internal force to prevent the robot arm from damaging the object and improve the safety of operation. Secondly, when grasping an object with large mass, it is necessary to reasonably distribute the load of the object, and control the load borne by each robot arm to be far away from the load limit as much as possible, so as to obtain better motion performance and dynamic characteristics. Finally, in the process of changing the position of the robot arm, the output capacity of the end force will decrease in a certain direction, and if the load distribution method is not adjusted in time, the overloading accident of the robot arm will occur, and therefore, it is necessary to reasonably distribute the dynamic load of the multi-robot arm.

[0003] In the prior art, most of the load distribution of the multi-robot arm adopts an even load distribution method, which is good when the robot arm is static, however, when the multi-robot arm system is in a motion state, the dynamic operability of the end thereof is also dynamically changed, and the output capacity of the end force of the robot arm will decrease, and if the load distribution method of the multi-robot arm system is not adjusted in time, the joint of the robot arm will be overloaded, and an accident will occur. SUMMARY

[0004] The present application aims to: by constructing the acceleration ellipsoid of the end of the robot arm, establishing a generalized grasp inverse matrix, and distributing the dynamic load according to the dynamic operability in the motion process of the robot arm, the joint overloading phenomenon due to the dynamic operability of the robot arm is effectively avoided.

[0005] The technical scheme of the application is: a multi-robot arm load distribution method based on a generalized grasping inverse matrix is provided, which comprises the following steps: step 1, calculating the end dynamic operability of each robot arm according to the end acceleration ellipsoid of the plurality of robot arms and the end acceleration straight line equation of the plurality of robot arms, and determining the load distribution coefficient of each robot arm according to the end dynamic operability; step 2, calculating the object virtual mass, object virtual inertia and object virtual center of mass of the grasped object according to the end virtual mass and end virtual inertia of the plurality of robot arms in combination with the load distribution coefficient; and step 3, constructing a generalized grasping inverse matrix according to the end virtual mass, end virtual inertia, object virtual mass, object virtual inertia and object virtual center of mass, and determining the end load of each robot arm according to the total load of the plurality of robot arms.

[0006] In any of the above technical schemes, further, in step 1, the end dynamic operability of each robot arm is calculated, specifically comprising: step 11, determining the joint acceleration of the robot arm according to the dynamic model of the robot arm, mapping the joint acceleration to the end of the robot arm, calculating the end acceleration of the robot arm, and constructing the acceleration ellipsoid of the robot arm; step 12, calculating the intersection of the acceleration ellipsoid and the straight line equation of the robot arm along the acceleration direction; and step 13, calculating the distance between the intersection and the center of the acceleration ellipsoid, and recording the distance as the end dynamic operability.

[0007] In any of the above technical schemes, further, the end acceleration of the robot arm is calculated according to the following formula:

[0008]

[0009] In the formula, J(q) is the Jacobian matrix of the robot arm, is the joint speed of the robot arm, is the joint acceleration, and q is the joint position of the robot arm.

[0010] The calculation formula of the acceleration ellipsoid is as follows:

[0011] (V a ) T J(q) -T QJ(q) -1 (v a )≤1

[0012]

[0013] Q=M(q)L -1 L -1 M(q)

[0014] In the formula, V a , Q are intermediate parameters, a H ​For spatial acceleration, J(q) is the Jacobian matrix of the robot arm, M(q) is the inertia matrix of the robot arm, and L is the limit torque matrix of the robot arm.

[0015] In any of the above technical solutions, further, in step 1, the load distribution coefficient β of each robot arm i The corresponding calculation formula is:

[0016]

[0017]

[0018] In the formula, d i is the distance, i is the serial number of the plurality of robot arms, i = 1, 2,..., n, P i is the intersection, p xi , p yi , p zi is the coordinate of the intersection P i .

[0019] In any of the above technical solutions, further, the calculation formula of the generalized grasp inverse matrix is:

[0020]

[0021]

[0022] In the formula, is the generalized grasp inverse matrix, is the end virtual mass, i is the serial number of the plurality of robot arms, i = 1, 2,..., n, is the object virtual mass, I3 is a three-dimensional unit matrix, is the end virtual inertia, S(·) is the anti-symmetric matrix operation, r i is the grasp position of the i-th robot arm on the grasped object, is the object virtual inertia, o is the object virtual center of mass of the grasped object.

