CN110421547A - A kind of tow-armed robot collaboration impedance adjustment based on estimated driving force model - Google Patents

A kind of tow-armed robot collaboration impedance adjustment based on estimated driving force model Download PDF

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CN110421547A
CN110421547A CN201910630375.9A CN201910630375A CN110421547A CN 110421547 A CN110421547 A CN 110421547A CN 201910630375 A CN201910630375 A CN 201910630375A CN 110421547 A CN110421547 A CN 110421547A
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tow
armed robot
target object
control
arms
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CN110421547B (en
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徐德刚
李德昀
苏志芳
阳春华
桂卫华
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Central South University
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Central South University
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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
    • B25J9/1612—Programme controls characterised by the hand, wrist, grip 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
    • 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
    • B25J9/1679—Programme controls characterised by the tasks executed
    • B25J9/1682—Dual arm manipulator; Coordination of several manipulators

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  • Engineering & Computer Science (AREA)
  • Robotics (AREA)
  • Mechanical Engineering (AREA)
  • Health & Medical Sciences (AREA)
  • General Health & Medical Sciences (AREA)
  • Orthopedic Medicine & Surgery (AREA)
  • Manipulator (AREA)

Abstract

The present invention discloses a kind of tow-armed robot collaboration impedance adjustment based on estimated driving force model.Desired trajectory first according to target object in cartesian space, Robot Dual-Arm end cartesian space desired trajectory is calculated, then the practical contact force that measurement obtains the end of two mechanical arms and target object generates, practical contact force and expectation contact are made every effort into deviation, then desired trajectory is modified.Then tow-armed robot joint angles track is calculated.It feeds back to obtain the estimated driving force model of tow-armed robot, and thus obtains the control moment in each joint of tow-armed robot by time delay estimation, desired speed feedback, desired locations, the movement that control tow-armed robot is completed.Kinematics and dynamics coordination in tow-armed robot and external environment interactive process may be implemented in the present invention, can quickly generate control moment by estimated driving force model, can be applied in the motion control of tow-armed robot work compound.

Description

A kind of tow-armed robot collaboration impedance adjustment based on estimated driving force model
Technical field
The present invention relates to a kind of robot control field, in particular to a kind of both arms machine based on estimated driving force model People cooperates with impedance adjustment.
Background technique
Tow-armed robot can complete the assembly movement more increasingly complex than traditional one armed robot, therefore tow-armed robot is assisted Control strategy and power, Torque Control is adjusted at home and abroad to obtain extensive research.However, two mechanical arms of control and target work Interaction between part, more difficult than control separate unit mechanical arm: the coordinative operation of both arms will not only consider both arms end Between kinematics coordinate, while be accounted for the dynamics between both arms and target workpiece coordination: kinematics coordination refer to Both arms end should move synchronously and meet always pose the constraint relationship, so that spacing and phase that tow-armed robot end is kept constant The task of carrying target object is completed to posture；Dynamics coordination must during referring to both arms end by desired trajectory movement Suitable contact force must be remained to meet collaborative task demand, guaranteeing will not be inadequate because of contact force during carrying Cause target object to slide from mechanical arm tail end greatly, or target object deformation damage will not be led to because of by excessive pressure It is bad.
In order to solve the above problem, common method has by power prosecutor method, power/Position Hybrid Control method, impedance control Method and power control end effector technology etc..For the apery characteristic for further increasing mechanical arm, the control of impedance controller is improved Effect processed becomes domestic and international by the impedance control based on kinetic model of inner ring, impedance control as outer ring of Torque Control Research hotspot.To obtain mechanical arm Torque Control amount, it is necessary to calculate its kinetic model, however, due to having more High freedom degree and more specifically application background, tow-armed robot kinetic model are difficult to realize calculate in real time.
Summary of the invention
Since manipulator model is a highly dynamic, coupling and has probabilistic nonlinear system, at two six Accurate dynamics calculation is carried out in the two arm robot system of degree-of-freedom manipulator composition, it is clear that a large amount of resource can be expended, And it is difficult to ensure the real-time of both arms impedance control.The present invention is aiming at the problem that both arms kinetic model real-time resolving, abundant On the basis of the dynamics constraint condition for understanding tow-armed robot clamping and carrying rigid body, propose that one kind can be to tow-armed robot The algorithm that kinetic model is quickly estimated, and applied in impedance control inner ring, and then realize and be based on kinetic simulation The tow-armed robot of type cooperates with impedance control, is finally reached the purpose that target object is carried using tow-armed robot.
