CN108326857A - Calligraphy based on Robust Adaptive Control algorithm and Sculpture robot control method - Google Patents

Calligraphy based on Robust Adaptive Control algorithm and Sculpture robot control method Download PDF

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CN108326857A
CN108326857A CN201810228368.1A CN201810228368A CN108326857A CN 108326857 A CN108326857 A CN 108326857A CN 201810228368 A CN201810228368 A CN 201810228368A CN 108326857 A CN108326857 A CN 108326857A
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robot
joint
error
controller
calligraphy
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CN108326857B (en
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刘秀兰
宋永端
张天凤
赖俊峰
李书浩
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Chongqing Yingdi Industrial Group Co ltd
DIBI Chongqing Intelligent Technology Research Institute Co Ltd
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Di Bi (chongqing) Intelligent Technology Research Institute Co Ltd
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    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J9/00—Programme-controlled manipulators
    • B25J9/16—Programme controls
    • B25J9/1602—Programme controls characterised by the control system, structure, architecture
    • B25J9/1607—Calculation of inertia, jacobian matrixes and inverses
    • 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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  • Engineering & Computer Science (AREA)
  • Physics & Mathematics (AREA)
  • Mathematical Physics (AREA)
  • Automation & Control Theory (AREA)
  • Robotics (AREA)
  • Mechanical Engineering (AREA)
  • Feedback Control In General (AREA)

Abstract

The invention discloses a kind of calligraphy based on Robust Adaptive Control algorithm and Sculpture robot control methods, including：Step 1：The kinetic model for establishing Three Degree Of Freedom calligraphy and Sculpture robot estimates moment of inertia term H, centripetal force and coriolis force square item C, the gravitational moment item G in each joint according to kinetics equation, finally obtains the torque estimation formula in each joint, step 2：Design Robust adaptive controller；Step 3：The calculated instructions of controller U are sent to the joint actuator of Three Degree Of Freedom calligraphy and Sculpture robot, the ideal track of control robot output tracking.The present invention is based on the calligraphy of Robust Adaptive Control algorithm and Sculpture robot control methods, it can be in the case where having unknown actuator failures and with unknown external interference, ensure the output tracking ideal trajectory of robot, tracking error can rapidly converge in ideal range, control accuracy is high, and can guarantee the mapping of the arbitrary error of robot.