[0023] In any of the above technical solutions, further, the calculation formula of the object virtual mass is:

[0024]

[0025] In the formula, β i is the load distribution coefficient.

[0026] In any of the above technical solutions, further, the calculation formula of the object virtual center of mass is:

[0027]

[0028] wherein o is a virtual centroid of the object, β i is a load distribution coefficient, r i is a gripping position.

[0029] In any of the technical solutions above, further, the virtual inertia of the object is calculated according to the following formula:

[0030]

[0031]

[0032] wherein o is a virtual centroid of the object to be gripped.

[0033] The application has the following advantages:

[0034] In the technical solution of the application, the acceleration ellipsoid of the end of the mechanical arm is constructed, the dynamic operability of the end of each mechanical arm is obtained by combining the acceleration straight line equation of the end of the mechanical arm, the load distribution coefficient of each mechanical arm is determined, the virtual mass and the virtual inertia of the object to be gripped are calculated by combining the load distribution coefficient of the mechanical arm, the virtual mass and the virtual inertia of the end of the mechanical arm, the generalized gripping inverse matrix is constructed, and the dynamic distribution of the load at the end of each mechanical arm is realized according to the total load of the mechanical arms, thereby improving the safety performance in the gripping movement of the mechanical arm, effectively avoiding the joint overload phenomenon of the mechanical arm, and optimizing the output ability of the force at the end of the mechanical arm.

[0035] In the application, in the process of constructing the generalized gripping inverse matrix, the load distribution coefficient is introduced to objectively reflect the output ability of the force of the mechanical arm under the current state, and the virtual mass and the virtual inertia of the object are confirmed by using the load distribution coefficient, thereby providing a basis for realizing the dynamic distribution of the load of the mechanical arm. In particular, when the load distribution coefficient of a certain mechanical arm decreases, the load of the mechanical arm is reduced by the generalized gripping inverse matrix, so as to avoid joint overload and damage to the mechanical arm. BRIEF DESCRIPTION OF DRAWINGS

[0036] The advantages of the above and / or additional aspects of the application will become apparent and easily understood from the following description of the embodiments, in conjunction with the accompanying drawings, in which:

[0037] Figure 1 is a schematic flowchart of a method for load distribution of multiple mechanical arms based on a generalized gripping inverse matrix according to an embodiment of the application;

[0038] Figure 2 is a simulation diagram of a dual-robot cooperative carrying model according to an embodiment of the application;

[0039] Figure 3is a simulation diagram of a motion trajectory according to an embodiment of the present application;

[0040] Figure 4 is a simulation diagram of an acceleration trajectory according to an embodiment of the present application;

[0041] Figure 5 is a simulation diagram of a load distribution coefficient according to an embodiment of the present application;

[0042] Fig. 6 is a simulation diagram of a mechanical arm end force load according to an embodiment of the present application;

[0043] Fig. 7 is a simulation diagram of a mechanical arm end torque load according to an embodiment of the present application;

[0044] Fig. 8 is a simulation diagram of a mechanical arm joint torque according to an embodiment of the present application. DETAILED DESCRIPTION

[0045] In order to enable a more complete understanding of the above-mentioned objects, features and advantages of the present application, the present application will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be noted that the embodiments of the present application and the features in the embodiments can be combined with each other without conflict.

[0046] In the following description, many specific details are set forth in order to provide a thorough understanding of the present application, but the present application can also be practiced in other ways different from those described herein, and therefore the scope of protection of the present application is not limited by the specific embodiments disclosed below.