In order to achieve the above technical purposes, the technical scheme is that,
A kind of tow-armed robot collaboration impedance adjustment based on estimated driving force model, comprising the following steps:
S1: according to the target object of tow-armed robot grasping in the expectation motion track of cartesian space, pass through both arms machine Device people's kinematics is coordinated to calculate, and obtains grabbing two mechanical arm tail end respective cartesian spaces when the object moves in space Desired trajectory；
S2: setting one will not only allow target object to slide, but also not will lead to target object and press from both sides bad both arms grasping target The expectation contact force of object, then the practical contact force between collection machinery arm and target object and with expectation contact make every effort to deviation Deviation is input in tow-armed robot collaboration impedance controller, repairs to the step S1 desired trajectory being calculated by value Just；
S3: mechanical arm inverse kinematics is utilized, revised both arms end cartesian space track is converted into both arms machine The angular region track in each joint of people finds out the angular acceleration control amount in each joint of tow-armed robot；
S4: anti-using time delay estimation, desired speed by each joint operating status of tow-armed robot last moment Feedback, desired locations feedback set up tow-armed robot estimated driving force model, and the angular region track that step S3 is obtained is converted to Each joint control torque signals, and input in robot servo controller, realize the operation of tow-armed robot Collaborative Control.
A kind of described tow-armed robot based on estimated driving force model cooperates with impedance adjustment, in the step S1 Tow-armed robot kinematics coordinates the method calculated are as follows:
S101: establishing coordinate system first for target object and tow-armed robot, the target object grasped with tow-armed robot When completing mobile, mechanical arm tail end is remained unchanged with target object relative position, and taking target object geometric center point is that origin is Establish coordinate system { OL, ifIt is position auto―control track of the target object relative to world coordinate system { O }, if target object size For L, coordinate system { O is established respectively in the end of two mechanical armsAAnd { OB, if { OLPosture and { O } it is identical, { OAOrigin In { OLAt the position-L/2 in coordinate system y-axis, posture is { OLRotated with the right-hand rule around itself negative direction of the x-axis{OBFormer Point is in { OLCoordinate system y-axis the position L/2 at, posture be { OLRotated with the right-hand rule around positive direction of the x-axisUse RnIndicate arrow Amount is n n dimensional vector n, uses Rn×nRepresenting matrix is that n × n ties up matrix；
S102: the coordinate system established by step S101 moves in cartesian space according to the central point of target object Desired trajectoryAnd the size L of target object, tow-armed robot is acquired using coordinate transformation method, and target is grabbed with the pose Pose of the ending coordinates system of two mechanical arms relative to target object center point coordinate system when object:
Wherein,Expression is rotated with the right-hand rule around negative direction of the x-axisSpin matrix,Expression is rotated with the right-hand rule around positive direction of the x-axisSpin matrix,It is respectively mechanical The end of arm A and mechanical arm B are relative to target object coordinate system { OLPosition auto―control；
S103: resulting by step S101WithUtilize coordinate transform operationAndObtain cartesian space track of two mechanical arm tail ends relative to world coordinate system { O }WithWherein,Indicate target object coordinate system { OLEnding coordinates system { O relative to mechanical arm A and mechanical arm BAAnd {OBPosition auto―control, it is rightMatrix inversion can be obtained.
A kind of tow-armed robot based on estimated driving force model cooperates with impedance adjustment, the step S2 In, it is expected that contact force is set according to practical engineering experience, both arms using desired contact force come when clamping target object, Not only target object will not be caused to slide from both arms end because of contact force is too small, but also physical damage will not be led to because excessive.
A kind of tow-armed robot based on estimated driving force model cooperates with impedance adjustment, the step S2 In, the practical contact force is acquired by being installed on six degree of freedom power/torque sensor of tow-armed robot end.