Description

Calligraphy based on Robust Adaptive Control algorithm and Sculpture robot control method
Technical field
The present invention relates to industrial robot control technology field, more particularly to the controlling party of a kind of calligraphy and Sculpture robot Method.
Background technology
Calligraphy and Sculpture robot are not only widely used in popularization exhibitions, in industrial circle and take the course of its own.In order to carry High calligraphy sculpture robot manipulating task ability and application range, the requirement to its control accuracy is higher and higher, needs calligraphy, engraving machine Device people's controller has very high tracking trajectory capacity.
Since microscopic carvings robot is MIMO nonlinear systems, belongs to incomplete property motion control scope, have Close coupling, time-varying and nonlinear kinetic characteristics.Trajectory Tracking Control is an important content in industrial robot control. Robotic tracking control refers to the driving moment by giving each joint, makes the state variables such as position, the speed of robot The given ideal trajectory of tracking is required for strictly controlling for entire track.Therefore, Trajectory Tracking Control is very multiple It is miscellaneous with it is difficult, but be also the control mode that is most widely used in industrial production.It studies robotic tracking control and carries The precision of high Trajectory Tracking Control has great significance to robot technology.
The controller for being now widely used for industrial robot is conventional PID controllers, when encountering unknown actuator failures When, working hour can be delayed or cause safety accident, and traditional PID control can not also ensure mapping.(Prescribed Performance Bound, PPB) technology refers to that tracking error in transient process converges to preset a small range, together When convergence rate be not less than a preset value, maximum overshoot is less than a small constant of setting, therefore the technology energy Enough ensure the mapping of system, but to meet initial error within the scope of assigned error using the algorithm, it cannot be guaranteed that appointing The mapping for error of anticipating.There is document to propose using monitoring controller convergence error to given range, then enables PPB controls and calculate Method ensures the mapping of entire error range, but does not do any processing in two controller switching parts, can not Ensure the continuity and stability of controller during entirely controlling.It is not only more demanding in microscopic carvings robot field Mapping also requires the robustness for having to unknown external disturbance and unexpected actuator failures.
Invention content
In view of this, the object of the present invention is to provide a kind of calligraphy and engraving machine based on Robust Adaptive Control algorithm People's control method, to ensure the robot control accuracy in the case where having unknown actuator failures and with unknown external interference And mapping.
The present invention is based on the calligraphy of Robust Adaptive Control algorithm and Sculpture robot control methods, include the following steps：
Step 1：The kinetic model for establishing Three Degree Of Freedom calligraphy and Sculpture robot estimates each pass according to kinetics equation The moment of inertia term H of section, centripetal force and coriolis force square item C, gravitational moment item G finally obtain the torque estimation formula in each joint：
Wherein
G2=m1l1c2+m2l1c2+m2l2c23, G3=m2l2c23,
FfriIt is the static state or dynamic friction of robot, FdisIt is the external disturbance of robot system；q1It is robot The rotational angle in pedestal joint, q2It is the rotational angle in robot's arm joint, q3It is the rotational angle in robot forearm joint；
In above formula, ci=cos (qi),cij=cos (qi+qj),si=sin (qi),sij=sin (qi+qj), liIt is robot The length of i-th joint shaft, miIt is the quality of the i-th joint shaft of robot, IiFor the rotary inertia of the i-th joint shaft of robot, i=1, 2,3, i correspond to the pedestal joint shaft of robot when being 1, i corresponds to the large-arm joint axis of robot when being 2, i corresponds to machine when being 3 The forearm joint shaft of people；qiThe value of middle i is 1,2,3, qjThe value of middle j is 1,2,3；T is time variable；
U in formulaaTorque is actually entered for motor, due to that there may be unexpected actuator failures in model, is set The input signal U and motor of the controller of meter actually enter torque UaIt is no longer identical, but there are following relationships：Ua=ρ U +Up, wherein：ρ is health factor, and value range is：0<ρ<1；UpIt is the uncontrollable part controlled in signal, Ke Yiwei Arbitrary bounded function；Therefore in actuator failures, the mathematical model of controller is：
Step 2：Design Robust adaptive controller, tracking error e=q-q*,
When error is more than PPB sphere of actions, that is, t>taWhen, taIt is equal to the time point of given range, designing supervision control for error Device processed will be in error attenuated to PPB sphere of actions；Introduce median errorWherein λ1>0, constant λ1Value by setting Meter person is given；ControllerAdaptive lawWherein,Constant k1>0, μ1>0, the value of the two It is given by designer；
When error is less than PPB sphere of actions, that is, t<taWhen, the robust adaptive fault-tolerant controller based on PPB is designed, is ensured The mapping of system, i.e.,Wherein,νWithGiven coboundary and lower boundary, f=[f are indicated respectively (0)-f(∞)]e-ιtIt is given performance function, defines ei=f Γ (ξi),It is Strictly increasing function, whereinTherefore ξ can be indicated by e, ξ=[ξ1,ξ2,ξ3]T, Introduce median error In formula, r=diag { r1,r2,r3, m=diag { m1,m2,m3},λ2>0, constant λ2Value by setting Meter person is given；ControllerAdaptive lawIts In, In formulaConstant k2> 0, μ2>0 is given by designer；
Step 3：The joint that the calculated instructions of controller U are sent to Three Degree Of Freedom calligraphy and Sculpture robot executes Device, the ideal track of control robot output tracking.
Beneficial effects of the present invention：
