CN110134013A - The parallel mechanical arm finite time convergence control motion control method of external disturbance can be fought - Google Patents

The parallel mechanical arm finite time convergence control motion control method of external disturbance can be fought Download PDF

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CN110134013A
CN110134013A CN201910379617.1A CN201910379617A CN110134013A CN 110134013 A CN110134013 A CN 110134013A CN 201910379617 A CN201910379617 A CN 201910379617A CN 110134013 A CN110134013 A CN 110134013A
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mechanical arm
parallel mechanical
control
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time
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CN110134013B (en
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陈德潮
李帅
吴卿
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Hangzhou Dianzi University
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Hangzhou Dianzi University
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    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
    • G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
    • G05B13/04—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators
    • G05B13/042—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators in which a parameter or coefficient is automatically adjusted to optimise the performance

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Abstract

The present invention provides the parallel mechanical arm finite time convergence control motion control methods that one kind can fight external disturbance, it is poor according to the real time position in three dimensions of the actuator on parallel mechanical arm motion platform and predefined expected path to include the following steps:, define the error function and intermediate variable of tracing control, the error dynamics equation of design confrontation external disturbance；In conjunction with the real-Time Tracking Control task of parallel mechanical arm, kinematic relation formula of the parallel mechanical arm on supporting leg velocity layer is solved；Error dynamics equation is substituted into, show that parallel mechanical arm real-Time Tracking Control controls signal dynamics equation；It calculates real-time parallel mechanical arm supporting leg and updates control signal, acquired results drive parallel mechanical arm to carry out tracing control operation, while so that actuator on a mobile platform realizes tracing control, generated location error can be with finite time convergence control, and effectively realizes the interference outside parallel mechanical arm confrontation.