The tow-armed robot based on estimated driving force model cooperates with impedance adjustment, both arms in the step S2 The building method of robot collaboration impedance controller are as follows:
S201: rodrigues formula is utilized, first by the end desired trajectory of two obtained mechanical arms of step S1 Homogeneous position auto―control indicatesBe converted to desired trajectory pose vector representation modeR6Indicate that vector is 6 N dimensional vector n, whereinIt is converted to
Wherein, RotA∈R3×3It is the terminal angle spin matrix for describing mechanical arm A, PA∈R3It is the end for describing mechanical arm A The position vector of end position, rA∈R3It is that the rotating vector that Douglas Rodríguez converts, α are passed through by spin matrixA,βA,γAIt is Rotating vector rAThree elements；Similarly,It is converted toProcess it is as follows:
S202: willWithGroup is combined intoSimilarly, the respective reality of both arms S2 measured Border contact force group is combined intoIt is expected that contact force is set asBy Xd,Fd, FeIt is updated in impedance control formula, the formula that tow-armed robot collaboration impedance control can be obtained cooperates with impedance controller:
Wherein, Md∈R12×12For inertial matrix, Bd∈R12×12For damping matrix, Kd∈R12×12For stiffness matrix,The respectively displacement of the desired trajectory of both arms end effector, speed and acceleration,Respectively by the revised displacement of impedance controller, velocity and acceleration vector.
A kind of tow-armed robot based on estimated driving force model cooperates with impedance adjustment, the step S2 In, desired trajectory is modified the following steps are included:
S203: each joint driven torque and the acceleration of mechanical arm tail end cartesian trajectories have when due to manipulator motion It closes, for the control moment for acquiring driving robot motion, need to first acquire the acceleration of desired trajectory, meet expectation contact to acquire The revised path acceleration of power obtains the impedance control formula phase shift in step S202:
It is by the path acceleration control amount of the revised tow-armed robot end cartesian space of impedance controller.
The tow-armed robot based on estimated driving force model cooperates with impedance adjustment, machinery in the step S3 Arm the computation of inverse- kinematics method are as follows:
S301: the Jacobian matrix of tow-armed robot is acquired first, it may be assumed that J=diag (JA,JB)∈R12×12, wherein JA,JB ∈R6×6The respectively Jacobian matrix of the Jacobian matrix of mechanical arm A and mechanical arm B, J ∈ R12×12It is each by two mechanical arms From the collaboration Jacobian matrix of tow-armed robot that obtains by combination of Jacobian matrix；
S302: by formulaBoth sides derivation is obtainedI.e.Wherein,It is the angular speed of 12 joint motions of tow-armed robot,It is the angle acceleration of 12 joint motions of tow-armed robot Degree；
S303: step S203 is acquiredIt substitutes into the formula that S302 is pushed away, obtains the revised both arms of impedance control Each joint angle Acceleration Control amount
The described tow-armed robot based on estimated driving force model cooperates with impedance adjustment, by estimating in the step S4 The method that control moment is calculated in meter kinetic model are as follows:
S401: step S303 is obtainedIntegral, obtains revised both arms angular speed control amountBy itself and this Moment actual magnitude of angular velocityMake difference and multiplied by gain coefficient Γv∈R12×12Desired speed feedback value is arrived to obtain the final product, it may be assumed that
S402: step S401 is obtainedIntegral, obtains revised both arms angle control amount qideal, by itself and this Moment actual angle value qrealMake difference and multiplied by gain coefficient Γp∈R12×12Obtain desired locations value of feedbackThat is:
S403: the sampling period of system is set as L, to current time t, records each joint control when a sampling instant Torque τ(t-L)And each joint actual angular acceleration under the control momentIt obtains combining desired speed feedback and phase Hope the both arms dynamics time delay estimation model of position feedback are as follows:
Wherein,
Thus the value of the control moment τ of tow-armed robot is acquired.
The technical effects of the invention are that the present invention fully considers compared with existing robot dynamics' control strategy The composition of tow-armed robot kinetic model and linear, nonlinear characteristic of each section, by time delay estimation to dynamic Linear segment in mechanical model is estimated, and is fed back by desired speed feedback, desired locations to kinetic model residue Non-linear partial compensate, and then obtain the control moment in each joint, and dynamics Controlling is built as the double of inner ring using this Arm cooperates with impedance controller.This method had both realized position and the contact force control that tow-armed robot carries target object process System, and the quick estimation of Manipulator Dynamic and quickly generating for control moment may be implemented, improve tow-armed robot The operation efficiency of control.