[0047] As shown in Figure 1 and Figure 2 , the embodiment provides a multi-robot arm load distribution method based on a generalized grasp inverse matrix, selects a common double-robot arm cooperative carrying system in industry as an example, and uses the multi-robot arm load distribution method in the embodiment to perform dynamic load distribution on the robot arms R1 and R2 in the system, thereby improving operation safety. The two robot arms are denoted as R1 and R2, respectively, the performance parameters of the two robot arms are the same, the grasp positions are r1 = [-0.1 0 0] T , r2 = [0.1 00] T , the mass of the grasped object is m = 5 kg, the limit torque of each joint of the robot arm is L = [150 120 100 80 50 50] T N·m, the motion time of the carried object is 3 s, the control period of the double-robot arm system is 10 ms, and a double-robot arm cooperative carrying model is built in matlab in cooperation with a robotic toolbox toolbox.

[0048] As shown in Figure 3As shown, for the above double-robot cooperative carrying model, a 3rd order B-spline method is used for trajectory planning to obtain the motion trajectory of the object:

[0049]

[0050]

[0051]

[0052] In the formula, Traj x , Traj y and Traj z are respectively the motion trajectories of the object in the workspace x, y and z, and the acceleration a of the object can be obtained by twice differentiating the motion trajectory, as shown in the formula. Figure 4

[0053] Therefore, the total load of the multiple robots of the system in the embodiment is:

[0054]

[0055] The total load is composed of two parts: one is the gravity of the object to be grabbed, and the other is the force required by the motion acceleration of the object to be grabbed. The total load needs to be dynamically distributed in the motion process of the object to be grabbed, that is, the total load is distributed in each control cycle.

[0056] When T=1s, taking the load distribution of the 100th control cycle of the system as an example, the multi-robot load distribution method in the embodiment is described, which includes the following steps.

[0057] Step 1, according to the end acceleration ellipsoid of the multiple robots and the end acceleration straight line equation of the multiple robots, the end dynamic operability of each robot is calculated, and the load distribution coefficient of each robot is determined according to the end dynamic operability.

[0058] Specifically, the Lagrange method is used to construct the rigid body dynamics equation of the robot as follows:

[0059]

[0060] In the formula, τ is the joint torque of each joint of the robot, which is in the form of a matrix, and in the embodiment, it is assumed that the robots R1 and R2 are respectively composed of 6 joints, so for the robot R1, the joint torque τ 1 =[τ1,...,τ6], M(q) is the inertia matrix of the robot, which is a positive definite symmetric matrix, ​​is the combined term of the Coriolis force, centrifugal force and gravity, q is the joint position of the robot arm, is the joint velocity of the robot arm, is the joint acceleration of the robot arm.

[0061] When T = 1s, the inertia matrix M1(q) of the robot arm R1 is:

[0062]

[0063] It should be noted that, since the combined term does not affect the end dynamic manipulability of the robot arm, it can not be calculated.

[0064] Therefore, based on the above dynamics equation, the end dynamic manipulability of each robot arm can be calculated, and the process specifically includes:

[0065] Step 11, according to the dynamics model of the robot arm, the joint acceleration of the robot arm is determined, the joint acceleration is mapped with the end of the robot arm, the end acceleration of the robot arm is calculated, and the acceleration ellipsoid of the robot arm is constructed;

[0066] Further, according to the Jacobian matrix, the mapping relationship between the joint velocity of the robot arm and the end velocity V of the robot arm is:

[0067]

[0068] In the formula, J(q) is the Jacobian matrix of the robot arm, and the Jacobian matrix J1(q) of the robot arm R1 is taken as an example:

[0069]

[0070] By derivation, the calculation formula of the end acceleration of the robot arm is:

[0071]

[0072] That is:

[0073]

[0074]

[0075] In the formula, a H is the spatial acceleration caused by the centrifugal force, the Coriolis force and the gravity.

[0076] In this embodiment, in order to construct the acceleration ellipsoid, the joint torque τ of the robot arm is also calculated:

[0077]

[0078]

[0079] In the formula, is the limit torque of the γth joint in the robot arm. After standardization, the standardized joint torque is brought into the calculation formula of the end acceleration .

