CN112518738B - Cable parallel robot kinematics calibration method based on pulley kinematics - Google Patents
Cable parallel robot kinematics calibration method based on pulley kinematics Download PDFInfo
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- B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
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Abstract
The application discloses a kinematic calibration method of a cable parallel robot based on pulley kinematics, which comprises the following steps: modeling the inverse kinematics of the cable parallel robot under the condition of considering the kinematics of the pulley; modeling an error model under the condition of considering the pulley kinematics; establishing an unknown parameter identification equation by using a rope length residual error function; solving an identification matrix under the condition of considering the pulley kinematics; calibrating and measuring pose optimization is carried out according to the condition number index of the identification matrix and the switching point method; controlling the robot terminal to move to each measurement pose in sequence for measurement; substituting the measured data into an identification equation to solve identification parameters; and updating the robot kinematic model by using the parameter values obtained by solving. Therefore, the method can take the pulley mechanism of the cable-out position of the cable-parallel robot into consideration, obtain a more complete and accurate kinematic model and geometric parameters of the cable-parallel robot, and improve the control precision of the calibrated terminal position of the cable-parallel robot.
Description
Technical Field
The application relates to the technical field of robot kinematics calibration, in particular to a cable parallel robot kinematics calibration method based on pulley kinematics.
Background
The precision is one of the important performances of the robot, and the necessary condition for realizing the operation of the robot is to ensure that the pose precision of the robot terminal meets the given requirement. After the robot finishes manufacturing and assembling, the actual value and the theoretical design value of the kinematic geometrical parameter have difference due to manufacturing and assembling errors. When the motion control is carried out according to the theoretical geometric parameters, the error occurs between the practical pose of the terminal and the instruction pose. Inaccurate geometric parameters are identified through kinematics calibration, and robot kinematics model parameters are updated, so that the method is a feasible method for ensuring the robot precision.
Compared with a rigid robot, the kinematic chain of the cable-driven parallel robot is very compact and has no internal joints, which indicates the potential precision advantage. However, the practical situation is different from the theoretical expectation, and the low pose accuracy of the terminal becomes one of the main factors for limiting the application of the cable parallel robot. The low precision of the terminal of the cable parallel robot is mainly caused by two errors, namely geometric error and non-geometric error. Geometric errors mainly result from manufacturing and assembly errors of the structure, and non-geometric errors mainly include rope deformation and inaccurate rope models. In non-geometric errors, the rope model can improve modeling accuracy by adopting a catenary or parabolic model, and rope deformation can be eliminated by selecting a proper rope material or adjusting the tension. Therefore, the geometric error becomes a main influence factor influencing the accuracy of the cable parallel robot, especially the small-scale cable parallel robot terminal applied in the industry.
In the kinematic modeling of the cable parallel robot, an approximate point-to-point modeling method is widely adopted, the method takes the cable connecting point on a static platform and a movable platform as a fixed point, and models the cable by adopting a point-to-point straight line. In practice, however, the cable, after exiting the drum, is redirected through a plurality of pulleys and then exits the stationary platform and is connected to the movable platform. The use of pulleys helps to reduce wear and extend the life of the rope. When the pulley structure is used, the actual connection point position of the rope on the static platform is determined by the pulley mechanism, and the position of the connection point changes along with the change of the pose of the movable platform, which can affect the kinematics of the rope parallel robot. In the occasion with higher requirement on precision, pulley kinematics is taken into account, a complete kinematics model is established, kinematics calibration is carried out on the basis of the kinematics model, more accurate parameters are identified, and the improvement of the control precision of the cable parallel robot terminal is necessary.
Content of application
The application provides a kinematics calibration method of a cable parallel robot based on pulley kinematics, which overcomes the defect of large terminal error caused by the adoption of a point-to-point approximate modeling method of the existing cable parallel robot, and establishes an accurate kinematics model by taking the pulley structure at a cable outlet point into consideration through a more complete and accurate kinematics calibration method of the cable parallel robot, thereby establishing an accurate error model on the basis of a second time, completing the kinematics geometric parameter calibration and solving the problem of inaccurate approximate fitting caused by the traditional point-to-point modeling method.