Detailed description of the invention
Fig. 1 is the flow diagram of tow-armed robot control method of the present invention.
Fig. 2 is that the MATLAB of two arm robot system described in the specific embodiment of the invention models schematic diagram.
Fig. 3 is both arms space structure and coordinate system schematic diagram.
In Fig. 4, (a) is that target object it is expected that motion track and actual path track effect diagram in xoz plane；(b) For the desired trajectory and actual path schematic diagram of the clamping of both arms end and carrying target object task in three-dimensional system of coordinate.
Fig. 5 is that desired contact force setting value and both arms cooperate with practical contact force tracking effect schematic diagram under impedance control.
Specific embodiment
Combined with specific embodiments below, and referring to attached drawing, invention is further described in detail.
Referring to figure 1, with the attached tow-armed robot system shown in Fig. 2 being made of two six degree of freedom KUKA mechanical arms For system, the tow-armed robot collaboration impedance adjustment described in this example based on estimated driving force model includes following step It is rapid:
S1: a cartesian space circle moving rail as shown in dotted line blue in attached drawing 4 (a) is designed for target object Mark.By target object in the expectation motion track of cartesian space, coordinates to calculate by tow-armed robot kinematics, be grabbed Two mechanical arm tail ends respective cartesian space desired trajectory when the object moves in space.Wherein, if two in space Mechanical arm is respectively mechanical arm A and mechanical arm B, and such as attached drawing 3, then tow-armed robot kinematics coordinates the specific steps calculated such as Under:
S101: establishing coordinate system first for target object and tow-armed robot, the target object grasped with tow-armed robot When completing mobile, mechanical arm tail end is remained unchanged with target object relative position, and taking target object geometric center point is that origin is Establish coordinate system { OL, ifIt is position auto―control track of the target object relative to world coordinate system { O }, if target object size For L, coordinate system { O is established respectively in the end of two mechanical armsAAnd { OB, such as attached drawing 3.If { OLPosture and { O } it is identical, {OAOrigin is in { OLAt the position-L/2 in coordinate system y-axis, posture is { OLRotated with the right-hand rule around itself negative direction of the x-axis{OBOrigin is in { OLCoordinate system y-axis the position L/2 at, posture be { OLRotated with the right-hand rule around positive direction of the x-axisWith RnExpression vector is n n dimensional vector n, uses Rn×nRepresenting matrix is that n × n ties up matrix；
S102: the coordinate system established by step S101 moves in cartesian space according to the central point of target object Desired trajectoryAnd the size L of target object, tow-armed robot is acquired using coordinate transformation method, and target is grabbed with the pose Pose of the ending coordinates system of two mechanical arms relative to target object center point coordinate system when object:
Wherein,Expression is rotated with the right-hand rule around negative direction of the x-axisSpin matrix,Expression is rotated with the right-hand rule around positive direction of the x-axisSpin matrix,It is respectively mechanical The end of arm A and mechanical arm B are relative to target object coordinate system { OLPosition auto―control；
S103: resulting by step S101WithUtilize coordinate transform operationAndObtain cartesian space track of two mechanical arm tail ends relative to world coordinate system { O }WithWherein,Indicate target object coordinate system { OLEnding coordinates system { O relative to mechanical arm A and mechanical arm BAAnd {OBPosition auto―control, it is rightMatrix inversion can be obtained.