[0080] According to the calculated end acceleration , the acceleration ellipsoid of the robot arm is constructed in combination with the definition of the velocity manipulability ellipsoid, and the calculation formula of the acceleration ellipsoid is:

[0081] (V a ) T J(q) -T QJ(q) -1 (V a )≤1

[0082]

[0083] Q=M(q)L -1 L -1 M(q)

[0084] In the formula, V a , Q are intermediate parameters, a H is spatial acceleration, J(q) is the Jacobian matrix of the robot arm, M(q) is the inertia matrix of the robot arm, is a positive definite matrix, and L is the limit torque matrix of the robot arm.

[0085] Since the inertia matrix M(q) is a positive definite matrix, L -1 L -1 is a positive definite matrix, so the intermediate matrix J(q) -T QJ(q) -1 is also positive definite. Therefore, the acceleration ellipsoid constructed in the embodiment is a 6-dimensional ellipsoid, wherein the intermediate matrix J(q) -T QJ(q) -1 determines the shape and size of the ellipsoid.

[0086] By analyzing the 6-dimensional ellipsoid constructed in the embodiment, the intermediate matrix J(q) -T QJ(q) -1 is divided into:

[0087]

[0088] In the formula, A 3×3This describes the acceleration capability of the robotic arm's end effector in a three-dimensional workspace, and also its force output capability in various directions within that workspace; D 3×3 It describes the ability of the robotic arm end effector to rotate and accelerate in a three-dimensional workspace, as well as the torque output capability of the robotic arm end effector in various directions in the three-dimensional workspace.

[0089] The intermediate matrix J(q) -T QJ(q) -1 The shape of the acceleration ellipsoid at the end of the robotic arm changes with the position of the robotic arm, indicating that the acceleration capability of the end of the robotic arm to move and rotate in the workspace is constantly changing. Therefore, the acceleration ellipsoid needs to be calculated once in each control cycle to achieve dynamic load distribution.

[0090] Step 12: Calculate the intersection point of the acceleration ellipsoid and the linear equation of the robotic arm along the acceleration direction;

[0091] Specifically, the direction coordinates of the acceleration in any direction passing through the center of the acceleration ellipsoid are defined as [a x a y a z ]=[-0.02 0.51 1.19], therefore, the linear equation of the robotic arm along the acceleration direction is obtained as:

[0092]

[0093] Right now:

[0094]

[0095] Correspondingly, in this acceleration ellipsoid, for a three-dimensional symmetric matrix A 3×3 The equation for the moving acceleration ellipsoid has the following form:

[0096] [xyz]·A 3×3 ·[xyz] T =1

[0097] Right now:

[0098]

[0099] Therefore, the intersection point P1 = (p) of the acceleration ellipsoid and the linear equation can be calculated. x1 p y1 p z1 = (-0.01, 0.14, 0.33).

[0100] Step 13: Calculate the distance between the intersection point and the center of the acceleration ellipsoid, and record the distance as the end-effector dynamic operability.

[0101] According to the intersection point P i =(p xi , p yi , p zi ), the distance d i between it and the center of the acceleration ellipsoid can be calculated:

[0102]

[0103] In the formula, d i is the distance, i is the serial number of the plurality of mechanical arms, i = 1, 2,..., n.

[0104] The distance describes the force output capability of the mechanical arm end in a certain direction in the workspace at a certain moment, since the acceleration ellipsoid of the mechanical arm end and the acceleration direction of the object are constantly changing, so the distance is also dynamically changing, so it is used as the dynamic operability of the mechanical arm end, and then the dynamic operability of the mechanical arm end of each mechanical arm can be obtained, and the force load distribution coefficient of each mechanical arm at a certain moment is determined by the ratio of the dynamic operability of the mechanical arm end, and the load distribution coefficient β i The corresponding calculation formula is:

[0105]

[0106]

[0107] In the formula, d i is the distance, i is the serial number of the plurality of mechanical arms, i = 1, 2,..., n, P i is the intersection point, p xi , p yi , p zi are coordinates of the intersection point P i .

[0108] In this embodiment, the load distribution coefficient β i is introduced to objectively reflect the output capability of the mechanical arm under the current state, and the load distribution coefficient β i is used to confirm the virtual mass of the object and the virtual inertia of the object, and then affect the constructed generalized grasp inverse matrix, so as to realize dynamic distribution of the load of the mechanical arm, especially when the load distribution coefficient β i of a certain mechanical arm decreases, the load of the mechanical arm is reduced through the generalized grasp inverse matrix, so as to avoid joint overload and cause damage to the mechanical arm.