The embodiment of the application provides a kinematic calibration method of a cable parallel robot based on pulley kinematics, which comprises the following steps:
s1: according to a preset cable parallel robot configuration, establishing a complete inverse kinematics model of the cable parallel robot containing pulley kinematics;
s2: analyzing an error term to be calibrated of the cable parallel robot, determining an adopted measuring method, and determining known parameters, measuring parameters and unknown parameters to be identified in calibration;
s3: establishing a cable parallel robot error model according to the mapping relation between the geometric kinematic parameter error to be identified and the measurement parameter error of the cable parallel robot;
s4: establishing an identification equation by using a rope length residual error function to obtain a nonlinear least squares target function for solving unknown parameters;
s5: respectively obtaining derivatives of the known parameters and the unknown parameters by the identification equation target function to obtain differential mapping relations of the known parameters and the unknown parameters, and obtaining a system identification matrix;
s6: optimizing calibration measurement poses according to the condition number index of the identification matrix and an exchange point method to obtain a measurement pose set for calibration, wherein the number of the measurement poses at least meets the solving requirement of a nonlinear least squares objective function;
s7: controlling the robot terminal moving platform to move to each measurement pose in sequence, measuring a measurement variable by using a corresponding instrument or sensor after the robot terminal moving platform is stopped and stabilized, simultaneously recording motor encoder data, and calculating rope elongation by using the motor encoder data;
s8: substituting the data measured in the step S7 into the nonlinear least squares objective function, solving by using an optimization algorithm, and solving to obtain an unknown geometric parameter or a geometric parameter error value of the robot;
s9: updating geometric kinematic parameters of the robot by using the calculation result obtained in the step S8, and simultaneously updating a kinematic model used for controlling the motion of the robot in the controller;
s10: and judging whether the precision requirement is met, if so, finishing the calibration, otherwise, repeatedly executing the steps S7-S9, and carrying out the next round of calibration iteration.
Optionally, the inverse kinematics model needs to obtain a relationship between the length of the rope and the pose of the terminal moving platform, where the length of the rope includes a length of a curve segment from a first tangent point of the rope entering the pulley to a second tangent point of the rope leaving the pulley and a length of a straight line segment from the second tangent point to a connecting point of the moving platform rope, an azimuth angle of the pulley mechanism at each rope exit point is first calculated according to the pose of the moving platform, then a position of the second tangent point is calculated, and accordingly, a wrap angle of the rope on the pulley is obtained to calculate the length of the curve segment and the length of the straight line segment, and the calculation methods respectively include:
Lr＝lc+rβ，
Ls＝||ci-bi||，
wherein L isrIs the length of the curve segment, LsIs the length of the straight line segment,/cIs a constant section and can be zero, beta is the wrap angle of the rope at the last rope outlet pulley, r is the arc radius of the rope wrapping section, ciIs a position vector of tangent point C, biIs the position vector of the cable connection point B.
Optionally, the error term comprises a rope initial length error δ L0The error delta a of the characteristic point position of the pulley mechanism can also comprise an error delta b of the connecting point position of the movable platform cable.
Alternatively, the calibration method can be divided into an external calibration method and an internal calibration method, and when the external calibration method is adopted, the unknown parameter is
Including the cable attachment point location a and the initial cable length L0Measured parameter is
When an internal calibration method is used, the unknown parameter is
Including a cable connection point position a and an initial cable length L0And the terminal real-time pose coordinate P; where m is the number of drive ropes and n is the number of terminal degrees of freedom.
Optionally, constructing the tether length residual function comprises: in any pose piAt this point, the rope length L obtained by the kinematic model calculation is calculatedciAnd the length L of the rope obtained by actual measurementmi＝L0+Lδi＝L0+γθiSubtracting and making it equal to zero to obtain rope residual function xiiThe calculation formula is as follows:
Lci＝fik(pi,a)，
Lmi＝L0+Lδi＝L0+γθi，
ξi(pi,a,L0,Lδi)＝fik(pi,a)-L0-Lδi＝0。
optionally, the method for establishing the target function of the identification equation includes: adding rope residual functions of all the measuring points together to obtain a residual equation set f (x, y), and constructing a least square problem g by using foptThe calculation formula is as follows:
f＝[ξ1 T…ξk T]T，
optionally, the system identification matrix H is obtained as follows: solving the objective function f in each element of x and yBy partial derivation, delta can be obtainedxAnd deltayThe relationship between them is:
the identification matrix H can be obtained as:
optionally, calibrating the measurement poses preferably comprises selecting a number of measurement poses and obtaining distribution coordinates of the given number of measurement poses within the working space.
Optionally, judging whether the accuracy requirement is met by a geometric parameter accuracy judgment method and a terminal error accuracy judgment method, wherein the geometric accuracy judgment method is used for calculating the error between the geometric parameter obtained by the current round of calibration and the geometric parameter obtained by the previous round of calibration and judging whether the error is within a given error limit; the terminal error precision judging method is to calculate the terminal error of the measuring point after the current round of calibration, compare the terminal error with the terminal error of the measuring point after the previous round of calibration and judge whether the error change is within the given limit.
Therefore, in the process of kinematic modeling, the pulley mechanism at the cable outlet position of the static platform is taken into consideration, the pulley radius and the cable outlet position time-varying characteristic brought by the accompanying motion of the pulley are taken into consideration, and a complete kinematic model is established, so that compared with the traditional approximate point-to-point modeling, the modeling precision is improved; in the kinematic calibration, the pulley kinematics is taken into account, a new error model and an error identification matrix are obtained, the invariant tangent point of the rope and the pulley is used as an identification characteristic position point, the identification precision is improved, and real geometric parameters rather than virtual fitting approximate points are obtained.
