CN106169003B - A kind of multiple degrees of freedom space mechanism motion planning method - Google Patents
A kind of multiple degrees of freedom space mechanism motion planning method Download PDFInfo
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Abstract
The invention discloses a kind of multiple degrees of freedom space mechanism motion planning methods, and multiple degrees of freedom space mechanism model is divided into the component submodel of several single-degree-of-freedoms including step；Establish component finite element model accordingly comprising kinematics freedom degree；It determines and executes displacement needed for each driving link, and determine Parametric motion function used by each driving link；The Parametric motion function of each driving link is applied in assembly finite element model as boundary condition；The motion simulation information of each component submodel in mechanism, multiple degrees of freedom space mechanism is obtained, and obtains vibration pickup point in turn relative to relative displacement, the velocity information for terminating ideal position；Judge whether multiple degrees of freedom space mechanism meets final positioning accuracy request；The mass motion time is minimized and is used as optimization aim；Find the optimized parameter of motion planning parameter in iterative process.Compared with prior art, the present invention can get most short corresponding motion planning Function Optimization parameter of effective general location time.
Description
Technical field
The present invention relates to space mechanism's motion planning method more particularly to a kind of motion planning sides, multiple degrees of freedom space mechanism
Method.
Background technique
In automation processing and manufacturing field, multiple degrees of freedom space mechanism is widely used with many advantages, such as its flexibility.
Jitter phenomenon during multiple degrees of freedom space mechanism is easy to appear motion positions in high-speed motion operating condition, this will be significantly affected
The positioning accuracy of multiple degrees of freedom space mechanism, and cause multiple degrees of freedom space mechanism to reach indirectly to have used in regulation positioning accuracy
The time is imitated, working efficiency is reduced.
Come in terms of control system optimizes to solve the above problems, generalling use suitable motion control arithmetic to above-mentioned vibration
It is dynamic to be controlled.Aforesaid way is in vibratory response and the space that the critical issue of practical application is determining space mechanism's position fixing process
Mechanism kinematic plans the relationship between function.Traditional S type curvilinear motion planning is mainly the curve movements such as collateral security acceleration
Fairness to reduce vibratory response in position fixing process indirectly, cannot obtain and take into account positioning accuracy allowable and most short effective position
The double requirements of time.
For example, patent 201310460878.9 proposes a kind of S type curve movement rule of high-speed mechanism reduction residual oscillation
The method of drawing, by increasing by one section of die-away time section for considering residual oscillation influence in conventional S type curve movement planing method,
And it establishes accordingly with motion planning time+die-away time section minimum target Optimized model.It is described in this patent
Die-away time section be mechanism with high speed motion be to guarantee residual oscillation amplitude less than allowable fixed after motion planning end time
Time quantum needed for the error of position.By abs (s-s*)+abs (v) < ε, (wherein s, s*, v, ε are respectively to transport to above-mentioned die-away time section
Dynamic displacement, expectation displacement, movement velocity, position error allowable) it obtains.Patent 201310460878.9 is based on traditional S
The residual oscillation die-away time of above-mentioned acquisition is contained in the Optimized model of type curve movement planning, obtains revised comprehensive fortune
Dynamic plan optimization model.
Patent 201410255068.4 proposes a kind of asymmetric fluctuating acceleration rule based on dominant frequency energy time domain Optimal Distribution
The method of drawing analyzes the positioning for obtaining the movement mechanism under parametrization asymmetrical movement function drive using Nonlinear FEM Simulation
Residual oscillation responds course, and (wherein s, s*, v, ε are respectively moving displacement, expectation position using abs (s-s*)+abs (v) < ε
Shifting, movement velocity, position error allowable) judgment criterion carrys out remnants needed for movement executing mechanism residual oscillation meets required precision
Vibrate die-away time.Patent 201410255068.4 is necessarily less than residual oscillation amplitude by introducing in optimizing and analyzing model
The analysis constraint of position error allowable obtains comprehensive optimal motion planning function parameter.