[0109] In this embodiment, as shown in Figure 5 the load distribution coefficient β iThe proportion of the virtual mass of each robot arm is a dynamic parameter, thus it needs to be calculated in each control cycle.

[0110] The intersection P1 = (-0.01, 0.14, 0.33) is brought into the above calculation process, and the distance d1 = 0.36 is obtained. The above process is repeated, and the distance d2 = 0.44 corresponding to the robot arm R2 is obtained, and the corresponding load distribution coefficients β1 = 0.45 and β2 = 0.55 are obtained.

[0111] Step 2, according to the end virtual mass and end virtual inertia of the plurality of robot arms, and in combination with the load distribution coefficients, the object virtual mass, the object virtual inertia and the object virtual center of mass of the object to be grabbed are calculated;

[0112] The object virtual mass and the object virtual inertia of the object to be grabbed at a certain moment in the embodiment are represented as The end virtual mass and the virtual inertia of the i-th robot arm are The object virtual mass is determined by the load distribution coefficients β i , and the corresponding calculation formula is:

[0113]

[0114] Correspondingly, the calculation formula of the object virtual inertia is:

[0115]

[0116]

[0117] In the formula, o is the object virtual center of mass of the object to be grabbed, r i is the gripping position of the i-th robot arm on the object to be grabbed, S(r i -o) is the skew-symmetric matrix of (r i -o), and S(·) is the skew-symmetric matrix operation.

[0118] In the embodiment, at t = 1s, the end virtual mass of the robot arm R1 is set as According to the proportion of the load distribution coefficients β1 and β2, the end virtual mass m2 = 1.22 of the robot arm R2 is obtained, and the end virtual inertia of the robot arm R1 and the robot arm R2 is set as a three-dimensional unit matrix, and then the object virtual mass is:

[0119]

[0120] The calculated object virtual center of mass is:

[0121]

[0122] Virtual inertia of an object for:

[0123]

[0124] Step 3: Construct a generalized gripping inverse matrix based on the virtual end mass, virtual end inertia, virtual object mass, virtual object inertia, and virtual object centroid, and determine the end load of each robotic arm based on the total load of the multiple robotic arms.

[0125] This embodiment is based on the aforementioned robotic arm acceleration ellipsoid and J(q). -T QJ(q) -1 Based on the analysis, in order to dynamically distribute the load to each robotic arm, a generalized gripping inverse matrix is ​​constructed according to the virtual end-effector mass, virtual end-effector inertia, virtual object mass, and virtual object inertia. The formula for calculating the generalized gripping inverse matrix is ​​as follows:

[0126]

[0127]

[0128] In the formula, For the generalized grasping inverse matrix, The virtual end effector mass is defined as i, where i is the index of the plurality of robotic arms, i = 1, 2, ..., n. I3 represents the virtual mass of the object, and I3 is the three-dimensional identity matrix. To compensate for inertia, Let S(·) be the terminal virtual inertia, and r be the antisymmetric matrix operation. i Let i be the gripping position of the i-th robotic arm on the object being gripped. Let o be the virtual inertia of the object, and let o be the virtual centroid of the object being grasped.

[0129] For the dual-robotic arm collaborative handling system in this embodiment, the constructed generalized gripping inverse matrix is:

[0130]

[0131] In the formula, For the distribution of force, where, The magnitude of the force distributed to the end effector of the first robotic arm. The force distribution term is used to determine the magnitude of the force allocated to the end effector of the second robotic arm. The value is determined by the virtual mass at the end of the robotic arm. The decision, and the end virtual quality The size of the adjustment term for force and torque distribution is determined by the corresponding load distribution coefficient β i The adjustment term is determined, so the load distribution can be performed according to the output capacity of each manipulator at different times, thereby avoiding joint overload.