Additional aspects and advantages of the present application will be set forth in part in the description which follows and, in part, will be obvious from the description, or may be learned by practice of the present application.
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The foregoing and/or additional aspects and advantages of the present application will become apparent and readily appreciated from the following description of the embodiments, taken in conjunction with the accompanying drawings of which:
fig. 1 is a flowchart of a kinematic calibration method for a cable parallel robot based on pulley kinematics according to an embodiment of the present application;
FIG. 2 is a flow chart of a kinematic calibration method of a cable parallel robot based on pulley kinematics according to an embodiment of the present application;
FIG. 3 is an example of a three-degree-of-freedom cable parallel robot with a pulley structure according to an embodiment of the present disclosure;
FIG. 4 is a kinematic diagram of a DOF cable parallel robot in consideration of pulley kinematics according to an embodiment of the present application;
FIG. 5 is a flow chart of an embodiment of the present application for a preferred method of measuring pose;
FIG. 6 is an example of a condition number versus number of measurement poses for the recognition matrix according to one embodiment of the present application.
Detailed Description
Reference will now be made in detail to embodiments of the present application, examples of which are illustrated in the accompanying drawings, wherein like or similar reference numerals refer to the same or similar elements or elements having the same or similar function throughout. The embodiments described below with reference to the drawings are exemplary and intended to be used for explaining the present application and should not be construed as limiting the present application.
The method for calibrating the kinematics of the cable parallel robot based on the pulley kinematics is described below with reference to the accompanying drawings.
Specifically, fig. 1 is a schematic flow chart of a method for calibrating kinematics of a cable parallel robot based on pulley kinematics according to an embodiment of the present disclosure.
As shown in fig. 1, the method for calibrating the kinematics of the cable parallel robot based on the pulley kinematics comprises the following steps:
s1: according to a preset cable parallel robot configuration, establishing a complete inverse kinematics model of the cable parallel robot containing pulley kinematics;
s2: analyzing an error term to be calibrated of the cable parallel robot, determining an adopted measuring method, and determining known parameters, measuring parameters and unknown parameters to be identified in calibration;
s3: establishing a cable parallel robot error model according to the mapping relation between the geometric kinematic parameter error to be identified and the measurement parameter error of the cable parallel robot;
s4: establishing an identification equation by using a rope length residual error function to obtain a nonlinear least squares target function for solving unknown parameters;
s5: respectively obtaining derivatives of the known parameters and the unknown parameters by the identification equation target function to obtain differential mapping relations of the known parameters and the unknown parameters and obtain a system identification matrix;
s6: optimizing calibration measurement poses according to the condition number index of the identification matrix and the exchange point method to obtain a measurement pose set for calibration, wherein the number of the measurement poses at least meets the solving requirement of a nonlinear least squares objective function;
s7: controlling the robot terminal moving platform to move to each measurement pose in sequence, measuring a measurement variable by using a corresponding instrument or sensor after the robot terminal moving platform is stopped and stabilized, simultaneously recording motor encoder data, and calculating rope elongation by using the motor encoder data;
s8: substituting the data measured in the step S7 into a nonlinear least squares objective function, solving by using an optimization algorithm, and solving an unknown geometric parameter or geometric parameter error value of the robot;
s9: updating the geometric kinematic parameters of the robot by using the calculation result obtained in the step S8, and simultaneously updating a kinematic model for controlling the motion of the robot in the controller;
s10: and judging whether the precision requirement is met, if so, finishing the calibration, otherwise, repeatedly executing the steps S7-S9, and carrying out the next round of calibration iteration.
Optionally, the inverse kinematics model needs to obtain a relationship between the length of the rope and the pose of the terminal moving platform, where the length of the rope includes a length of a curve segment from a first tangent point of the rope entering the pulley to a second tangent point of the rope leaving the pulley and a length of a straight line segment from the second tangent point to a connecting point of the moving platform rope, an azimuth angle of the pulley mechanism at each rope exit point is first calculated according to the pose of the moving platform, then a position of the second tangent point is calculated, and accordingly, a wrap angle of the rope on the pulley is obtained to calculate the length of the curve segment and the length of the straight line segment, and the calculation methods respectively include:
Lr＝lc+rβ，
Ls＝||ci-bi||，
wherein L isrIs the length of the curve segment, LsIs the length of the straight line segment,/cIs a constant section and can be zero, beta is the wrap angle of the rope at the last rope outlet pulley, r is the arc radius of the rope wrapping section, ciIs a position vector of tangent point C, biIs the position vector of the cable connection point B.
Optionally, the error term comprises a rope initial length error δ L0The error delta a of the characteristic point position of the pulley mechanism can also comprise an error delta b of the connecting point position of the movable platform cable.
Alternatively, the calibration method can be divided into an external calibration method and an internal calibration method, and when the external calibration method is adopted, the unknown parameter is
Including the cable attachment point location a and the initial cable length L0Measured parameter is
When an internal calibration method is used, the unknown parameter is
Including a cable connection point position a and an initial cable length L0And the terminal real-time pose coordinate P; where m is the number of drive ropes and n is the number of terminal degrees of freedom.
