CN113547506A - Double-arm robot precise assembly method based on six-dimensional force sensor - Google Patents

Double-arm robot precise assembly method based on six-dimensional force sensor Download PDF

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CN113547506A
CN113547506A CN202110721136.1A CN202110721136A CN113547506A CN 113547506 A CN113547506 A CN 113547506A CN 202110721136 A CN202110721136 A CN 202110721136A CN 113547506 A CN113547506 A CN 113547506A
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mechanical arm
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joint
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CN113547506B (en
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张俊宁
李晓琪
杨帆
吕博瀚
刘书选
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Beijing Research Institute of Precise Mechatronic Controls
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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
    • B25J9/0084—Programme-controlled manipulators comprising a plurality of manipulators
    • B25J9/0087—Dual arms
    • 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
    • B25J9/1602—Programme controls characterised by the control system, structure, architecture
    • B25J9/1605—Simulation of manipulator lay-out, design, modelling of manipulator
    • 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
    • B25J9/163—Programme controls characterised by the control loop learning, adaptive, model based, rule based expert control
    • 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
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02P—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN THE PRODUCTION OR PROCESSING OF GOODS
    • Y02P90/00—Enabling technologies with a potential contribution to greenhouse gas [GHG] emissions mitigation
    • Y02P90/02—Total factory control, e.g. smart factories, flexible manufacturing systems [FMS] or integrated manufacturing systems [IMS]

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Abstract

The invention discloses a precision assembly method of a double-arm robot based on a six-dimensional force sensor, which comprises the following steps: the robot controller reads the joint angles of the left mechanical arm and the right mechanical arm; obtaining Cartesian space poses of the left mechanical arm and the right mechanical arm; obtaining Cartesian space poses of the pin hole workpieces at the tail ends of the left arm and the right arm relative to the base coordinates of the robot through coordinate transformation according to the Cartesian space poses of the left arm and the right arm; obtaining a left arm tail end pin hole and a right arm tail end pin hole planning path by using a random tree exploring method based on rapid potential energy; the planning path is short in movement distance, short in assembly operation time, low in energy consumption of the mechanical arm and capable of avoiding interference; and controlling the smooth assembly of the left mechanical arm and the right mechanical arm by using a control method based on a learning variable impedance control system according to the planned paths of the pin holes at the tail end of the left arm and the pin holes at the tail end of the right arm. The invention can plan a path with high quality and has compliant assembly capability.

Description

Double-arm robot precise assembly method based on six-dimensional force sensor
Technical Field
The invention belongs to the technical field of double-arm robots of six-dimensional force sensors, and particularly relates to a precision assembling method of a double-arm robot based on a six-dimensional force sensor.
Background
Aerospace manufacturing has very high requirements on precision, reliability, standard flow and the like, so a large number of national craftsmen are cultivated in the field of aerospace manufacturing. However, as time goes on, some skilled artisans become retired, and the new 80 th and 90 th labour population is not interested in doing simple and repetitive industrial work with poor working environment, so that it is a good choice to complete a part of the work by robot instead of manpower while cultivating the new generation of the great national craftsman, and the shift from aerospace manufacturing to aerospace manufacturing becomes a great trend.
The industrial robot assembly applied in the manufacturing industry at present is mainly single mechanical arm assembly or assembly of a plurality of independent mechanical arms on a flow line. According to the assembling method, the mechanical arms are not matched with each other, and the assembling action is edited in advance, so that the mechanical arms are poor in assembling precision, low in assembling efficiency and poor in adaptability.
The robot assembly belongs to a contact operation task under a non-structural environment, and due to the complex task and the variable and unpredictable contact environment, an accurate dynamic model of a system is difficult to establish, so that how to enable the robot to safely, efficiently and quickly execute a new task and accurately control contact force under different environments is a new challenge faced by the robot. The impedance control is widely applied to the robot interaction control task due to good adaptability and robustness. Since the force control characteristics are determined by the impedance parameters of the robot, the selection of the inertia, stiffness and damping parameters is highly dependent on the task, and it is often difficult to infer a priori, in order to obtain good control performance, an in-depth knowledge of the controller design and its parameters is often required, and a good method of adjusting the control parameters is still required. Therefore, learning the variable impedance control capability is the key to a modern robot to safely and quickly complete complex operation tasks.
For the path planning of the double mechanical arms, the existing methods include a manual potential field method, an A-star algorithm, an RRT algorithm and the like. In the process of automatic assembly, in order to ensure that parts are not damaged and can be stably matched, the moving speed of the parts needs to be restricted, and an efficient suitable path is planned under the condition that the parts can be stably assembled. However, the artificial potential field method is easy to fall into local optimization, the a-x algorithm is difficult to play a role in a dynamic road network, the RRT algorithm has poor path quality and the like, so that a high-quality path is difficult to plan in the aspect of cooperative assembly operation of two mechanical arms.
Disclosure of Invention
The technical problem solved by the invention is as follows: the defects of the prior art are overcome, the precision assembling method of the double-arm robot based on the six-dimensional force sensor is provided, a high-quality path can be planned, and the method has the advantages of being flexible and capable of being assembled.