[0132] The adjustment term for force and torque distribution is determined by adjusting the virtual mass of the end of the manipulator and the virtual inertia of the object The adjustment term can convert a part of the pure force output by the end of the manipulator into torque, thereby increasing the output of the force at the end of the manipulator and achieving the effect of reducing torque output. When the torque output capacity of the manipulator is insufficient, by increasing the virtual mass of the end of the manipulator, the adjustment term can convert a part of the pure force into torque, thereby further optimizing the gripping performance of the manipulator.

[0133] The adjustment term for torque compensation is determined by the non-uniform gripping disturbance torque The adjustment term is used to offset the disturbance torque generated by non-uniform gripping, and the compensation inertia and the virtual mass of the object are distributed to the end of the i-th manipulator to ensure stable gripping of the object by the multiple manipulators.

[0134] The adjustment term for torque distribution is determined by the virtual inertia of the end of the manipulator .

[0135] After the above-mentioned generalized gripping inverse matrix is constructed, the load of the multiple manipulators of the system is distributed to the manipulators R1 and R2 according to the generalized gripping inverse matrix and the total load of the multiple manipulators of the system The load distribution is as follows:

[0136]

[0137] In the formula, h1 is the distributed load of the manipulator R1, and h2 is the distributed load of the manipulator R1.

[0138] In this embodiment, the plot function of MATLAB is used to draw the change curves of the manipulators R1 and R2 in the system, including force load and torque load, as shown in FIGS. 6 and 6,

[0139] In the formula, f 1x , f 1y , f 1z are the force load components of the manipulator R1 along the x, y, and z coordinate axes, and f 2x , f 2y , f 2z are the force load components of the manipulator R2 along the x, y, and z coordinate axes.

[0140] t 1x t 1y t 1z Let t be the torque load components at the end of the robotic arm R1 along the x, y, and z coordinate axes. 2x t 2y t 2z Let x be the torque load components at the end of the robotic arm R2 along the three coordinate axes x, y, and z.

[0141] As can be seen from the figure, during the movement of the two robotic arms, the total load... The components were rationally allocated to the end effector of each robotic arm. When the dual-arm system had run for 2.8 seconds, the components were... Figure 4 It can be seen that the load distribution coefficient β1 of the robotic arm R1 is 0.255, which reduces its end effector dynamic operability and also reduces its force output capability. At this time, the load borne by the robotic arm R1 is reduced, and the force load component f 1x f 1y f 1z The strengths are 0.92N, 0.53N, and 5.6N, respectively.

[0142] Correspondingly, by Figure 4 It can be seen that the load distribution coefficient β2 of the robotic arm R2 is 0.745. The increased dynamic operability of its end effector means enhanced force output capability, thus it bears a larger load. To avoid joint overload, the force load component f of the robotic arm R2... 2x f 2y f 2z The values ​​are 7.366N, 4.2554N, and 44.962N, respectively.

[0143] By calculating the joint torques of robotic arms R1 and R2 using inverse dynamics, the curves of the joint torques of robotic arms R1 and R2 over time can be obtained, as shown in Figures 8(a) and (b), respectively. In the figures, τ1 to τ6 represent the joint torques of each joint in each robotic arm.

[0144] As shown in Figure 8, the torques of all joints in robotic arms R1 and R2 were controlled between 10 and -50 N·m and 40 and -80 N·m, respectively. The joint torque changes were stable without abrupt changes or joint overload due to decreased end-effector maneuverability, further demonstrating the overall load... The load was reasonably distributed to the end of each robotic arm, verifying the rationality of the load distribution method in this embodiment.

[0145] The technical scheme of the application is described in detail above with reference to the drawings. The application provides a multi-robot arm load distribution method based on a generalized grasping inverse matrix, which comprises the following steps: step 1, calculating the end dynamic operability of each robot arm according to the end acceleration ellipsoid of the robot arms and the end acceleration straight line equation of the robot arms, and determining the load distribution coefficient of each robot arm according to the end dynamic operability; step 2, calculating the object virtual mass, object virtual inertia and object virtual center of mass of the object to be grasped according to the end virtual mass and end virtual inertia of the robot arms in combination with the load distribution coefficient; and step 3, constructing the generalized grasping inverse matrix according to the end virtual mass, end virtual inertia, object virtual mass, object virtual inertia and object virtual center of mass, and determining the end load of each robot arm according to the total load of the robot arms. Through the technical scheme in the application, the dynamic load distribution coefficient of the robot arm is determined, the generalized grasping inverse matrix is established by using the virtual mass, virtual inertia and virtual mass center, and the end dynamic load distribution of the multi-robot arm is realized.