S2: setting one will not only allow target object to slide, but also not will lead to target object and press from both sides bad both arms grasping target The expectation contact force of object, as shown in dotted line blue in attached drawing 5, then practical between collection machinery arm and target object is contacted Power simultaneously contact with expectation and makes every effort to deviation, deviation is input in tow-armed robot collaboration impedance controller, to step S1 meter Obtained desired trajectory is modified.Wherein, it is expected that contact force is set according to practical engineering experience, both arms are used It is expected that contact force come when clamping target object, not only will not cause target object to slide from both arms end because of contact force is too small, but also It will not lead to physical damage because excessive；The practical contact force is the six degree of freedom by being installed on tow-armed robot end Power/torque sensor acquires.Wherein, tow-armed robot collaboration impedance controller builds that steps are as follows:
S201: rodrigues formula is utilized, first by the end desired trajectory of two obtained mechanical arms of step S1 Homogeneous position auto―control indicatesBe converted to desired trajectory pose vector representation modeR6Indicate that vector is 6 N dimensional vector n, whereinIt is converted to
Wherein, RotA∈R3×3It is the terminal angle spin matrix for describing mechanical arm A, PA∈R3It is the end for describing mechanical arm A The position vector of end position, rA∈R3It is that the rotating vector that Douglas Rodríguez converts, α are passed through by spin matrixA,βA,γAIt is Rotating vector rAThree elements；Similarly,It is converted toProcess it is as follows:
S202: willWithGroup is combined intoSimilarly, the respective reality of both arms S2 measured Border contact force group is combined intoIt is expected that contact force is set asBy Xd,Fd, FeIt is updated in impedance control formula, the formula that tow-armed robot collaboration impedance control can be obtained cooperates with impedance controller:
Wherein, Md∈R12×12For inertial matrix, Bd∈R12×12For damping matrix, Kd∈R12×12For stiffness matrix,The respectively displacement of the desired trajectory of both arms end effector, speed and acceleration,Respectively by the revised displacement of impedance controller, velocity and acceleration vector.
In the step S2, desired trajectory is modified the following steps are included:
S203: each joint driven torque and the acceleration of mechanical arm tail end cartesian trajectories have when due to manipulator motion It closes, for the control moment for acquiring driving robot motion, need to first acquire the acceleration of desired trajectory, meet expectation contact to acquire The revised path acceleration of power obtains the impedance control formula phase shift in step S202:
It is by the path acceleration control amount of the revised tow-armed robot end cartesian space of impedance controller.
S3: mechanical arm inverse kinematics is utilized, revised both arms end cartesian space track is converted into both arms machine The angular region track in each joint of people.Wherein, mechanical arm the computation of inverse- kinematics method is as follows:
S301: the Jacobian matrix of tow-armed robot is acquired first, it may be assumed that J=diag (JA,JB)∈R12×12, wherein JA,JB ∈R6×6The respectively Jacobian matrix of the Jacobian matrix of mechanical arm A and mechanical arm B, J ∈ R12×12It is each by two mechanical arms From the collaboration Jacobian matrix of tow-armed robot that obtains by combination of Jacobian matrix；
S302: by formulaBoth sides derivation is obtainedI.e.Wherein,It is the angular speed of 12 joint motions of tow-armed robot,It is the angle acceleration of 12 joint motions of tow-armed robot Degree；
S303: step S203 is acquiredIt substitutes into the formula that S302 is pushed away, obtains the revised both arms of impedance control Each joint angle Acceleration Control amount
S4: anti-using time delay estimation, desired speed by each joint operating status of tow-armed robot last moment Feedback, desired locations feedback set up tow-armed robot estimated driving force model, and the angular region track that step S3 is obtained is converted to The moment each joint control torque signals, and input in robot servo controller, realize the operation of tow-armed robot Collaborative Control. Wherein, the step of control moment being calculated by estimated driving force model is as follows:
S401: step S303 is obtainedIntegral, obtains revised both arms angular speed control amountBy itself and this Moment actual magnitude of angular velocityMake difference and multiplied by gain coefficient Γv∈R12×12Desired speed feedback value is arrived to obtain the final product, it may be assumed that
S402: step S401 is obtainedIntegral, obtains revised both arms angle control amount qideal, by itself and this Moment actual angle value qrealMake difference and multiplied by gain coefficient Γp∈R12×12Obtain desired locations value of feedbackThat is:
S403: the sampling period of system is set as L, to current time t, records each joint control when a sampling instant Torque τ(t-L)And each joint actual angular acceleration under the control momentIt obtains combining desired speed feedback and expectation The both arms dynamics time delay estimation model of position feedback are as follows:
Wherein,
Thus the value of the control moment τ of tow-armed robot can be acquired.Under the control of this control moment, tow-armed robot Shown in the Actual Control Effect of Strong of position tracking such as attached drawing 4 (a) (b), the control effect of force tracking is as shown in Fig. 5.