The purpose of the invention is realized by the following technical scheme: a precision assembly method of a double-arm robot based on a six-dimensional force sensor comprises the following steps: the method comprises the following steps: the robot controller reads the joint angles of the left mechanical arm and the right mechanical arm; step two: establishing a kinematics model and a dynamics model of the double-mechanical-arm robot; obtaining the Cartesian space pose of the left mechanical arm by applying a six-degree-of-freedom mechanical arm positive kinematics algorithm according to each joint angle of the left mechanical arm and the kinematics model and the dynamics model of the double-mechanical-arm robot in the step one; obtaining the Cartesian space pose of the right mechanical arm by applying a six-degree-of-freedom mechanical arm positive kinematics algorithm according to each joint angle of the right mechanical arm in the step one and a kinematics model and a dynamics model of the double-mechanical-arm robot; step three: obtaining a Cartesian space pose of the left arm tail end pin hole workpiece relative to a robot base coordinate through coordinate conversion according to the Cartesian space pose of the left arm in the second step; obtaining a Cartesian space pose of the right arm tail end pin hole workpiece relative to the robot base coordinate through coordinate conversion according to the Cartesian space pose of the right arm in the second step; step four: obtaining a left arm tail end pin hole and a right arm tail end pin hole planning path by using a random tree exploring method based on rapid potential energy; the planning path is short in movement distance, short in assembly operation time, low in energy consumption of the mechanical arm and capable of avoiding interference; step five: and controlling the smooth assembly of the left mechanical arm and the right mechanical arm by using a control method based on a learning variable impedance control system according to the planning paths of the pin holes at the tail ends of the left arm and the right arm in the fourth step.
In the precision assembly method of the dual-arm robot based on the six-dimensional force sensor, in the second step, the kinematic model and the dynamic model of the dual-arm robot are obtained by the following formulas:
Figure BDA0003136890120000031
Figure BDA0003136890120000032
Figure BDA0003136890120000033
Figure BDA0003136890120000034
Figure BDA0003136890120000035
Figure BDA0003136890120000036
wherein the content of the first and second substances,
Figure BDA0003136890120000037
is a coordinate transformation matrix of the joints i-1 and i of the double-mechanical-arm robot, c represents cos, s represents sin, thetai,αi-1,ai-1,diD-H parameters of a joint i of the double-mechanical-arm robot are respectively set;
Figure BDA0003136890120000038
is a conversion matrix from a left mechanical arm end pin workpiece to the left mechanical arm end, and m is the distance from the left mechanical arm end pin workpiece to the left mechanical arm endSeparating;
Figure BDA0003136890120000039
the transformation matrix is from a hole workpiece at the tail end of the right mechanical arm to the tail end of the right mechanical arm, and m is the distance from a pin workpiece at the tail end of the right mechanical arm to the tail end of the right mechanical arm;
Figure BDA00031368901200000310
a transformation matrix from a left mechanical arm tail end pin workpiece to a left mechanical base coordinate;
Figure BDA00031368901200000311
a transformation matrix from a workpiece at the tail end hole of the right mechanical arm to a base coordinate of the right mechanical arm; τ is the joint control moment, M (Θ) is the mass matrix of n × n of the robotic arm,
Figure BDA00031368901200000312
is the centrifugal force and the coriolis force vector of n x 1, G (Θ) is the gravity vector of n x 1, Θ is the mechanical arm joint position vector,
Figure BDA00031368901200000313
is the velocity vector of the joint of the mechanical arm,
Figure BDA00031368901200000314
is the acceleration vector of the mechanical arm joint.
In the precision assembly method of the double-arm robot based on the six-dimensional force sensor, in the fourth step, the method for exploring the random tree based on the rapid potential energy comprises the following steps:
(41) setting initial parameters and carrying out initial sampling;
(42) calculating the distance between the tree node of the random tree and the sampling point according to the kinematic model and the dynamic model of the double-mechanical-arm robot and the initial parameters in the step (41), and finding the nearest tree node as a father node;
(43) obtaining an expansion child node according to the father node, judging whether the expansion child node collides, and adding a candidate sampling point if the expansion child node does not collide;
(44) calculating potential energy of the candidate sampling points;
(45) modifying the sampling step length and the sampling probability; repeating steps (42) - (44) until the candidate sampling point reaches num;
(46) carrying out roulette selection according to the reciprocal of the potential energy of the num candidate sampling points to obtain sampling points, and taking the sampling points as new sub-nodes;
(47) and (4) selecting the connection mode with the shortest cost to connect the new child node in the step (46) with the parent node, and determining the planning path of the pin hole at the tail end of the left arm and the pin hole at the tail end of the right arm.
In the above method for precisely assembling a six-dimensional force sensor-based two-arm robot, in step five, the control method based on the learning variable impedance control system includes the following steps:
(51) acting a preset initialization control variable on a control system of the mechanical arm;
(52) establishing a Gaussian process dynamic model of the control system according to preset sampling data, and taking the Gaussian process dynamic model as a transformation dynamic model of the system;
(53) searching for an optimal impedance control strategy using a strategy learning algorithm based on the transformed dynamical model of the system in step (52);
(54) according to the optimal impedance control strategy, the method is applied to a variable impedance controller to control the force and acquire data;
(55) repeating steps (52) - (54) until a preset force tracking effect is obtained.
In the precision assembly method of the two-arm robot based on the six-dimensional force sensor, in step (41), the initial parameters include: the method comprises the steps of starting pose left _ start of a left mechanical arm, target pose left _ goal, starting pose right _ start of a right mechanical arm, target pose right _ goal, initial path random tree, initial sampling step size, initial sampling probability, sampling upper limit _ limit, single candidate sampling point num, reconnection cost, collision distance and final position potential energy error h.