Although comprehensive motion planning optimization provided by patent 201310460878.9 and patent 201410255068.4 is calculated
Method is used equally for meeting positioning accuracy needed for obtaining high-speed mechanism and minimizes the optimal motion of the requirements such as general location time
Projecting parameter, but the core point of above-mentioned two patent is to the residual oscillation die-away time amount for meeting positioning accuracy request
Judgement.In above-mentioned two patent, used acquisition meets institute in judgment criterion used in movement mechanism positioning accuracy request
The positioning accuracy ε allowable used does not have direct physical significance, belongs to and true positioning displacement error relevant one allowable
The approximate relative indicatrix of kind.Since the positioning accuracy ε allowable in above-mentioned patent is only a kind of relative indicatrix, and in actual complex operating condition
ε used in the movement mechanism that middle same accuracy requires is not necessarily the same, i.e., the ε in judgment criterion used in above-mentioned two patent with
Simultaneously a specific functional relation is not present in true position error allowable, this will lead to the final motion planning optimization of above-mentioned patent
As a result the optimal motion planning of true positioning accuracy request is not necessarily matched.
Summary of the invention
In order to overcome the deficiencies of the prior art, the present invention proposes a kind of multiple degrees of freedom space mechanism motion planning method.
The technical scheme is that a kind of such, multiple degrees of freedom space mechanism motion planning method, comprising steps of
S1: if being divided into multiple degrees of freedom space mechanism model according to the freedom degree compositive relation of multiple degrees of freedom space mechanism
The component submodel of dry single-degree-of-freedom, wherein the connection relationship of the component submodel of each component submodel and next hierarchical link
Position is vibration pickup point；
S2: according to the geological information of each component submodel, component finite element accordingly comprising kinematics freedom degree is established
Model, by each component finite element model according to its drive diarthrodial assembly relation generate multiple degrees of freedom space mechanism comprising movement
Learn the assembly finite element model of freedom degree；
S3: execution needed for determining each driving link according to the anti-solution of movement of multiple degrees of freedom space mechanism point operation acts
Displacement, and determine Parametric motion function used by each driving link；
S4: using the Parametric motion function of each driving link as boundary condition be applied to it is described comprising kinematics oneself
By in the assembly finite element model spent；
S5: according to the geometric nonlinear finite element model and Parametric motion function of mechanism, the multiple degrees of freedom space mechanism
Boundary condition, obtains the motion simulation information of each component submodel in mechanism, multiple degrees of freedom space mechanism, and obtains institute in turn
Vibration pickup point is stated relative to relative displacement, the velocity information for terminating ideal position；
S6: come real-time judge multiple degrees of freedom space mechanism it is according to the relative displacement at each vibration pickup point, velocity information
It is no to meet final positioning accuracy request, step S5 is repeated, until meeting positioning accuracy request, and obtains the end time and movement
Plan the residual oscillation die-away time length used between end time；
S7: it sums residual oscillation die-away time and movement driving time to obtain mass motion positioning time, and will be whole
Body run duration, which minimizes, is used as optimization aim；
S8: it if can be determined that the mass motion time is minimum value by iteration convergence criterion, corresponds in iterative process
Motion planning parameter be optimized parameter；If the mass motion time is not minimum value, movement is calculated based on gradient optimal method
The Optimizing Search direction of parameter and step-size in search, and the Parametric motion function in step S3 is updated, it repeats step S3-S7 and carries out
Iterative calculation, until finding the optimized parameter of motion planning parameter in iterative process.