Description

The parallel mechanical arm finite time convergence control motion control method of external disturbance can be fought
Technical field
The present invention relates to manipulator motions and robust control field, and in particular to one kind can fight the parallel machine of external disturbance Tool arm finite time convergence control motion control method.
Background technique
Parallel mechanical arm is usually passed through at least two or more independent movement supporting leg by mobile platform and fixed pedestal It is connected, parallel mechanical arm generally has two or more freedom degrees, and a kind of closed-loop control system driven with parallel way The mechanical device of system.Parallel mechanical arm usually has no accumulated error, and motion control accuracy is high, and dynamic response is good, compact-sized, The advantages such as rigidity is high, and load capacity is strong, and human arm can be replaced, the operation of high precision is completed, therefore it is widely used in work In industry manufacture, aerospace even military equipment field.Development of the real time kinematics control research of parallel mechanical arm after many years, Relevant motion control theoretical research and actual practice application obtain great breakthrough and progress, also accordingly have developed various The parallel mechanical arm of type, for improving production efficiency, homework precision, instead of the case of manual work.Wherein real-time tracking control The research of system is a highly important research contents of parallel mechanical arm motion study.Traditional parallel mechanical arm is used in the past Tracking and controlling method can not usually be effective against external interference, and solving error can not be the Finite-time convergence the deficiencies of. Above-mentioned problem has become " bottleneck " problem of parallel mechanical arm real time kinematics control problem, frequently can lead to parallel manipulator There is low precision tracking result, or even will appear external disturbance and lead when carrying out tracing control operation for a long time in the actuator of arm Cause the failure of tracing control task.
Summary of the invention
In view of the deficiencies of the prior art, the present invention provides one kind can fight the parallel mechanical arm finite time receipts of external disturbance Hold back motion control method.
In order to solve the above technical problems, the present invention is achieved by the following technical programs:
A kind of parallel mechanical arm finite time convergence control motion control method fighting external disturbance, specifically includes following step It is rapid:
1) according to the real time position in three dimensions of the actuator on parallel mechanical arm motion platform and predefined phase It hopes path difference, defines the error function and intermediate variable of tracing control, the error dynamics equation of design confrontation external disturbance；It obtains The error dynamics equation for fighting external disturbance, i-th of subsystem equation be described as
WhereinIndicate i-th of element of actuator and motion control task location error function,Indicate εi(t) time-derivative, λ indicate that the predefined design parameter of user, sign () indicate symbol letter Number mapping.
Preferably, kinematic relation formula of the parallel mechanical arm on supporting leg velocity layer:
WhereinIndicate the Jacobian matrix of parallel mechanical arm actuator,Indicate parallel mechanical arm supporting leg Real time kinematics speed,Indicate and mechanical arm actuator cartesian space live actual motion profile when Between derivative,Indicate parallel mechanical arm actuator in the time of the predefined path curve equation of cartesian space Derivative.
2) the error dynamics equation of the confrontation external disturbance based on step 1) design, in conjunction with the real-time tracking of parallel mechanical arm Control task solves kinematic relation formula of the parallel mechanical arm on supporting leg velocity layer；
3) the kinematic relation formula for combining step 2), substitutes into error dynamics equation, obtains parallel mechanical arm real-time tracking control System control signal dynamics equation；
4) the parallel mechanical arm real-Time Tracking Control for obtaining step 3) controls signal dynamics equation, calculates real-time parallel connection Mechanical arm supporting leg updates control signal, and acquired results drive parallel mechanical arm to carry out tracing control operation, so that in mobile platform On actuator realize tracing control while, generated location error can be with finite time convergence control, and effectively realizes simultaneously Join the interference outside mechanical arm confrontation.
Preferably, the dynamical equation of parallel mechanical arm real-Time Tracking Control control signal:
Wherein u (t) indicates that parallel mechanical arm real-Time Tracking Control controls signal, Ψk() representative function map array, I-th of element definition is as follows:
The present invention compared with the existing technology possessed by effect: the present invention calculates real-time parallel mechanical arm supporting leg and updates control Signal processed, acquired results drive parallel mechanical arm to carry out real-Time Tracking Control operation, realize the actuator tracking on mobile platform While control, generated location error can be with finite time convergence control, and realizes the influence for effectively antagonizing external disturbance.
Detailed description of the invention
Fig. 1 is flow chart of the present invention；
Fig. 2 is the parallel mechanical arm three-dimensional model diagram of specific implementation of the invention.
Specific embodiment
Following further describes the present invention with reference to the drawings.
One kind shown in FIG. 1 can fight the parallel mechanical arm finite time convergence control motion control method of external disturbance, first It is poor according to the real time position of parallel mechanical arm actuator and predefined expected path, the error function of tracing control is defined in Between variable, design confrontation external disturbance error dynamics equation；Later in conjunction with the real-Time Tracking Control task of parallel mechanical arm, ask Solve kinematic relation formula of the parallel mechanical arm on supporting leg velocity layer；Kinematic relation formula is further substituted into error dynamics side Journey show that parallel mechanical arm real-Time Tracking Control controls signal dynamics equation；Finally calculate real-time parallel mechanical arm supporting leg more New control signal, acquired results drive parallel mechanical arm to carry out real-Time Tracking Control operation, realize the actuator on mobile platform While tracing control, generated location error can be with finite time convergence control, and realizes the influence for effectively antagonizing external disturbance.
Fig. 2, which is illustrated, realizes parallel mechanical arm model of the invention, which is one with six degree of freedom Parallel mechanical arm.The parallel mechanical arm is made of six telescopic supporting legs and fixed platform and mobile platform, passes through supporting leg 1, supporting leg 2, supporting leg 3, supporting leg 4, supporting leg 5 and supporting leg 6 form, and actuator is assembled in the mobile platform center of parallel mechanical arm, can hold Row path following control motor task.
Firstly, the present invention is according to the real time position in three dimensions of the actuator on parallel mechanical arm motion platform and pre- The expected path of definition is poor, defines the error function equation of tracing control:
ε (t)=rp(t)-ra(t),
WhereinIndicate the error function of actuator and motion control task location,It indicates Parallel mechanical arm actuator cartesian space predefined path curve equation,It indicates and mechanical arm executes Live actual motion profile of the device in cartesian space.For the influence for further eliminating model external disturbance, it is defined as follows centre Variable:
WhereinIndicate that intermediate variable function, λ indicate the predefined design parameter of user, sign () Indicate sign function mapping.In conjunction with following dynamical equation, i-th of subsystem equation be can be described as
The error dynamics equation for fighting external disturbance as follows can be obtained, i-th of subsystem equation is described as
Then, according to parallel mechanical arm kinematics model:
WhereinIndicate the coefficient matrix of parallel mechanical arm,Indicate the movement velocity of parallel mechanical arm supporting leg. In conjunction with the real-Time Tracking Control task of parallel mechanical arm, kinematic relation of the parallel mechanical arm on supporting leg velocity layer can be obtained Formula:
WhereinIndicate the Jacobian matrix of parallel mechanical arm actuator.
In turn, the kinematics in conjunction with the error dynamics equation and parallel mechanical arm of confrontation external disturbance on supporting leg velocity layer Relational expression can obtain the dynamical equation of parallel mechanical arm real-Time Tracking Control control signal:
Wherein u (t) indicates that parallel mechanical arm real-Time Tracking Control controls signal,Indicate the reality of parallel mechanical arm supporting leg When movement velocity, Ψk() representative function map array, it is as follows to be defined as i-th of element definition:
Finally, being calculated in real time simultaneously using the dynamical equation of obtained parallel mechanical arm real-Time Tracking Control control signal The update for joining each supporting leg of mechanical arm controls signal, and acquired results drive parallel mechanical arm to carry out tracing control movement, so that simultaneously Join actuator while realizing tracing control, generated location error can be realized with finite time convergence control so that parallel machine Tool arm effectively antagonizes the influence of external disturbance.
The embodiment of invention described above, is not intended to limit the scope of the present invention..It is any in this hair Made modifications, equivalent substitutions and improvements etc. within bright spiritual principles should be included in claim protection of the invention Within the scope of.