In the precision assembling method of the double-arm robot based on the six-dimensional force sensor, in the step (41), a straight line is connected between the target pose left _ goal of the left mechanical arm and the target pose right _ goal of the right mechanical arm, a point with a distance L between the left side of the left _ goal and the left _ goal on the straight line is defined as left _ visual point, and a point with a distance L between the right side of the right _ goal and the right _ goal on the straight line is defined as right _ visual point;
initializing and sampling from a left _ start point to a left _ view point of the left mechanical arm, from a left _ good point to a left _ view point of the left mechanical arm, from the left _ view point to the left _ start point of the left mechanical arm and from the left _ view point to the left _ good point of the left mechanical arm according to a sampling formula;
initializing sampling according to a sampling formula from the right _ start point to the right _ view point of the right arm, from the right _ goal point to the right _ view point of the right arm, from the right _ view point to the right _ start point of the right arm, and from the right _ view point to the right _ goal point of the right arm.
In the precision assembly method of the double-arm robot based on the six-dimensional force sensor, a sampling formula is as follows:
Figure BDA0003136890120000051
wherein q issamkIs the sampling angle of the joint k, random is the randomly chosen joint angle, qkmaxIs the maximum angle of the joint k, qkminIs the minimum angle of joint k, probability is the sampling probability, qkgoalIs the angle of the joint k in the goal position.
In the precision assembly method of the dual-arm robot based on the six-dimensional force sensor, in step (43), the expanded child nodes obtained according to the parent node are obtained by the following formula:
Figure BDA0003136890120000052
wherein q isnearestkIs the joint k angle, q, of the parent node of the random treekExpanding the joint k angle of the child node, step _ size being the initial sampling step size, qsamkIs the sampling angle of the joint k.
In the precision assembly method of the double-arm robot based on the six-dimensional force sensor, in step (44), the potential energy of the candidate sampling point is obtained by the following formula:
Figure BDA0003136890120000061
Figure BDA0003136890120000062
Figure BDA0003136890120000063
Figure BDA0003136890120000064
U(j)＝Fgra(j)+Frepinter(gj)+Frepexter(j)+Freptree(gj)；
wherein, Fgra(j) Is the gravitational potential energy of node j, λ is the gravitational proportionality coefficient, gjIs the end position of the arm at node j, gviaEnd position of the robot arm, g, which is the point of the viapointstartEnd position of the arm, g, which is the start pointgoalThe end position of the mechanical arm at the goal point; frepinter(gj) Is the repulsive potential energy generated by the internal pose of the node j, epsilon is the repulsive proportionality coefficient, gjk1Is the position of the joint k of the node j of the robot arm 1, gjk2Is the position of the joint k of the joint j of the robot arm 2, drobIs the minimum distance between the two arms, dminIs the minimum collision distance, dinterIs an internal repulsive force boundary; frepexter(j) Is the repulsive potential energy between the node j and the outside, epsilon is the repulsive proportionality coefficient, gjkIs the mechanical arm position of node j, obs is the outer envelope center of the barrier, dobsIs the distance of the joint j from the obstacle, dminIs the minimum collision distance, dexterIs an external repulsive force boundary; freptree(gj) Is node jThe repulsion potential energy generated between the mechanical arm and other random trees is equal to epsilon, which is the proportion coefficient of repulsion,
Figure BDA0003136890120000065
is a random tree m1The position of the joint k of the node j,
Figure BDA0003136890120000066
is a random tree m2Position of joint k of node j, dtreeIs the minimum distance between random trees, dminIs the minimum collision distance, dtreesIs an inter-tree repulsion boundary; u (j) is the potential energy of node j, Fgra(j) Is the gravitational potential energy of node j, Frepinter(gj) Is the repulsive potential energy generated by the internal pose of the node j, Frepexter(j) Is the repulsive potential energy of the node j and the outside, Freptree(gj) Is the repulsive potential energy generated between the node j and other random trees of the same mechanical arm.
In the precision assembling method of the double-arm robot based on the six-dimensional force sensor, in the third step, the pin hole workpiece at the tail end of the left arm is in a structure with the front end being a blunt cone and the rear end being a cylinder.
Compared with the prior art, the invention has the following beneficial effects:
(1) according to the invention, the six-dimensional force sensor is arranged at the tail end of the double-arm robot, so that the mechanical arm can be conveniently finely adjusted according to the contact force and the contact torque when moving according to a planned path, the pin holes can be accurately assembled, and the assembly accuracy is less than 0.1 mm.
(2) The invention takes RRT algorithm as the basis, introduces the passing point on the motion path of the mechanical arm, and expands to generate four random trees starting from the starting point, the passing point and the target point at the same time, thereby greatly accelerating the exploration speed of the random trees to the state space.
(3) According to the invention, on the basis of ensuring the sampling randomness, the repulsive potential energy between random trees is added in the potential energy function, so that the random tree sampling is better guided, and meanwhile, the acceleration cost is added in the method for reconnecting the random trees according to the cost, so that the motion path of the mechanical arm is smoother.
(4) The invention adds a self-adaptive step length adjusting function and a self-adaptive sampling probability adjusting function, and the two functions respectively and self-adaptively adjust the step length and the sampling probability of the random tree under the condition that the space has obstacles and has no obstacles, thereby improving the expansion speed of the random tree.
(5) The invention introduces the improved RRT algorithm, ensures that the random tree can generate the optimal path when the random tree is explored in a three-dimensional space with obstacles, and simultaneously avoids the algorithm from falling into local optimization.
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Various other advantages and benefits will become apparent to those of ordinary skill in the art upon reading the following detailed description of the preferred embodiments. The drawings are only for purposes of illustrating the preferred embodiments and are not to be construed as limiting the invention. Also, like reference numerals are used to refer to like parts throughout the drawings. In the drawings:
fig. 1 is a flowchart of a precision assembly method of a six-dimensional force sensor-based dual-arm robot according to an embodiment of the present invention;
FIG. 2 is a schematic view of the structure of the left arm end according to the present invention;
fig. 3 is a schematic structural diagram of a right arm end according to an embodiment of the present invention.