Optionally, a rope length residual function is constructedThe method comprises the following steps: in any pose piAt this point, the rope length L obtained by the kinematic model calculation is calculatedciAnd the length L of the rope obtained by actual measurementmi＝L0+Lδi＝L0+γθiSubtracting and making it equal to zero to obtain rope residual function xiiThe calculation formula is as follows:
Lci＝fik(pi,a)，
Lmi＝L0+Lδi＝L0+γθi，
ξi(pi,a,L0,Lδi)＝fik(pi,a)-L0-Lδi＝0。
optionally, the method for establishing the target function of the identification equation includes: adding rope residual functions of all the measuring points together to obtain a residual equation set f (x, y), and constructing a least square problem g by using foptThe calculation formula is as follows:
f＝[ξ1 T … ξk T]T，
optionally, the system identification matrix H is obtained as follows: the target function f is subjected to partial derivation on each element in x and y to obtain deltaxAnd deltayThe relationship between them is:
the identification matrix H can be obtained as:
optionally, calibrating the measurement poses preferably comprises selecting a number of measurement poses and obtaining distribution coordinates of the given number of measurement poses within the working space.
Optionally, judging whether the accuracy requirement is met by a geometric parameter accuracy judgment method and a terminal error accuracy judgment method, wherein the geometric accuracy judgment method is used for calculating the error between the geometric parameter obtained by the current round of calibration and the geometric parameter obtained by the previous round of calibration and judging whether the error is within a given error limit; the terminal error precision judging method is to calculate the terminal error of the measuring point after the current round of calibration, compare the terminal error with the terminal error of the measuring point after the previous round of calibration and judge whether the error change is within the given limit.
Specifically, with reference to fig. 2, a cable parallel robot inverse kinematics model (01) considering the pulley kinematics is established; analyzing a main error term (02); establishing a cable parallel robot error model (03); establishing a parameter identification equation and an identification matrix (04) of the cable parallel robot under the condition of considering the pulleys; measuring pose optimization (05) is carried out by utilizing the condition number of the identification matrix; substituting robot name parameter values into the inverse kinematics model (06); controlling the robot terminal to move to each measurement pose in sequence, and measuring the actual pose encoder reading (07) arriving at each pose by using an instrument or a sensor; calculating rope elongation using the encoder readings (08); substituting the measured data into an identification equation, and solving a parameter to be identified by using an algorithm (09); updating (10) parameters within the controller; calculating a parameter residual (11); judging whether the precision reaches the standard (12); until it is finished (13).
As shown in fig. 3, fig. 3 is an example of a three-degree-of-freedom parallel cable robot with a pulley structure and a kinematic structure diagram thereof, the robot is driven by six cables, the six cables are divided into three groups, two cables of each group are arranged in parallel and are wound on a roller after being guided by pulleys. The parallel ropes can ensure that the movable platform is always parallel to the static platform and does not rotate under the condition that the ropes are fully tensioned, and three-degree-of-freedom translational motion is realized. The middle driven rod consists of a rigid rod and a compression spring which are coaxially arranged, the driven rod can longitudinally extend, and two ends of the driven rod are respectively connected with the centers of the static platform and the movable platform through hooke joints. The spring is located between the static platform and the moving platform and is compressed throughout the movement to create a downward pressure on the moving platform to keep all the cords in tension and achieve the desired downward acceleration. The robot uses a dual pulley configuration at the exit point. The following describes the implementation method of each step in sequence with reference to the robot example.