Claims (3)

1. the parallel mechanical arm finite time convergence control motion control method of external disturbance can be fought, which is characterized in that this method packet Include following steps:
1) according to the real time position in three dimensions of the actuator on parallel mechanical arm motion platform and predefined expectation road Diameter is poor, defines the error function and intermediate variable of tracing control, the error dynamics equation of design confrontation external disturbance；
The error dynamics equation of external disturbance can be fought obtained in it, i-th of subsystem equation is described as
WhereinIndicate i-th of element of actuator and motion control task location error function,Table Show εi(t) time-derivative, λ indicate that the predefined design parameter of user, sign () indicate sign function mapping；
2) the error dynamics equation of the confrontation external disturbance based on step 1) design, in conjunction with the real-Time Tracking Control of parallel mechanical arm Task solves kinematic relation formula of the parallel mechanical arm on supporting leg velocity layer；
3) it is based on the kinematic relation formula of step 2), substitutes into error dynamics equation, show that parallel mechanical arm real-Time Tracking Control is believed Number dynamical equation；
4) the parallel mechanical arm real-Time Tracking Control signal dynamics equation obtained based on step 3), calculates real-time parallel mechanical arm Supporting leg updates control signal, and acquired results drive parallel mechanical arm to carry out tracing control operation, so that holding on a mobile platform While row device realizes tracing control, generated location error can be with finite time convergence control, and effectively realizes parallel manipulator Interference outside arm confrontation.
2. the parallel mechanical arm finite time convergence control motion control method according to claim 2 for fighting external disturbance, It is characterized in that kinematic relation formula of the parallel mechanical arm in the step 2) on supporting leg velocity layer:
WhereinIndicate the Jacobian matrix of parallel mechanical arm actuator,Indicate the real-time fortune of parallel mechanical arm supporting leg Dynamic speed,Indicate and mechanical arm actuator the live actual motion profile of cartesian space time-derivative,Indicate parallel mechanical arm actuator in the time-derivative of the predefined path curve equation of cartesian space.
3. the parallel mechanical arm finite time convergence control motion control side that one kind according to claim 3 can fight external disturbance Method, it is characterised in that the dynamical equation of the parallel mechanical arm real-Time Tracking Control control signal in the step 3):
Wherein u (t) indicates that parallel mechanical arm real-Time Tracking Control controls signal, Ψk() representative function map array, definition It is as follows for i-th of element definition:
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CN114167722A (en) * 2021-11-26 2022-03-11 杭州电子科技大学 Parallel robot tracking control method based on super-exponential convergence neural network

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EP2705934A2 (en) * 2012-09-10 2014-03-12 CVUT V Praze, Fakulta Strojní A method and a device for change of rigidity of a serial or parallel basic movable mechanism, especially of industrial robots and machining machines
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CN114167722B (en) * 2021-11-26 2024-03-29 杭州电子科技大学 Parallel robot tracking control method based on super-exponential convergence neural network

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