Detailed Description
Exemplary embodiments of the present disclosure will be described in more detail below with reference to the accompanying drawings. While exemplary embodiments of the present disclosure are shown in the drawings, it should be understood that the present disclosure may be embodied in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the disclosure to those skilled in the art. It should be noted that the embodiments and features of the embodiments may be combined with each other without conflict. The present invention will be described in detail below with reference to the embodiments with reference to the attached drawings.
Fig. 1 is a flowchart of a precision assembly method of a six-dimensional force sensor-based dual-arm robot according to an embodiment of the present invention. As shown in fig. 1, the precision assembly method of the dual-arm robot based on the six-dimensional force sensor comprises the following steps:
the method comprises the following steps: the robot controller reads the joint angles of the left mechanical arm and the right mechanical arm;
step two: establishing a kinematics model and a dynamics model of the double-mechanical-arm robot; obtaining the Cartesian space pose of the left mechanical arm by applying a six-degree-of-freedom mechanical arm positive kinematics algorithm according to each joint angle of the left mechanical arm and the kinematics model and the dynamics model of the double-mechanical-arm robot in the step one; obtaining the Cartesian space pose of the right mechanical arm by applying a six-degree-of-freedom mechanical arm positive kinematics algorithm according to each joint angle of the right mechanical arm in the step one and a kinematics model and a dynamics model of the double-mechanical-arm robot;
step three: obtaining a Cartesian space pose of the left arm tail end pin hole workpiece relative to a robot base coordinate through coordinate conversion according to the Cartesian space pose of the left arm in the second step; obtaining a Cartesian space pose of the right arm tail end pin hole workpiece relative to the robot base coordinate through coordinate conversion according to the Cartesian space pose of the right arm in the second step;
step four: obtaining a left arm tail end pin hole and a right arm tail end pin hole planning path by using a random tree exploring method based on rapid potential energy; the planning path is short in movement distance, short in assembly operation time, low in energy consumption of the mechanical arm and capable of avoiding interference;
step five: and controlling the smooth assembly of the left mechanical arm and the right mechanical arm by using a control method based on a learning variable impedance control system according to the planning paths of the pin holes at the tail ends of the left arm and the right arm in the fourth step.
In the fourth step, the method for exploring the random tree based on the rapid potential energy comprises the following steps: (41) setting initial parameters and carrying out initial sampling; (42) calculating the distance between the tree node of the random tree and the sampling point according to the kinematic model and the dynamic model of the double-mechanical-arm robot and the initial parameters in the step (41), and finding the nearest tree node as a father node; (43) obtaining an expansion child node according to the father node, judging whether the expansion child node collides, and adding a candidate sampling point if the expansion child node does not collide; (44) calculating potential energy of the candidate sampling points; (45) modifying the sampling step length and the sampling probability; repeating steps (42) - (44) until the candidate sampling point reaches num; (46) carrying out roulette selection according to the reciprocal of the potential energy of the num candidate sampling points to obtain sampling points, and taking the sampling points as new sub-nodes; (47) and (4) selecting the connection mode with the shortest cost to connect the new child node in the step (46) with the parent node, and determining the planning path of the pin hole at the tail end of the left arm and the pin hole at the tail end of the right arm.
In step five, the control method based on the learning variable impedance control system comprises the following steps: (51) acting a preset initialization control variable on a control system of the mechanical arm; (52) establishing a Gaussian process dynamic model of the control system according to preset sampling data, and taking the Gaussian process dynamic model as a transformation dynamic model of the system; (53) searching for an optimal impedance control strategy using a strategy learning algorithm based on the transformed dynamical model of the system in step (52); (54) according to the optimal impedance control strategy, the method is applied to a variable impedance controller to control the force and acquire data; (55) repeating steps (52) - (54) until a preset force tracking effect is obtained.
The robot in the embodiment comprises an all-directional moving platform, a robot body, two six-degree-of-freedom mechanical arms, two six-dimensional force sensors and a tail end assembly workpiece. The robot truck is installed on a moving platform, two six-degree-of-freedom mechanical arms are symmetrically installed on two sides of the robot truck, two six-dimensional force sensors are installed on end flanges of the mechanical arms respectively, assembling pin workpieces are installed on the end six-dimensional force sensor flange of the left mechanical arm, and assembling hole workpieces are installed on the end six-dimensional force sensor flange of the right mechanical arm.
Specifically, the method comprises the following steps:
step 1: establishing a kinematics model and a dynamics model of the double-mechanical-arm robot:
Figure BDA0003136890120000101
Figure BDA0003136890120000102
Figure BDA0003136890120000103
Figure BDA0003136890120000104
Figure BDA0003136890120000105
Figure BDA0003136890120000106
in formula (1):
Figure BDA0003136890120000107
is a coordinate transformation matrix of the joints i-1 and i of the double-mechanical-arm robot, c represents cos, s represents sin, thetai,αi-1,ai-1,diD-H parameters of a joint i of the double-mechanical-arm robot are respectively set; in formula (2):
Figure BDA0003136890120000108
the transformation matrix from the left mechanical arm tail end pin workpiece to the left mechanical arm tail end is shown, and m is the distance from the left mechanical arm tail end pin workpiece to the left mechanical arm tail end; in formula (3):
Figure BDA0003136890120000109
the transformation matrix is from a hole workpiece at the tail end of the right mechanical arm to the tail end of the right mechanical arm, and m is the distance from a pin workpiece at the tail end of the right mechanical arm to the tail end of the right mechanical arm; in formula (4):
Figure BDA00031368901200001010
for a transformation matrix of left mechanical arm end pin workpiece to left mechanical base coordinate(ii) a In formula (5):
Figure BDA00031368901200001011
a transformation matrix from a workpiece at the tail end hole of the right mechanical arm to a base coordinate of the right mechanical arm; in formula (6): τ is the joint control moment, M (Θ) is the mass matrix of n × n of the robotic arm,
Figure BDA00031368901200001012
is the centrifugal force and the coriolis force vector of n x 1, G (Θ) is the gravity vector of n x 1, Θ is the mechanical arm joint position vector,
Figure BDA00031368901200001013
is the velocity vector of the joint of the mechanical arm,
Figure BDA00031368901200001014
is the acceleration vector of the mechanical arm joint.