Establishing an inverse kinematics model (01) of the cable parallel robot considering the pulley kinematics:
fig. 4 shows a kinematic diagram of the robot in consideration of the pulley kinematics. Since the parallel ropes move synchronously all the time, they can be considered as one rope when modeling kinematics. Equilateral triangle A1A2A3Is a static platform, and the radius of the circumscribed circle is R, AiIs the tangent point of the rope outlet pulley and the vertical rope. A. theiIs a fixed point and does not change position during movement. Equilateral triangle B1B2B3The radius of the circumscribed circle of the movable platform is r. B isiIs a cable connecting point on the movable platform. P is the center of the movable platform. Rope from point AiEnters a pulley mechanism, winds a section of circular arc on the pulley and passes through a tangent point CiAway from the pulley. A. theiAnd BiThe actual rope length in between is equal to line segment BiCiLength of (d) plus arc AiCiLength of (d). Establishing a basic coordinate system { O-XYZ } in the center of the static platform, wherein the X axis is parallel to A1A2Coincidence, Y-axis and OA3Coinciding with the Z axis vertically upward. In AiPoint establishing local coordinate system { A }i-xiyiziIn which xiFrom AiPointing to the point O, ziVertically upwards, yiPerpendicular to AiO and meets the right hand rule. Note the i-th set of pulley planes and xiThe included angle of the axes (i.e. the attitude of the set of sheaves) is alphaiThe wrap angle of the rope on the pulley being betai. The radius of the arc segment of the rope is recorded as rpThe radius is the sum of the pulley radius and the rope radius. Coordinate system { A }i-xiyiziThe rotation matrix with respect to the global coordinate system { O-XYZ } is notediROObtaining:
wherein phi1＝4π/3，φ2Is equal to 0 and phi3＝2π/3。
Cable connection point BiIn the coordinate system { Ai-xiyiziThe position in (v) } is noted asAbiAnd, and:
Abi＝iRO(p+bi)＝iROp+iRObi＝[xi yi zi]T。
azimuth angle alpha of rope planeiCan be calculated by the following inverse trigonometric function:
the center point of the pulley is marked as Mi，MiIn the coordinate system { Ai-xiyiziThe position vector under (v) } is miAnd:
mi＝[rp cosαi rp sinαi 0]T。
point MiAnd BiThe distance d of (d) is:
where ρ isiIs a cable connecting point BiAnd the origin AiA horizontal distance of
The wrap angle of the rope on the pulley can be obtained as：
Point CiIn the coordinate system { Ai-xiyiziThe position vector coordinates of are:
Aci＝[rp(1-cosβi)cosαi rp(1-cosβi)sinαi-rp sinβi]T，
thus, the rope is at tangent point CiAnd moving platform cable connecting point BiThe straight line segment between is li＝A ci-AbiThe actual length of the rope is as follows:
Li＝li+rpβi＝||Aci-A bi||+rpβi。
given pulley radius rpAnd a movable platform position p, the expression of the actual rope length can be obtained by using the formula, and the inverse kinematics modeling of the rope parallel robot under the condition of considering the pulley kinematics is completed.
Analysis of the main error term (02):
common error items of the cable parallel robot include a static platform cable outlet point error, a cable length error and a movable platform cable connecting point error. In the robot example given in fig. 2, since the robot adopts a parallel cable structure, the static platform cannot be pulled out of the cable point aiAnd movable platform cable connecting point biAre considered unknown error parameters that would otherwise result in an array-less solution. Thus suppose biIs accurate because biIs often significantly less than aiThe error of (2). Therefore, the error terms considered in the calibration are determined as the dead platform rope-out point error delta a and the rope initial length error delta L0。
Establishing a cable parallel robot error model (03):
position of cable-out point uses ai(i-1, 2, …, m) represents aiWhich represents the tangent point at which the rope enters the pulley and is also a constant point in the operation of the pulley. For an n-degree-of-freedom cable parallel robot driven by m cables (corresponding to m cable outlet points), the aim of calibration is to identify the installation positions a of the m cable outlet points of the pulleysiAnd initial length L of m ropesi0. Suppose m pulley exit points AiThe position vector of (a) constitutes a resultant vector:
during calibration, the movable platform moves to k selected measuring point positions in sequence, and a measuring point position set is represented as follows:
at each given terminal position p by means of an inverse kinematics modeliAnd a rope length value can be obtained under the condition of a rope outlet point a:
Li＝fik(pi,a)。
in the formula (f)ik(piA) implicit function representing inverse kinematics, fik(piAnd a) is obtainable by step (01). At calibration time a is the unknown number to be identified, piIs the terminal true position. To solve the geometric parameter a, the rope length L needs to be obtainediThe value of (c). In cable parallel robot motion control, typically a motor encoder is used to record rope length changes and for feedback control. The position p can be establishediThe relationship between the measured rope length and the motor rotation angle is as follows:
Lmi＝L0+Lδi＝L0+γθi，
wherein L isiIs the actual length of the i-th group of ropes, L0Initial length of rope before robot movement, LδIs the amount of change of the rope relative to the initial pose. L isδ＝γθi，θiFor the angle of rotation of the motor, by encodersRecording and obtaining; gamma is the comprehensive transmission ratio, is determined by the reduction ratio, the radius of the roller and the like, and the value of gamma is known in advance before calibration.
At each measuring point piCalculating the difference between the rope length predicted by the geometric kinematic model and the rope length actually measured, a set of closed loop equations can be obtained, as follows:
ξi(pi,a,L0,Lδi)＝fik(pi,a)-L0-Lδi＝0。
ξi(pi,a,L0,Lδi) Is shown at point piThe rope residual function of (a). Under the condition that all groups of parameters are true and accurate, the residual function xii(pi,a,L0,Lδi) Should be zero. All the parameters which can be measured and obtained are summarized into a resultant vector y, and all the unknowns to be calibrated are summarized into a resultant vector x. The robot moves to k measured target poses in sequence, corresponding measurement parameter values are recorded respectively, and a residual error equation set consisting of k sets of residual errors can be obtained. Let f be xi1 T … ξk T]TFor the set of closed-loop equations for all k measurement points, ξi(pi,a,L0,Lδi) Stacking from 1 to k, to obtain:
f(x,y)＝0。
supposing that external measurement is adopted for measurement and calibration, the pose of a terminal measuring point is generally obtained through measurement, and the position of a cable exit point and the initial cable length are used as unknown parameters to be identified, and then:
in calibration, the measurement parameter value y inevitably contains a measurement error δyThis will result inA calibration identification error deltax. The target function f is subjected to partial derivation on each element in x and y to obtain deltaxAnd deltayThe relationship between them is:
from the above formula, two Jacobian matrices, J, can be obtainedxAnd Jy. Taking a mapping matrix of the terminal error and the geometric parameter error to be identified as an identification matrix, and marking the mapping matrix as H (P), delta and deltayAnd deltaxThe mapping expression of (a) is:
and establishing an error model of the cable parallel robot.