The present invention is based on the calligraphy of Robust Adaptive Control algorithm and Sculpture robot control methods, can have unknown hold Row device failure and in the case of unknown external interference, ensureing that the output tracking ideal trajectory of robot, tracking error can be fast Speed converges in ideal range, and control accuracy is high, and can guarantee the mapping of the arbitrary error of robot.
Description of the drawings
Fig. 1 is calligraphy and Sculpture robot dimensional structure diagram, joint1, that is, robot base joint in figure, joint2 That is robot's arm joint, joint3, that is, robot forearm joint；
Fig. 2 is PPB schematic diagrams, when error is less thanAnd more than-υWhen (0) ρ, which ensures that tracking error restrained Journey is located at curveWith curve-υBetween ρ (t), finally converge onOr-υρ(∞)；Due to curveWith-υ ρ (t) is restrained with exponential form, so the algorithm ensure that the mapping of error convergence；
Fig. 3 is that fault-tolerant parameter ρ changes over time curve graph；
Fig. 4 is fault-tolerant parameter UpChange over time curve graph；
Fig. 5 is the fault-tolerant track position error (e=q-q of robust adaptive based on PPB*) simulation result；
Fig. 6 is the fault-tolerant tracking velocity error of robust adaptive based on PPBSimulation result.
Specific implementation mode
The present invention is described in detail with reference to the accompanying drawings and examples.
Calligraphy based on Robust Adaptive Control algorithm in the present embodiment and Sculpture robot control method, including following step Suddenly：
Step 1：The kinetic model for establishing Three Degree Of Freedom calligraphy and Sculpture robot estimates each pass according to kinetics equation The moment of inertia term H of section, centripetal force and coriolis force square item C, gravitational moment item G finally obtain the torque estimation formula in each joint：
Wherein
G2=m1l1c2+m2l1c2+m2l2c23, G3=m2l2c23,
FfriIt is the static state or dynamic friction of robot, FdisIt is the external disturbance of robot system, FfriAnd FdisOnly Want bounded；q1It is the rotational angle in robot base joint, q2It is the rotational angle in robot's arm joint, q3It is machine The rotational angle of the small shoulder joint of people；
In above formula, ci=cos (qi),cij=cos (qi+qj),si=sin (qi),sij=sin (qi+qj), liIt is robot The length of i-th joint shaft, miIt is the quality of the i-th joint shaft of robot, IiFor the rotary inertia of the i-th joint shaft of robot, i=1, 2,3, i correspond to the pedestal joint shaft of robot when being 1, i corresponds to the large-arm joint axis of robot when being 2, i corresponds to machine when being 3 The forearm joint shaft of people；qiThe value of middle i is 1,2,3, qjThe value of middle j is 1,2,3；T is time variable；
U in formulaaTorque is actually entered for motor, due to that there may be unexpected actuator failures in model, is set The input signal U and motor of the controller of meter actually enter torque UaIt is no longer identical, but there are following relationships：Ua=ρ U+Up, Wherein ρ is health factor, UpIt is the uncontrollable part controlled in signal；Therefore in actuator failures, the number of controller Learning model is：
Step 2：Design Robust adaptive controller, tracking error e=q-q*,
When error is more than PPB sphere of actions, designing supervision controller will be in error attenuated to PPB sphere of actions；It introduces Median errorWherein λ1>0, constant λ1Value given by designer；ControllerAdaptive lawWherein, Constant k1>0, μ1>0, the value of the two is given by designer；
When error is less than PPB sphere of actions, the robust adaptive fault-tolerant controller based on PPB is designed, is ensured The mapping of system, i.e.,Wherein,νWithGiven coboundary and lower boundary, f=[f (0)-are indicated respectively f(∞)]e-ιtIt is given performance function, defines ei=f Γ (ξi),It is a strictly increasing Function, whereinTherefore ξ can be indicated by e；Introduce median error In formula, r and m are and the relevant multinomials of ξ, λ2>0, constant λ2Value given by designer；Control DeviceAdaptive lawWherein, In formulaConstant k2>0, μ2>0 is given by designer；
Step 3：The joint that the calculated instructions of controller U are sent to Three Degree Of Freedom calligraphy and Sculpture robot executes Device, the ideal track of control robot output tracking.
By the reliability of control method in MATLAB simulating, verifying the present embodiment, Fig. 3,4 is in faults-tolerant controls in emulation Healthy coefficient ρ and uncontrollable part UpSelection；By Fig. 5, the tracking process of angular error shown in 6 and angular acceleration error The controller designed in the present embodiment, which can be worth, realizes good tracking performance, there are actuator unknown failures and external dry In the case of disturbing, tracking error can be rapidly converged to given range in the form of index and realize smooth cut at switching point It changes.
The controller designed in the present embodiment is divided into two parts, i.e., except the range of PPB algorithms within the scope of：Range Except controller be monitoring controller, will be greater than the error attenuated of given range within the scope of；Within the scope of be then and biography PPB algorithms of uniting are identical, ensure that the mapping of system, and the time by zone boundary is ta, t>taWhen, U=U1；t<taWhen, U=U2, from the stability that can guarantee system known to simulation results, in t=taWhen, pass through the device that is flexible coupling of introducingIt can ensure continuity of the input signal in entire working range.
Finally illustrate, the above examples are only used to illustrate the technical scheme of the present invention and are not limiting, although with reference to compared with Good embodiment describes the invention in detail, it will be understood by those of ordinary skill in the art that, it can be to the skill of the present invention Art scheme is modified or replaced equivalently, if but without departing from the objective and range of technical solution of the present invention, just should cover at this In the right of invention.