As shown in fig. 2, the left mechanical arm end pin workpiece is of a structure in which the front end is a blunt cone and the rear end is a cylinder, and is connected with a six-dimensional force sensor, and then the six-dimensional force sensor is connected with a left mechanical arm end flange.
As shown in FIG. 3, the right arm mechanical end hole workpiece is of a structure that the front end is cylindrical and is provided with an observation window, the rear end is a disc, the hole workpiece is connected with a six-dimensional force sensor, and then the six-dimensional force sensor is connected with a right arm end flange. The mounting clearance between the pin holes is 0.1 mm.
Step 2: setting initial parameters, an initial pose left _ start, a target pose left _ goal of a left mechanical arm, an initial pose right _ start, a target pose right _ goal of a right mechanical arm, an initial path random tree, an initial sampling step size, an initial sampling probability, an upper sampling limit _ limit, a single candidate sampling point num, a reconnection cost price, a collision distance and a final position potential energy error h;
and step 3: and (3) connecting the target pose left _ goal of the left mechanical arm and the target pose right _ goal of the right mechanical arm in the step (2) with a straight line, selecting a point on the straight line, wherein the distance between the left _ goal left side and the left _ goal is L, as left _ visual, and selecting a point on the straight line, wherein the distance between the right _ goal right side and the right _ goal is L, as right _ visual.
And 4, step 4: according to the step 2 and the step 3, carrying out initialization sampling according to a formula (7) from a left _ start point to a left _ view point of the left mechanical arm, from a left _ goal point to a left _ view point of the left mechanical arm, from a left _ view point to a left _ start point of the left mechanical arm, and from a left _ view point to a left _ goal point of the left mechanical arm; initializing sampling from the right _ start point to the right _ view point of the right arm, from the right _ goal point to the right _ view point of the right arm, from the right _ view point to the right _ start point of the right arm, and from the right _ view point to the right _ goal point of the right arm according to the formula (7):
Figure BDA0003136890120000111
in formula (7): q. q.ssamkIs the sampling angle of the joint k, random is the randomly chosen joint angle, qkmaxIs the maximum angle of the joint k, qkminIs the minimum angle of joint k, probability is the sampling probability, qkgoalIs the angle of the joint k in the goal position.
And 5: and 4, selecting the tree node q _ nearest to the sampling point as a father node according to the sampling point in the step 4.
Step 6: and (4) obtaining the sub-nodes according to the sampling points by using a formula (8), judging whether the sub-nodes collide, adding the candidate sampling points if the sub-nodes do not collide, and abandoning the sub-nodes if the sub-nodes collide.
Figure BDA0003136890120000121
In formula (8): q. q.snearestkIs the joint k angle, q, of the parent node of the random treekIs the joint k angle of the obtained sampling point.
And 7: and (4) calculating the potential energy of the candidate sampling point by using the formulas (9) to (13) according to the candidate sampling point obtained in the step 6.
Figure BDA0003136890120000122
Figure BDA0003136890120000123
Figure BDA0003136890120000124
Figure BDA0003136890120000125
U(j)＝Fgra(j)+Frepinter(gj)+Frepexter(j)+Freptree(gj) (13)
In formula (9): fgra(j) Is the gravitational potential energy of node j, λ is the gravitational proportionality coefficient, gjIs the end position of the arm at node j, gviaEnd position of the robot arm, g, which is the point of the viapointstartEnd position of the arm, g, which is the start pointgoalIs the end position of the arm at the goal point. In formula (10): frepinter(gj) Is the repulsive potential energy generated by the internal pose of the node j, epsilon is the repulsive proportionality coefficient, gjk1Is the position of the joint k of the node j of the robot arm 1, gjk2Is the position of the joint k of the joint j of the robot arm 2, drobIs the minimum distance between the two arms, dminIs the minimum collision distance, dinterIs an internal repulsive force boundary. In formula (11): frepexter(j) Is the repulsive potential energy between the node j and the outside, epsilon is the repulsive proportionality coefficient, gjkIs the mechanical arm position of node j, obs is the outer envelope center of the barrier, dobsIs the distance of the joint j from the obstacle, dminIs the minimum collision distance, dexterIs the boundary of the external repulsive force. In formula (12): freptree(gj) Is the repulsive potential energy generated between the node j and other random trees of the same mechanical arm, and epsilon isThe coefficient of proportionality of the repulsive force,
Figure BDA0003136890120000131
is a random tree m1The position of the joint k of the node j,
Figure BDA0003136890120000132
is a random tree m2Position of joint k of node j, dtreeIs the minimum distance between random trees, dminIs the minimum collision distance, dtreesIs the inter-tree repulsive force boundary. In formula (13): u (j) is the potential energy of node j, Fgra(j) Is the gravitational potential energy of node j, Frepinter(gj) Is the repulsive potential energy generated by the internal pose of the node j, Frepexter(j) Is the repulsive potential energy of the node j and the outside, Freptree(gj) Is the repulsive potential energy generated between the node j and other random trees of the same mechanical arm.