Further, step S6 comprising steps of
S61: Fast Fourier Transform (FFT), band logical are carried out to the relative displacement at the vibration pickup point of each component, velocity information
The signal processings such as filtering obtain each rank intrinsic frequency pair in each rank intrinsic frequency and its positioning residual oscillation course on each component
The displacement answered, speed motor message；
S62: displacement and speed corresponding to each rank intrinsic frequency are obtained using the intrinsic frequency and displacement, speed signal of acquisition
Time domain course curve is spent, and obtains the vibrational energy envelope of vibration pickup point on each component, the width of the energy envelope line
Value is the equivalent potential energy maximum displacement of each component temporal motion course energy corresponding to the moment intrinsic frequency；
S63: energy envelope line corresponding to each rank intrinsic frequency to each section of component obtained is overlapped, and obtains the section
Single-degree-of-freedom complex energy envelope on component, the single-degree-of-freedom complex energy envelope are the moment positioning of this section of component
Error maximum amplitude；
S64: each moment position error of each section of component is overlapped, and obtains the very big positioning of multiple degrees of freedom space mechanism
Error；
S65: compared with by the displacement error value allowable of the amplitude of very big placement error value and space mechanism work actuating station, when
When the amplitude of very big placement error value is less than movement mechanism displacement error allowable, then meet in the moment multiple degrees of freedom space mechanism
Positioning accuracy request.
The beneficial effects of the present invention are compared with prior art, it is most short that the present invention can get effective general location time
Corresponding motion planning Function Optimization parameter has taken into account the double requirements of positioning accuracy allowable and most short positioning time, while this
Invention uses the motion positions error decision procedure based on energy, avoids and carries out motion positions mistake using displacement vibration curve
Difference is judged by accident caused by determining, and formula used in motion positions error judgment of the present invention is explicit formula, can be to position error
Real-time judge is carried out, convenient for implementing in embedded controller.
Detailed description of the invention
Fig. 1 is multiple degrees of freedom space mechanism motion planning method flow chart of the present invention.
Fig. 2 is multiple degrees of freedom space mechanism motion planning method algorithm flow chart of the present invention.
Fig. 3 is that positioning accuracy used in multiple degrees of freedom space mechanism of the present invention motion planning method determines in multi-modal operating condition
Under residual oscillation schematic diagram.
Fig. 4 is the corresponding residual oscillation analysis schematic diagram of 1 rank basic frequency under multi-modal operating condition shown in Fig. 3.
Fig. 5 is the corresponding residual oscillation analysis schematic diagram of 2 rank basic frequencies under multi-modal operating condition shown in Fig. 3
Fig. 6 is the corresponding residual oscillation analysis schematic diagram of 3 rank basic frequencies under multi-modal operating condition shown in Fig. 3.
Specific embodiment
Following will be combined with the drawings in the embodiments of the present invention, and technical solution in the embodiment of the present invention carries out clear, complete
Site preparation description, it is clear that described embodiments are only a part of the embodiments of the present invention, instead of all the embodiments.It is based on
Embodiment in the present invention, it is obtained by those of ordinary skill in the art without making creative efforts every other
Embodiment shall fall within the protection scope of the present invention.
Referring to Figure 1 and Fig. 2, a kind of multiple degrees of freedom space mechanism of the invention motion planning method, including step
S1: if being divided into multiple degrees of freedom space mechanism model according to the freedom degree compositive relation of multiple degrees of freedom space mechanism
The component submodel of single-degree-of-freedom is done, all drives link containing corresponding in each component submodel, and according to articulamentum
Secondary rank carries out 1-n number to each component.Wherein the connection of the i+1 component submodel and i-th of component submodel is closed
Section is set to the vibration pickup point M of i-th of component submodeli, the vibration pickup point M of n-th of component submodelnFor multiple degrees of freedom
The work of space mechanism executes end position；
S2: obtaining the geological information of each component submodel according to S1 step, and establish includes kinematics freedom degree accordingly
Each component finite element model is driven diarthrodial assembly relation according to it and forms multiple degrees of freedom space mechanism by component finite element model
The assembly nonlinear finite element model comprising kinematics freedom degree；
S3: it is held needed for each driving link determined according to the anti-solution of movement of multiple degrees of freedom space mechanism point operation acts
Line position moves Si(i=1..n), and Parametric motion function used by each driving link, each parameter for driving link to use are determined
The motion planning execution time determined by change movement function is all made of identical time tplan, the n vibration pickup point MiPoint
The starting of position operation acts and the ideal position of end time are respectivelyWith
S4: will respectively be driven in S3 step the Parametric motion function of link as boundary condition be applied to S2 described in include
In the assembly finite element model of kinematics freedom degree；
S5: it is resolved described in model and S3 step using the finite element that S2 step obtains mechanism, multiple degrees of freedom space mechanism
Parametric motion functional boundary condition obtains the motion simulation of each component submodel in mechanism, the multiple degrees of freedom space mechanism
Information, and vibration pickup point M described in S1 step is obtained in turni(i=1..n) relative to termination ideal position
The Dynamic Response Informations such as relative displacement, speed.