So far, it has been combined and describes technical solution of the present invention shown in attached drawing.In this example, first by Dual-Arm Coordination Kinematic calculation obtains the respective end orbit of both arms, and obtains practical contact force information by force snesor, later using double Arm collaboration impedance control, which is modified desired trajectory, makes it meet contact force request, finally, utilizing time delay estimation algorithm The tow-armed robot kinetic model of estimation is constituted in conjunction with desired speed feedback, desired locations feedback, and thus estimates both arms machine Device people reaches the control moment that expected pose should export.

Claims (8)

1. a kind of tow-armed robot based on estimated driving force model cooperates with impedance adjustment, which is characterized in that including following Step:
S1: according to the target object of tow-armed robot grasping in the expectation motion track of cartesian space, pass through tow-armed robot Kinematics is coordinated to calculate, and obtains the phase for grabbing two mechanical arm tail end respective cartesian spaces when the object moves in space Hope track；
S2: setting one will not only allow target object to slide, but also not will lead to target object and press from both sides bad both arms grasping target object Expectation contact force, then the practical contact force between collection machinery arm and target object and contact with expectation and make every effort to deviation, Deviation is input in tow-armed robot collaboration impedance controller, the step S1 desired trajectory being calculated is modified；
S3: mechanical arm inverse kinematics is utilized, it is each that revised both arms end cartesian space track is converted into tow-armed robot The angular region track in a joint finds out the angular acceleration control amount in each joint of tow-armed robot；
S4: by each joint operating status of tow-armed robot last moment, time delay estimation, desired speed feedback, phase are utilized It hopes position feedback set up tow-armed robot estimated driving force model, the angular region track that step S3 is obtained is converted into each joint Control moment signal, and input in robot servo controller, realize the operation of tow-armed robot Collaborative Control.
2. a kind of tow-armed robot based on estimated driving force model according to claim 1 cooperates with impedance control side Method, which is characterized in that tow-armed robot kinematics coordinates the method calculated in the step S1 are as follows:
S101: establishing coordinate system first for target object and tow-armed robot, is completed with the target object of tow-armed robot grasping When mobile, mechanical arm tail end is remained unchanged with target object relative position, and it is foundation that take target object geometric center point, which be origin, Coordinate system { OL, ifPosition auto―control track of the target object relative to world coordinate system { O }, if target object having a size of L, Coordinate system { O is established respectively in the end of two mechanical armsAAnd { OB, if { OLPosture and { O } it is identical, { OAOrigin is in { OL} At the position-L/2 in coordinate system y-axis, posture is { OLRotated with the right-hand rule around itself negative direction of the x-axis{OBOrigin exists {OLCoordinate system y-axis the position L/2 at, posture be { OLRotated with the right-hand rule around positive direction of the x-axisUse RnExpression vector is n N dimensional vector n uses Rn×nRepresenting matrix is that n × n ties up matrix；
S102: the coordinate system established by step S101, the expectation moved in cartesian space according to the central point of target object TrackAnd the size L of target object, tow-armed robot is acquired using coordinate transformation method, and target object is grabbed with the pose When two mechanical arms pose of the ending coordinates system relative to target object center point coordinate system:
Wherein,Expression is rotated with the right-hand rule around negative direction of the x-axisSpin matrix,Expression is rotated with the right-hand rule around positive direction of the x-axisSpin matrix,It is respectively mechanical The end of arm A and mechanical arm B are relative to target object coordinate system { OLPosition auto―control；
S103: resulting by step S101WithUtilize coordinate transform operationAndObtain cartesian space track of two mechanical arm tail ends relative to world coordinate system { O }WithWherein,Indicate target object coordinate system { OLEnding coordinates system { O relative to mechanical arm A and mechanical arm BAAnd {OBPosition auto―control, it is rightMatrix inversion can be obtained.
3. a kind of tow-armed robot based on estimated driving force model according to claim 1 cooperates with impedance control side Method, which is characterized in that in the step S2, it is expected that contact force is set according to practical engineering experience, both arms are used It is expected that contact force come when clamping target object, not only will not cause target object to slide from both arms end because of contact force is too small, but also It will not lead to physical damage because excessive.