And 8: the sampling probability is modified according to equation (14), and the sampling step size is modified according to equation (15):
Figure BDA0003136890120000133
Figure BDA0003136890120000134
in formula (14): alpha and beta are step length adjusting coefficients, and d is the distance between the tail end of the mechanical arm and the envelope outside the obstacle. In formula (15): μ, σ is the probability adjustment coefficient, d is the distance between the end of the arm and the outer envelope of the obstacle.
And step 9: and repeating the sampling process until the number of the selected points reaches num after sampling.
Step 10: and (4) selecting a roulette according to the reciprocal of the potential energy U (j) to obtain a sampling point q _ new.
Step 11: when the random tree expansion encounters an obstacle, we use the sampling point q _ nearest (x)n,yn,zn) Is the center of sphere, with a radius r of 2 × step _ sizeeThe ball is made outwards,then, 8 nodes are sampled on the spherical surface at intervals of 90 degrees, and the coordinates of the nodes are obtained by equations (16) to (18). After 8 nodes are obtained, collision detection is carried out on each node obtained, all nodes which do not have collision with the obstacle are recorded, the distance from each node to a target point (a start point, a goal point or a viapoint) is calculated respectively, finally, a point which is free of collision and is closest to a fixed point is selected as a next expansion direction, and a step length is expanded forwards to a node q _ new. And repeating the process by taking q _ new as the sphere center until the random tree gets rid of the obstacles.
Figure BDA0003136890120000141
Figure BDA0003136890120000142
ze＝zn+recosθ(18)
Step 12: calculating the cost from each node to q _ new on the random tree according to the formulas (19) to (27), adding the point with the cost less than price into the reconnection point, calculating the cost of forming a path between the q _ new and each reconnection point, selecting the connection mode with the minimum cost, and determining the connection father node of the q _ new.
W(gj,gk)＝τaWa(aj,ak)+τqWq(qj,qk)+τTWT(Tj,Tk)+τEWE(Ej,Ek) (19)
Figure BDA0003136890120000143
Figure BDA0003136890120000144
Figure BDA0003136890120000145
Figure BDA0003136890120000146
Figure BDA0003136890120000147
Figure BDA0003136890120000148
Figure BDA0003136890120000149
Figure BDA00031368901200001410
In formula (19): w (g)j,gk) Is the total cost, Wa(aj,ak) Is the terminal acceleration penalty, Wq(qj,qk) Is the change cost of joint angle, WT(Tj,Tk) Is the end velocity penalty, WE(Ej,Ek) Is the energy consumption penalty and τ is the weight. In the formula (20), costaj,kIs the acceleration change cost from the jth node to the kth node,
Figure BDA00031368901200001411
is the acceleration change value from the jth node to the kth node. In the formula (22), costqj,kIs the joint angle cost, Δ q, from the jth node to the kth nodej,kIs the acceleration change value from the jth node to the kth node. In formula (24), costTj,kIs the cost of the change in velocity from the jth node to the kth node, Δ vj,kIs the speed change from the jth node to the kth node. In the formula (26), costEj,kIs the energy consumption penalty from the jth node to the kth node, c is the joint motor torque, kcIs the ratio coefficient of the torque and the current of the joint motor.
Step 13: removing the connection relation between the reconnection points, calculating the path cost required by all connection modes between the reconnection points, and selecting the connection mode with the lowest cost to re-establish the parent-child relation of the nodes;
step 14: and if the potential energy difference between the q _ new and the q _ good (or the q _ start or the q _ via) is less than h, replacing the q _ new with the q _ good (or the q _ start or the q _ via) to complete the random tree.
Step 15: and generating a planned path according to the determined parent-child node relationship.
Step 16: and (3) obtaining the external force and the external moment measured by the six-dimensional force sensor according to the formulas (28) and (29), and finely adjusting the motion process of the mechanical arm moving along the planned path according to the formulas (28) to (29).
Figure BDA0003136890120000151
Figure BDA0003136890120000152
Figure BDA0003136890120000153
Figure BDA0003136890120000154
In the formula (28), FeIs the external force applied by the six-dimensional force sensor, F is the force measured by the six-dimensional force sensor, F0Is the force zero value of the six-dimensional force sensor and G is the gravity component of the six-dimensional force sensor. In formula (29), MeIs the external moment to which the six-dimensional force sensor is subjected, M is the moment measured by the six-dimensional force sensor, M0Is the moment zero value of the six-dimensional force sensor, MgIs sixThe moment of gravity component of the force sensor. In the formula (30), Δ v is the linear velocity variable at the end of the mechanical arm, σ f is the sensitivity of the mechanical arm to the force-applied motion at the end, M is the end load mass of the mechanical arm, and f isTIs the external force measured by the six-dimensional force sensor. In the formula (31), Δ ω is the angular velocity variable of the end of the mechanical arm, σ m is the sensitivity of the end of the mechanical arm to moment motion, I is the moment inertia of the end of the mechanical arm, and m isTIs the external moment measured by the six-dimensional force sensor.
And step 17: the pin hole precision assembly of the double-arm robot is successful.