Claims (1)

1. a kind of calligraphy and Sculpture robot control method based on Robust Adaptive Control algorithm, it is characterised in that：Including with Lower step：
Step 1：The kinetic model for establishing Three Degree Of Freedom calligraphy and Sculpture robot estimates each joint according to kinetics equation Moment of inertia term H, centripetal force and coriolis force square item C, gravitational moment item G finally obtain the torque estimation formula in each joint：
Wherein
G2=m1l1c2+m2l1c2+m2l2c23, G3=m2l2c23,
FfriIt is the static state or dynamic friction of robot, FdisIt is the external disturbance of robot system；q1It is that robot base closes The rotation rotational angle of section, q2It is the rotational angle in robot's arm joint, q3It is the rotational angle in robot forearm joint；
In above formula, ci=cos (qi),cij=cos (qi+qj),si=sin (qi),sij=sin (qi+qj), liIt is that robot i-th closes The length of nodal axisn, miIt is the quality of the i-th joint shaft of robot, IiFor the rotary inertia of the i-th joint shaft of robot, i=1,2,3, i The pedestal joint shaft of robot is corresponded to when being 1, i corresponds to the large-arm joint axis of robot when being 2, i corresponds to the small of robot when being 3 Shoulder joint axis；qiThe value of middle i is 1,2,3, qjThe value of middle j is 1,2,3；T is time variable；
U in formulaaTorque is actually entered for motor, due to that may have unexpected actuator failures, the control of design in model The input signal U and motor of device processed actually enter torque UaIt is no longer identical, but there are following relationships：Ua=ρ U+Up, wherein：ρ It is health factor, value range is：0<ρ<1；UpIt is the uncontrollable part controlled in signal, can is arbitrary bounded function； Therefore in actuator failures, the mathematical model of controller is：
Step 2：Design Robust adaptive controller, tracking error
When error is more than PPB sphere of actions, that is, t>taWhen, taIt is equal to the time point of given range, designing supervision controller for error It will be in error attenuated to PPB sphere of actions；Introduce median errorWherein λ1>0, constant λ1Value by designer It is given；ControllerAdaptive lawWherein,Constant k1>0, μ1>0, the value of the two It is given by designer；
When error is less than PPB sphere of actions, that is, t<taWhen, the robust adaptive fault-tolerant controller based on PPB is designed, ensures system Mapping, i.e.,Wherein,νWithGiven coboundary and lower boundary, f=[f (0)-f (∞)] are indicated respectively e-ιtIt is given performance function, defines ei=f Γ (ξi),It is a strictly increasing letter Number, whereinTherefore ξ can be indicated by e, ξ=[ξ1,ξ2,ξ3]T, I=1,2,3；Introduce median error In formula, r=diag { r1,r2,r3, m= diag{m1,m2,m3},λ2>0, constant λ2Value given by designer；ControllerAdaptive lawWherein, In formulaConstant k2> 0, μ2>0 is given by designer；
Step 3：The calculated instructions of controller U are sent to the joint actuator of Three Degree Of Freedom calligraphy and Sculpture robot, control The ideal track of robot output tracking processed.
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CN112213949A (en) * 2020-11-18 2021-01-12 重庆大学 Robot joint system tracking control method based on robust self-adaption
CN114265364A (en) * 2021-12-21 2022-04-01 江苏师范大学 Monitoring data processing system and method for industrial Internet of things

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CN114265364A (en) * 2021-12-21 2022-04-01 江苏师范大学 Monitoring data processing system and method for industrial Internet of things
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