S6: each vibration pickup point M obtained using S5 stepi(i=1..n) relative displacement, velocity information at come real
When judge whether multiple degrees of freedom space mechanism meets final positioning accuracy request.Such as meet positioning accuracy request, then terminates immediately
Multiple degrees of freedom space mechanism finite element model solution process described in S5 step, and obtain the end time and motion planning termination
Moment TplanDifference be residual oscillation die-away time length T usedres, and go to S7 step；Otherwise, S5 step is continued to execute.
S7: the residual oscillation die-away time T that S6 step is obtainedresAnd movement driving time TplanSummation obtains entirety
Motion positions time Ttotal(=Tres+Tplan), and T will be minimizedtotalAs optimization aim.
S8: if can be determined that T by iteration convergence criteriontotalWhen for minimum value, then the movement rule in iterative process are corresponded to
Drawing parameter is optimized parameter；Conversely, Optimizing Search direction and the step-size in search of kinematic parameter are then calculated based on gradient optimal method,
And the Parametric motion function in S3 step is updated, it returns to S5 step and is iterated calculating, moved until finding in iterative process
The optimized parameter of projecting parameter.
The method for carrying out positioning accuracy judgement using residual oscillation dynamic respond curve in S6 step specifically:
S61: the vibration pickup point M to each component obtained in S5 stepi(i=1..n) relative displacement, speed letter at
Breath carries out the signal processings such as Fast Fourier Transform (FFT), bandpass filtering, obtains each rank intrinsic frequency on each componentAnd its each rank intrinsic frequency in positioning residual oscillation courseCorresponding displacementSpeed
Grade motor messages (j is the order of intrinsic frequency,For M on i-th section of componentiRelative to ideal final positionT moment
Shift value is in frequencyOn component,For M on i-th section of componentiRelative to ideal final positionIn the speed of t moment
Value is in frequencyOn component)；
S62: the intrinsic frequency obtained using S61 stepWith displacementSpeedEqual signals obtain each intrinsic frequency of rank
RateCorresponding displacementAnd speedTime domain course curve, and utilize formula
Obtain vibration pickup point M on i-th section of componentiVibrational energy envelope, the energy envelope lineAmplitude be i-th section of structure
Part is in t moment natural frequency ωiThe equivalent potential energy maximum displacement of corresponding temporal motion course energy；
S63: right: each rank intrinsic frequency for i-th section of component that S62 step is obtainedCorresponding energy envelope lineInto
Row superposition, obtains the single-degree-of-freedom complex energy envelope on i-th section of componentIt is describedFor i-th section of component
T moment position error maximum amplitude；
S64: by each t moment position error of each section of component in S63 stepIt is overlapped, it is empty to obtain multiple degrees of freedom
Between mechanism very big position error Emax(t)。
S65: the very big placement error value E that S64 step is obtainedmax(t) amplitude is permitted with space mechanism's work actuating station
Compared with displacement error value, as very big placement error value Emax(t) when amplitude is less than movement mechanism displacement error allowable, then exist
The moment multiple degrees of freedom space mechanism meets positioning accuracy request.