According to the invention, the six-dimensional force sensor is arranged at the tail end of the double-arm robot, so that the mechanical arm can be conveniently finely adjusted according to contact force and contact torque when moving according to a planned path, the pin holes can be precisely assembled, and the assembly precision is less than 0.1 mm; the method is based on the RRT algorithm, the passing points are introduced on the motion path of the mechanical arm, and four random trees are generated by starting from the starting point, the passing points and the target point at the same time in an expanding way, so that the exploration speed of the random trees on the state space is greatly accelerated; on the basis of ensuring the sampling randomness, the repulsive potential energy between random trees is added into the potential energy function to better guide the sampling of the random trees, and meanwhile, the acceleration cost is added into the method for reconnecting the random trees according to the cost, so that the motion path of the mechanical arm is smoother, the two points are innovated, the sampling quality of the random trees is improved, the connection mode between all nodes is optimized, and the high quality of the planned path is ensured; the invention adds a self-adaptive step length adjusting function and a self-adaptive sampling probability adjusting function, and the two functions respectively and self-adaptively adjust the step length and the sampling probability of the random tree under the condition that the space has obstacles and has no obstacles, thereby improving the expansion speed of the random tree; the invention introduces the improved RRT algorithm, ensures that the random tree can generate the optimal path when the random tree is explored in a three-dimensional space with obstacles, and simultaneously avoids the algorithm from falling into local optimization.
Although the present invention has been described with reference to the preferred embodiments, it is not intended to limit the present invention, and those skilled in the art can make variations and modifications of the present invention without departing from the spirit and scope of the present invention by using the methods and technical contents disclosed above.

Claims (10)

1. A precision assembly method of a double-arm robot based on a six-dimensional force sensor is characterized by comprising the following steps:
the method comprises the following steps: the robot controller reads the joint angles of the left mechanical arm and the right mechanical arm;
step two: establishing a kinematics model and a dynamics model of the double-mechanical-arm robot;
obtaining the Cartesian space pose of the left mechanical arm by applying a six-degree-of-freedom mechanical arm positive kinematics algorithm according to each joint angle of the left mechanical arm and the kinematics model and the dynamics model of the double-mechanical-arm robot in the step one;
obtaining the Cartesian space pose of the right mechanical arm by applying a six-degree-of-freedom mechanical arm positive kinematics algorithm according to each joint angle of the right mechanical arm in the step one and a kinematics model and a dynamics model of the double-mechanical-arm robot;
step three: obtaining a Cartesian space pose of the left arm tail end pin hole workpiece relative to a robot base coordinate through coordinate conversion according to the Cartesian space pose of the left arm in the second step;
obtaining a Cartesian space pose of the right arm tail end pin hole workpiece relative to the robot base coordinate through coordinate conversion according to the Cartesian space pose of the right arm in the second step;
step four: obtaining a left arm tail end pin hole and a right arm tail end pin hole planning path by using a random tree exploring method based on rapid potential energy;
step five: and controlling the smooth assembly of the left mechanical arm and the right mechanical arm by using a control method based on a learning variable impedance control system according to the planning paths of the pin holes at the tail ends of the left arm and the right arm in the fourth step.
2. The six-dimensional force sensor based two-arm robot precise assembly method according to claim 1, characterized in that: in step two, the kinematic model and the dynamic model of the double-arm robot are obtained by the following formulas:
Figure FDA0003136890110000011
Figure FDA0003136890110000012
Figure FDA0003136890110000021
Figure FDA0003136890110000022
Figure FDA0003136890110000023
Figure FDA0003136890110000024
wherein the content of the first and second substances,
Figure FDA0003136890110000025
is a coordinate transformation matrix of the joints i-1 and i of the double-mechanical-arm robot, c represents cos, s represents sin, thetai,αi-1,ai-1,diD-H parameters of a joint i of the double-mechanical-arm robot are respectively set;
Figure FDA0003136890110000026
is a conversion matrix from a left mechanical arm end pin workpiece to the left mechanical arm end, and m is from the left mechanical arm end pin workpiece to the left mechanical arm end pin workpieceDistance of the end of the left mechanical arm;
Figure FDA0003136890110000027
the transformation matrix is from a hole workpiece at the tail end of the right mechanical arm to the tail end of the right mechanical arm, and m is the distance from a pin workpiece at the tail end of the right mechanical arm to the tail end of the right mechanical arm;
Figure FDA0003136890110000028
a transformation matrix from a left mechanical arm tail end pin workpiece to a left mechanical base coordinate;
Figure FDA0003136890110000029
a transformation matrix from a workpiece at the tail end hole of the right mechanical arm to a base coordinate of the right mechanical arm; τ is the joint control moment, M (Θ) is the mass matrix of n × n of the robotic arm,
Figure FDA00031368901100000210
is the centrifugal force and the coriolis force vector of n x 1, G (Θ) is the gravity vector of n x 1, Θ is the mechanical arm joint position vector,
Figure FDA00031368901100000211
is the velocity vector of the joint of the mechanical arm,
Figure FDA00031368901100000212
is the acceleration vector of the mechanical arm joint.
3. The six-dimensional force sensor based two-arm robot precise assembly method according to claim 1, characterized in that: in the fourth step, the method for exploring the random tree based on the rapid potential energy comprises the following steps:
(41) setting initial parameters and carrying out initial sampling;
(42) calculating the distance between the tree node of the random tree and the sampling point according to the kinematic model and the dynamic model of the double-mechanical-arm robot and the initial parameters in the step (41), and finding the nearest tree node as a father node;
(43) obtaining an expansion child node according to the father node, judging whether the expansion child node collides, and adding a candidate sampling point if the expansion child node does not collide;
(44) calculating potential energy of the candidate sampling points;
(45) modifying the sampling step length and the sampling probability; repeating steps (42) - (44) until the candidate sampling point reaches num;
(46) carrying out roulette selection according to the reciprocal of the potential energy of the num candidate sampling points to obtain sampling points, and taking the sampling points as new sub-nodes;
(47) and (4) selecting the connection mode with the shortest cost to connect the new child node in the step (46) with the parent node, and determining the planning path of the pin hole at the tail end of the left arm and the pin hole at the tail end of the right arm.