Establishing a parameter identification equation and an identification matrix (04) of the cable parallel robot under the condition of considering the pulleys:
in the ideal case, i.e. in the absence of calculation and measurement errors, the equation ξi＝fik(pi,a)-L0-LδiIf 0 is true, the unknown geometric parameter can be identified by solving the equation f (x, y) to 0. However, due to the presence of measurement errors and calculation truncation errors, the residual function ξ described aboveiIt cannot be completely zero. The target of the kinematic calibration is changed into a group of optimal solutions for searching geometric parameters to be identified, so that the optimal solution is obtained by the following least square problem:
the above equation is the parameter identification equation of the robot. To solve the error identification matrix, it is necessary to obtain the partial derivatives of the geometric parameters to be identified of the target equation
And partial derivatives of the measured parameters
The results were respectively:
wherein I represents an identity matrix of the corresponding dimension.
And because of
Therefore, it is not only easy to use
Wherein
And
the corrected linear segment unit vectors of the driving ropes are respectively obtained. In addition, the following are available:
wherein
Is the inverse jacobian matrix of the cable parallel robot. To this end, matrix HiAnalytic expressions of all sub-matrices in (1)Are all obtained, HiCan be rewritten as:
the robot system identification matrix H consisting of k measurement points is:
and (5) measuring pose optimization is carried out by utilizing the condition number of the identification matrix (05):
to select a number of measurement points, the operating space is first discretized and each discrete measurement point is numbered sequentially. And selecting the condition number of the error identification matrix H as a judgment index for judging whether the measuring point set is good or not. The preferred problem of the survey point can be summarized as an optimization model as follows: selecting k measuring points as few as possible in the measuring point set to be selected, so that the condition number kappa of an identification matrix H consisting of the k measuring point positions is ensuredkAnd minimum. The mathematical expression is as follows:
in the formula, gcWorking space constraint, ξ, representing pose of moving platformiPopulation representing the composition of the measurement points, κk(H) And the condition number of an identification matrix formed by k measuring point poses is represented. The preferred steps of determining the measuring points in the operation space of the cable parallel robot by combining the exchange point method are shown in FIG. 5 and mainly comprise the following steps:
step 1: randomly and primarily selecting k measurement points in a discrete measurement point set in an operation space to form an initial measurement point population xik。
Step 2: selecting a point xi from the remaining discrete measurement points in turneAnd xikCombining to obtain N-k new measuring point populations consisting of k +1 measuring points
Sequentially calculating the condition numbers of the identification matrix corresponding to each new population, and recording
And obtaining a corresponding new population xik+1。
And step 3: in a new population xik+1In turn, remove a point xiRObtaining k +1 populations composed of the remaining k measuring points
Calculate each
Corresponding condition value is found so that
Is the minimum condition number ofR。
And 4, step 4: judging the newly added measuring point xi in step 2eAnd removing the measuring point xi in step 3RWhether it is the same point. If yes, the optimization is finished, and the solved k is solved at the momentk(H) For the minimum value of the optimization problem, the corresponding population is the optimal measurement point population; otherwise, returning to the step 2 and the step 3, and performing the next cycle operation until xieAnd xiRAre the same point.
The measuring points preferably need to select the number of the measuring points and the pose of the measuring points. Setting the value of the number k of the measuring points, executing an optimal program according to the flow, and calculating the obtained identification matrix condition values of the k optimal measuring points. Because the initial selected measuring point population has randomness, the point selection program is executed for multiple times under each k value condition, and the average value of multiple results is taken as the condition numerical value corresponding to k preferred measuring points. The condition number of the identification matrix of the example robot is shown as a function of the number k of the preferred measuring points under the condition of considering the kinematics of the pulley in figure 6. And according to the curve change result, comprehensively considering condition number minimization and calibration efficiency, and selecting k as 15.
And running the optimization program under the condition that the number k of the optimization points is set to be 15, so that a set of optimization measurement poses and the numbers thereof can be obtained. And the measurement pose coordinates and the distribution thereof in the working space can be obtained by combining the coordinates corresponding to each pose number in the dispersion process.
Substituting robot name parameter values into the inverse kinematics model (06):
and during the first calibration, taking the geometric parameter design value of the robot as a nominal value before calibration, substituting the nominal value into the robot controller, and completing the writing of the inverse kinematics model. In the subsequent iteration process, the latest geometric parameters of the robot obtained in the last calibration identification step are used as nominal values before calibration.