[0146] The steps in the application can be adjusted in sequence, combined and reduced according to actual needs.

[0147] The units in the device in the application can be combined, divided and reduced according to actual needs.

[0148] Although the application is disclosed in detail with reference to the drawings, it should be understood that the description is only exemplary and is not intended to limit the application. The scope of protection of the application is defined by the appended claims, and can include various modifications, improvements and equivalent schemes made to the application without departing from the scope and spirit of the application.

Claims

1. A method for multi-arm load distribution based on generalized grasp inverse matrix, characterized in that, The method comprises: Step 1, calculating the end dynamic operability of each of the plurality of mechanical arms according to the end acceleration ellipsoid of the plurality of mechanical arms and the end acceleration straight line equation of the plurality of mechanical arms, and determining the load distribution coefficient of each of the plurality of mechanical arms according to the end dynamic operability; Step 2, calculating the object virtual mass, object virtual inertia and object virtual centroid of the object to be grabbed according to the end virtual mass and end virtual inertia of the plurality of mechanical arms in combination with the load distribution coefficient; Step 3, constructing a generalized grasping inverse matrix according to the end virtual mass, the end virtual inertia, the object virtual mass, the object virtual inertia and the object virtual centroid, and determining the end load of each of the plurality of mechanical arms according to the total load of the plurality of mechanical arms, The calculation formula of the generalized grasping inverse matrix is: wherein, is the generalized grasp inverse matrix, is the end virtual mass, i is the index of the plurality of robotic arms, i = 1, 2,..., n, is the object virtual mass, I3is a three-dimensional identity matrix, is the end virtual inertia, S(·) is a skew-symmetric matrix operation, r i is the grasp position of the ith robotic arm on the grasped object, is the object virtual inertia, o is the object virtual center of mass, The object virtual mass The formula for calculating is: wherein β i is the load distribution coefficient, The calculation formula of the object virtual centroid is: wherein o is the virtual center of mass of the object, β i is the load distribution coefficient, r i is the gripping position, The object virtual inertia The formula for calculating is: In the formula, o is the object virtual centroid.

2. The generalized grasp inverse matrix based multi-arm load distribution method of claim 1, wherein, In the step 1, the end dynamic operability of each of the plurality of mechanical arms is calculated, and 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 to the end of the mechanical arm, calculating the end acceleration of the mechanical arm, and constructing the acceleration ellipsoid of the mechanical arm; Step 12, calculating the intersection of the acceleration ellipsoid and the straight line equation of the acceleration direction of the mechanical arm; Step 13, calculating the distance between the intersection and the center of the acceleration ellipsoid, and recording the distance as the end dynamic operability.

3. The generalized grasp inverse matrix based multi-arm load distribution method of claim 2, wherein, End acceleration of the robot arm The formula is: where J(q) is a Jacobian matrix of the robot arm, is a joint velocity of the robot arm, is a joint acceleration of the robot arm, q is a joint position of the robot arm; The calculation formula of the acceleration ellipsoid is: (V -1 ) -1 J(q) a QJ(q) H (V i )≤1 Q = M(q) L -1 L -1 M(q) where V a , Q is an intermediate parameter, a H is the spatial acceleration, J(q) is the Jacobian matrix of the robot arm, M(q) is the inertia matrix of the robot arm, and L is the limit torque matrix of the robot arm.

4. The generalized grasp inverse matrix based multi-arm load distribution method of claim 2, wherein, In the step 1, the load distribution coefficient β of each mechanical arm i The corresponding calculation formula is: In the formula, d i is the distance, i is the serial number of the plurality of mechanical arms, i = 1, 2, …, n, P i is the intersection point, p xi , p yi , p zi is the coordinate of the intersection point P i .

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