4. The six-dimensional force sensor based two-arm robot precise assembly method according to claim 1, characterized in that: in step five, the control method based on the learning variable impedance control system comprises the following steps:
(51) acting a preset initialization control variable on a control system of the mechanical arm;
(52) establishing a Gaussian process dynamic model of the control system according to preset sampling data, and taking the Gaussian process dynamic model as a transformation dynamic model of the system;
(53) searching for an optimal impedance control strategy using a strategy learning algorithm based on the transformed dynamical model of the system in step (52);
(54) according to the optimal impedance control strategy, the method is applied to a variable impedance controller to control the force and acquire data;
(55) repeating steps (52) - (54) until a preset force tracking effect is obtained.
5. The six-dimensional force sensor based two-arm robot precise assembly method according to claim 3, characterized in that: in step (41), the initial parameters include: the method comprises the steps of starting pose left _ start of a left mechanical arm, target pose left _ goal, starting pose right _ start of a right mechanical arm, target pose right _ goal, initial path random tree, initial sampling step size, initial sampling probability, sampling upper limit _ limit, single candidate sampling point num, reconnection cost, collision distance and final position potential energy error h.
6. The six-dimensional force sensor based two-arm robot precise assembly method according to claim 5, characterized in that: in step (41), connecting a straight line between the target pose left _ goal of the left mechanical arm and the target pose right _ goal of the right mechanical arm, defining a point on the straight line, which is at a distance L from the left _ goal on the left side of the left _ goal, as left _ visual, and defining a point on the straight line, which is at a distance L from the right _ goal on the right side of the right _ goal, as right _ visual;
initializing and sampling from a left _ start point to a left _ view point of the left mechanical arm, from a left _ good point to a left _ view point of the left mechanical arm, from the left _ view point to the left _ start point of the left mechanical arm and from the left _ view point to the left _ good point of the left mechanical arm according to a sampling formula;
initializing sampling according to a sampling formula from the right _ start point to the right _ view point of the right arm, from the right _ goal point to the right _ view point of the right arm, from the right _ view point to the right _ start point of the right arm, and from the right _ view point to the right _ goal point of the right arm.
7. The six-dimensional force sensor based two-arm robot precise assembly method according to claim 6, characterized in that: the sampling formula is as follows:
Figure FDA0003136890110000041
wherein q issamkIs the sampling angle of the joint k, random is the randomly chosen joint angle, qkmaxIs the maximum angle of the joint k, qkminIs the minimum angle of joint k, probability is the sampling probability, qkgoalIs the angle of the joint k in the goal position.
8. The six-dimensional force sensor based two-arm robot precise assembly method according to claim 5, characterized in that: in step (43), the child node of the expansion obtained from the parent node is obtained by the following formula:
Figure FDA0003136890110000042
wherein q isnearestkIs the joint k angle, q, of the parent node of the random treekExpanding the joint k angle of the child node, step _ size being the initial sampling step size, qsamkIs the sampling angle of the joint k.
9. The six-dimensional force sensor based two-arm robot precise assembly method according to claim 5, characterized in that: in step (44), the potential energy of the candidate sampling point is obtained by the following formula:
Figure FDA0003136890110000043
Figure FDA0003136890110000051
Figure FDA0003136890110000052
Figure FDA0003136890110000053
U(j)＝Fgra(j)+Frepinter(gj)+Frepexter(j)+Freptree(gj)；
wherein, Fgra(j) Is the gravitational potential energy of node j, λ is the gravitational proportionality coefficient, gjIs the end position of the arm at node j, gviaEnd position of the robot arm, g, which is the point of the viapointstartIs staEnd position of the arm at rt, ggoalThe end position of the mechanical arm at the goal point; frepinter(gj) Is the repulsive potential energy generated by the internal pose of the node j, epsilon is the repulsive proportionality coefficient, gjk1Is the position of the joint k of the left arm node j, gjk2Is the position of the joint k of the right arm node j, drobIs the minimum distance between the two arms, dminIs the minimum collision distance, dinterIs an internal repulsive force boundary; frepexter(j) Is the repulsive potential energy between the node j and the outside, epsilon is the repulsive proportionality coefficient, gjkIs the mechanical arm position of node j, obs is the outer envelope center of the barrier, dobsIs the distance of the joint j from the obstacle, dminIs the minimum collision distance, dexterIs an external repulsive force boundary; freptree(gj) Is the repulsive force potential energy generated between the node j and other random trees of the same mechanical arm, epsilon is the repulsive force proportionality coefficient,
Figure FDA0003136890110000054
is a random tree m1The position of the joint k of the node j,
Figure FDA0003136890110000055
is a random tree m2Position of joint k of node j, dtreeIs the minimum distance between random trees, dminIs the minimum collision distance, dtreesIs an inter-tree repulsion boundary; u (j) is the potential energy of node j, Fgra(j) Is the gravitational potential energy of node j, Frepinter(gj) Is the repulsive potential energy generated by the internal pose of the node j, Frepexter(j) Is the repulsive potential energy of the node j and the outside, Freptree(gj) Is the repulsive potential energy generated between the node j and other random trees of the same mechanical arm.
10. The six-dimensional force sensor based two-arm robot precise assembly method according to claim 5, characterized in that: in the fourth step, the planned path is short in movement distance, short in assembly operation time, low in energy consumption of the mechanical arm and capable of avoiding interference.
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