Controlling the robot terminal to move to each measuring pose in sequence, and measuring the actual pose and the motor encoder reading (07) reached at each pose by using an instrument or a sensor;
rope elongation was calculated using encoder readings (08):
at each position and position measuring point, the reading of each servo motor encoder when the robot actually reaches the point is recorded and converted into the rotation angle theta of each motoriThen calculating the rope length elongation L according to the known transmission ratioδi＝γθi。
Substituting the measured data into an identification equation, and solving a parameter to be identified by using an algorithm (09):
the actual pose coordinate p obtained by measurement in the step (07)iAnd the rope elongation L obtained by calculation in the step (08)δiSubstituted into the following equation
ξi(pi,a,L0,Lδi)＝fik(pi,a)-L0-Lδi＝0。
Combining rope length residual functions of all the measurement pose points to form a least square equation set
And solving the above formula by using an algorithm to obtain unknown parameters to be identifieda and L0Wherein the algorithm can be Levenberg-Marquardt (L-M) algorithm.
Updating (10) parameters within the controller:
using the newly obtained parameters a and L0And updating the parameters of the kinematic model of the controller, wherein the updating method is to replace the corresponding old parameters with the new parameters, and the others are unchanged.
Calculating the parameter residual (11):
calculating newly obtained parameters a and L0Parameters a and L of the previous round0The difference value of (a).
Judging whether the precision reaches the standard (12):
and judging whether the difference value zeta is within a given allowable range epsilon, namely judging that zeta is less than or equal to epsilon. If the range is within the given range, the calibration is finished, and a and L are finally identified0The final calibration result is obtained. And if the requirement is not met, repeating the steps 06 to 13, performing the next round of calibration iteration until the identification precision meets the requirement, and ending the calibration (13).
According to the method for calibrating the kinematics of the cable parallel robot based on the pulley kinematics, the method is provided.
In the description herein, reference to the description of the term "one embodiment," "some embodiments," "an example," "a specific example," or "some examples," etc., means that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the application. In this specification, the schematic representations of the terms used above are not necessarily intended to refer to the same embodiment or example. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or N embodiments or examples. Furthermore, various embodiments or examples and features of different embodiments or examples described in this specification can be combined and combined by one skilled in the art without contradiction.
Furthermore, the terms "first", "second" and "first" are used for descriptive purposes only and are not to be construed as indicating or implying relative importance or implicitly indicating the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one such feature. In the description of the present application, "N" means at least two, e.g., two, three, etc., unless specifically limited otherwise.
Any process or method descriptions in flow charts or otherwise described herein may be understood as representing modules, segments, or portions of code which include one or more N executable instructions for implementing steps of a custom logic function or process, and alternate implementations are included within the scope of the preferred embodiment of the present application in which functions may be executed out of order from that shown or discussed, including substantially concurrently or in reverse order, depending on the functionality involved, as would be understood by those reasonably skilled in the art of implementing the embodiments of the present application.
The logic and/or steps represented in the flowcharts or otherwise described herein, e.g., an ordered listing of executable instructions that can be considered to implement logical functions, can be embodied in any computer-readable medium for use by or in connection with an instruction execution system, apparatus, or device, such as a computer-based system, processor-containing system, or other system that can fetch the instructions from the instruction execution system, apparatus, or device and execute the instructions. For the purposes of this description, a "computer-readable medium" can be any means that can contain, store, communicate, propagate, or transport the program for use by or in connection with the instruction execution system, apparatus, or device. More specific examples (a non-exhaustive list) of the computer-readable medium would include the following: an electrical connection (electronic device) having one or N wires, a portable computer diskette (magnetic device), a Random Access Memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber device, and a portable compact disc read-only memory (CDROM). Additionally, the computer-readable medium could even be paper or another suitable medium upon which the program is printed, as the program can be electronically captured, via for instance optical scanning of the paper or other medium, then compiled, interpreted or otherwise processed in a suitable manner if necessary, and then stored in a computer memory.
It should be understood that portions of the present application may be implemented in hardware, software, firmware, or a combination thereof. In the above embodiments, the N steps or methods may be implemented in software or firmware stored in a memory and executed by a suitable instruction execution system. If implemented in hardware, as in another embodiment, any one or combination of the following techniques, which are known in the art, may be used: a discrete logic circuit having a logic gate circuit for implementing a logic function on a data signal, an application specific integrated circuit having an appropriate combinational logic gate circuit, a Programmable Gate Array (PGA), a Field Programmable Gate Array (FPGA), or the like.
It will be understood by those skilled in the art that all or part of the steps carried by the method for implementing the above embodiments may be implemented by hardware related to instructions of a program, which may be stored in a computer readable storage medium, and when the program is executed, the program includes one or a combination of the steps of the method embodiments.