4. a kind of tow-armed robot based on estimated driving force model according to claim 1 cooperates with impedance control side Method, which is characterized in that in the step S2, the practical contact force is by being installed on the six of tow-armed robot end certainly It is acquired by degree power/torque sensor.
5. the tow-armed robot according to claim 1 based on estimated driving force model cooperates with impedance adjustment, It is characterized in that, the building method of tow-armed robot collaboration impedance controller in the step S2 are as follows:
S201: rodrigues formula is utilized, first by the homogeneous of the end desired trajectory of two obtained mechanical arms of step S1 Position auto―control indicatesBe converted to desired trajectory pose vector representation modeR6Indicate that vector is 6 dimension arrows Amount, whereinIt is converted to
Wherein, RotA∈R3×3It is the terminal angle spin matrix for describing mechanical arm A, PA∈R3It is the end position for describing mechanical arm A The position vector set, rA∈R3It is that the rotating vector that Douglas Rodríguez converts, α are passed through by spin matrixA,βA,γAIt is rotation Vector rAThree elements；Similarly,It is converted toProcess it is as follows:
S202: willWithGroup is combined intoSimilarly, the respective practical contact of both arms S2 measured Power group is combined intoIt is expected that contact force is set asBy Xd,Fd,FeIt substitutes into Into impedance control formula, the formula that tow-armed robot collaboration impedance control can be obtained cooperates with impedance controller:
Wherein, Md∈R12×12For inertial matrix, Bd∈R12×12For damping matrix, Kd∈R12×12For stiffness matrix,The respectively displacement of the desired trajectory of both arms end effector, speed and acceleration,Respectively by the revised displacement of impedance controller, velocity and acceleration vector.
6. a kind of tow-armed robot based on estimated driving force model according to claim 5 cooperates with impedance control side Method, which is characterized in that in the step S2, desired trajectory is modified the following steps are included:
S203: each joint driven torque is related with the acceleration of mechanical arm tail end cartesian trajectories when due to manipulator motion, is The control moment for acquiring driving robot motion, need to first acquire the acceleration of desired trajectory, meet desired contact force to acquire Revised path acceleration obtains the impedance control formula phase shift in step S202:
It is by the path acceleration control amount of the revised tow-armed robot end cartesian space of impedance controller.
7. the tow-armed robot according to claim 6 based on estimated driving force model cooperates with impedance adjustment, It is characterized in that, mechanical arm the computation of inverse- kinematics method in the step S3 are as follows:
S301: the Jacobian matrix of tow-armed robot is acquired first, it may be assumed that J=diag (JA,JB)∈R12×12, wherein JA,JB∈R6 ×6The respectively Jacobian matrix of the Jacobian matrix of mechanical arm A and mechanical arm B, J ∈ R12×12It is respective by two mechanical arms The collaboration Jacobian matrix for the tow-armed robot that Jacobian matrix is obtained by combination；
S302: by formulaBoth sides derivation is obtainedI.e.Wherein,It is The angular speed of 12 joint motions of tow-armed robot,It is the angular acceleration of 12 joint motions of tow-armed robot；
S303: step S203 is acquiredIt substitutes into the formula that S302 is pushed away, obtains the revised both arms of impedance control and respectively close Save angular acceleration control amount
8. the tow-armed robot according to claim 1 based on estimated driving force model cooperates with impedance adjustment, It is characterized in that, the method that control moment is calculated by estimated driving force model in the step S4 are as follows:
S401: step S303 is obtainedIntegral, obtains revised both arms angular speed control amountBy itself and the moment Actual magnitude of angular velocityMake difference and multiplied by gain coefficient Γv∈R12×12Desired speed feedback value is arrived to obtain the final product, it may be assumed that
S402: step S401 is obtainedIntegral, obtains revised both arms angle control amount qideal, by itself and the moment Actual angle value qrealMake difference and multiplied by gain coefficient Γp∈R12×12Obtain desired locations value of feedbackThat is:
S403: the sampling period of system is set as L, to current time t, records each joint control torque when a sampling instant τ(t-L)And each joint actual angular acceleration under the control momentIt obtains combining desired speed feedback and desired locations The both arms dynamics time delay estimation model of feedback are as follows:
Wherein,
Thus the value of the control moment τ of tow-armed robot is acquired.
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