It is as follows to the principle of end positioning accuracy judgment criterion:
According to Fourier transform principle, complicated Vibration Condition can be decomposed into the superposition of several simple harmonic oscillations.It is assumed that fortune
Each rank THE CURVES ON WHICH A POINT MASS OSCILLATES HARMONICALLY equation in dynamic end residual oscillation is si(t)=Aie-αtsin(ωiT), wherein AiFor vibration frequency
ωiThe amplitude of oscillating curve, α are system structure damping.The vibration velocity equation of above-mentioned each rank simple harmonic oscillation isIn above-mentioned simple harmonic oscillation course, the vibrational energy of each moment point
It is the sum of kinetic energy and the potential energy at the moment point, i.e.,By above-mentioned total energy expression
Being converted to equal potential energy expression-form can obtainPass through analogy
General potential energy expression formulaIt can be seen thatIt is corresponding etc. for gross energy in simple harmonic oscillation course
Imitate potential energy maximum displacement.And it is substantial,Energy envelope curve is ωiThe vibration position of frequency simple harmonic oscillation
Move the high accuracy approximation approximating curve of envelope curve.Therefore it can useEnergy envelope curve is as ωi
The displacement envelope curve of frequency simple harmonic oscillation determines for vibrating precision.
Due toIt is to be derived from energy point of view, according to the scalar nature of energy, multiple frequency letters
The corresponding gross energy envelope of the superimposed complex vibration curve of harmonic motion is the corresponding energy envelope line of each rank vibration frequency
Superposition and, i.e.,According to ESum(t) amplitude can carry out the vibrational energy of complex vibration
Quickly determine, and then determines whether the residual oscillation amplitude at the moment meets positioning accuracy request.
One embodiment of positioning accuracy judgement used in the mentioned motion planning of the present invention is as seen in figures 3-6.
S (t) residual oscillation displacement curve shown in Fig. 3 is that positioning of the movement mechanism under set motion planning model cootrol is remaining
Vibration course curve, solid line represents s (t) residual oscillation displacement curve in Fig. 3, and dotted line represents gross energy envelope.The s (t)
The time zero of displacement curve is the end time of former setting motion planning curve, and the vibration displacement is that movement mechanism is opposite
The displacement of locating endpoints.Also due to the factors such as structural damping existing for movement mechanism itself, the energy of movement mechanism with when
Between course gradually decay.In the present embodiment, movement mechanism mainly includes 3 intrinsic frequencies.3 intrinsic frequencies can be with
It is obtained by carrying out Fourier transformation analysis to s (t) residual oscillation displacement curve.As shown in Fig. 2, due in multi-modal operating condition
Movement mechanism includes multiple intrinsic frequencies, causes directly to be difficult directly to utilize s (t) to original s (t) residual oscillation displacement curve
Residual oscillation displacement curve carries out positioning accuracy judgement.
In the three mode operating condition embodiments described in Fig. 3, obtained first with the signals analysis means such as Fast Fourier Transform (FFT)
Then each rank basic frequency extracts each rank basic frequency from original s (t) residual oscillation displacement curve in the way of bandpass filtering etc.
ωi(i=1,2,3) corresponding vibration response curve, the s in respectively Fig. 4-Fig. 6i(t) response of (i=1,2,3) vibration displacement is bent
Line, solid line represents each rank dominant frequency displacement response curve in Fig. 4-Fig. 6, and it is bent that long phantom line segments represent each order frequency/intrinsic frequency displacement
Line, short dash line section represent each rank equivalent energy envelope.Since each vibration displacement response isolated according to each rank basic frequency is bent
Line can actually be equivalent to several single mode operating conditions etc., therefore can use processing method acquisition pair identical with single mode operating condition
si(t) the corresponding energy envelope line of (i=1,2,3) vibration displacement response curve
Finally by above-mentioned each rank basic frequency ωiCorresponding energy envelope line Ei(t) displacement envelope progress amplitude is superimposed to obtain gross energy packet
Winding thread ESum(t).Pass through gross energy envelopeAmplitude and vibration displacement error allowable it
Between comparison whether position completion come the movement mechanism judged under multi-modal operating condition.
The above is a preferred embodiment of the present invention, it is noted that for those skilled in the art
For, various improvements and modifications may be made without departing from the principle of the present invention, these improvements and modifications also regard
For protection scope of the present invention.
Claims (2)
1. a kind of multiple degrees of freedom space mechanism motion planning method, which is characterized in that comprising steps of
S1: multiple degrees of freedom space mechanism model is divided by several lists according to the freedom degree compositive relation of multiple degrees of freedom space mechanism
The component submodel of freedom degree, wherein the connection relationship position of the component submodel of each component submodel and next hierarchical link
For vibration pickup point；
S2: according to the geological information of each component submodel, establishing component finite element model accordingly comprising kinematics freedom degree,
By each component finite element model according to its drive diarthrodial assembly relation generate multiple degrees of freedom space mechanism comprising kinematics from
By the assembly finite element model spent；
S3: execution position needed for determining each driving link according to the anti-solution of movement of multiple degrees of freedom space mechanism point operation acts
It moves, and determines Parametric motion function used by each driving link；
S4: it is applied to using the Parametric motion function of each driving link as boundary condition described comprising kinematics freedom degree
Assembly finite element model in；
S5: according to the geometric nonlinear finite element model and Parametric motion functional boundary of mechanism, the multiple degrees of freedom space mechanism
Condition, obtains the motion simulation information of each component submodel in mechanism, multiple degrees of freedom space mechanism, and obtains the vibration in turn
Dynamic measurement point is relative to relative displacement, the velocity information for terminating ideal position；
S6: whether full come real-time judge multiple degrees of freedom space mechanism according to the relative displacement at each vibration pickup point, velocity information
The final positioning accuracy request of foot, repeats step S5, until meeting positioning accuracy request, and obtains vibration pickup point and meets positioning accurate
Degree requires the residual oscillation die-away time length used between moment and motion planning end time；
S7: residual oscillation die-away time and movement driving time are summed to obtain mass motion positioning time, and by whole fortune
The dynamic time, which minimizes, is used as optimization aim；
S8: if can be determined that the mass motion time is minimum value by iteration convergence criterion, the fortune in iterative process is corresponded to
Dynamic projecting parameter is optimized parameter；If the mass motion time is not minimum value, kinematic parameter is calculated based on gradient optimal method
Optimizing Search direction and step-size in search, and update the Parametric motion function in step S3, repeat step S3-S7 and be iterated
It calculates, until finding the optimized parameter of motion planning parameter in iterative process.
2. multiple degrees of freedom space mechanism as described in claim 1 motion planning method, which is characterized in that step S6 includes step
It is rapid:
S61: Fast Fourier Transform (FFT), bandpass filtering are carried out to the relative displacement at the vibration pickup point of each component, velocity information
Signal processing obtains the corresponding position of each rank intrinsic frequency in each rank intrinsic frequency on each component and its positioning residual oscillation course
It moves, speed motor message；
S62: when obtaining displacement corresponding to each rank intrinsic frequency and speed using the intrinsic frequency and displacement, speed signal of acquisition
Domain course curve, and the vibrational energy envelope of vibration pickup point on each component is obtained, the amplitude of the energy envelope line is
The equivalent potential energy of each component temporal motion course energy corresponding to the intrinsic frequency at each moment in temporal motion course
Maximum displacement；
S63: energy envelope line corresponding to each rank intrinsic frequency to each section of component obtained is overlapped, and obtains this section of component
On single-degree-of-freedom complex energy envelope, the single-degree-of-freedom complex energy envelope be this section of component in temporal motion course
Each moment position error maximum amplitude；
S64: each moment position error of each section of component is overlapped, and the very big positioning for obtaining multiple degrees of freedom space mechanism misses
Difference；
S65: compared with by the displacement error value allowable of the amplitude of very big placement error value and space mechanism work actuating station, when greatly fixed
When the amplitude of position error amount is less than movement mechanism displacement error allowable, then multiple degrees of freedom space mechanism meets positioning accuracy request.
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