In addition, functional units in the embodiments of the present application may be integrated into one processing module, or each unit may exist alone physically, or two or more units are integrated into one module. The integrated module can be realized in a hardware mode, and can also be realized in a software functional module mode. The integrated module, if implemented in the form of a software functional module and sold or used as a stand-alone product, may also be stored in a computer readable storage medium.
The storage medium mentioned above may be a read-only memory, a magnetic or optical disk, etc. Although embodiments of the present application have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present application, and that variations, modifications, substitutions and alterations may be made to the above embodiments by those of ordinary skill in the art within the scope of the present application.
Claims (9)
1. A kinematic calibration method of a cable parallel robot based on pulley kinematics is characterized by comprising the following steps:
s1: according to a preset cable parallel robot configuration, establishing a complete inverse kinematics model of the cable parallel robot containing pulley kinematics;
s2: analyzing an error term to be calibrated of the cable parallel robot, determining an adopted measuring method, and determining known parameters, measuring parameters and unknown parameters to be identified in calibration;
s3: establishing a cable parallel robot error model according to the mapping relation between the geometric kinematic parameter error to be identified and the measurement parameter error of the cable parallel robot;
s4: establishing an identification equation by using a rope length residual error function to obtain a nonlinear least squares target function for solving unknown parameters;
s5: respectively obtaining derivatives of the known parameters and the unknown parameters by the identification equation target function to obtain differential mapping relations of the known parameters and the unknown parameters, and obtaining a system identification matrix;
s6: optimizing calibration measurement poses according to the condition number index of the identification matrix and an exchange point method to obtain a measurement pose set for calibration, wherein the number of the measurement poses at least meets the solving requirement of a nonlinear least squares objective function;
s7: controlling the robot terminal moving platform to move to each measurement pose in sequence, measuring a measurement variable by using a corresponding instrument or sensor after the robot terminal moving platform is stopped and stabilized, simultaneously recording motor encoder data, and calculating rope elongation by using the motor encoder data;
s8: substituting the data measured in the step S7 into the nonlinear least squares objective function, solving by using an optimization algorithm, and solving to obtain an unknown geometric parameter or a geometric parameter error value of the robot;
s9: updating geometric kinematic parameters of the robot by using the calculation result obtained in the step S8, and simultaneously updating a kinematic model used for controlling the motion of the robot in the controller;
s10: and judging whether the precision requirement is met, if so, finishing the calibration, otherwise, repeatedly executing the steps S7-S9, and carrying out the next round of calibration iteration.
2. The method for calibrating the kinematics of the cable parallel robot based on the pulley kinematics as recited in claim 1,
the inverse kinematics model needs to obtain the relationship between the length of the rope and the pose of the terminal moving platform, wherein the length of the rope comprises the length of a curve segment from a first tangent point of the rope entering a pulley to a second tangent point of the rope leaving the pulley and the length of a straight line segment from the second tangent point to a connecting point of the moving platform rope, the azimuth angle of a pulley mechanism at each rope outlet point is firstly calculated according to the pose of the moving platform, then the position of the second tangent point is calculated, the wrap angle of the rope on the pulley is obtained according to the position, and the length of the curve segment and the length of the straight line segment are calculated by the calculation methods which respectively comprise:
Lr＝lc+rβ，
Ls＝||ci-bi||，
wherein L isrIs the length of the curve segment, LsIs the length of the straight line segment,/cIs a constant section and can be zero, beta is the wrap angle of the rope at the last rope outlet pulley, r is the arc radius of the rope wrapping section, ciIs a position vector of tangent point C, biIs the position vector of the cable connection point B.
3. The method for calibrating kinematics of a cable parallel robot based on pulley kinematics as recited in claim 1, wherein said error term comprises a rope initial length error δ L0The pulley mechanism characteristic point position error delta a also comprises a movable platform cable connecting point position error delta b.
4. Method for calibrating kinematics of a cable parallel robot based on pulley kinematics according to claim 1, wherein the calibration methods are divided into an external calibration method and an internal calibration method, when an external calibration method is usedUnknown parameter is
Including the cable attachment point location a and the initial cable length L0Measured parameter is
When an internal calibration method is used, the unknown parameter is
Including a cable connection point position a and an initial cable length L0And the terminal real-time pose coordinate P; where m is the number of drive ropes and n is the number of terminal degrees of freedom.
5. The method for calibrating the kinematics of the cable parallel robot based on the pulley kinematics as recited in claim 1,
constructing a cord length residual function includes: in any pose piAt this point, the rope length L obtained by the kinematic model calculation is calculatedciAnd the length L of the rope obtained by actual measurementmi＝L0+Lδi＝L0+γθiSubtracting and making it equal to zero to obtain rope residual function xiiThe calculation formula is as follows:
Lci＝fik(pi,a)，
Lmi＝L0+Lδi＝L0+γθi，
ξi(pi,a,L0,Lδi)＝fik(pi,a)-L0-Lδi＝0。
6. the kinematics calibration method of the cable parallel robot based on the pulley kinematics as claimed in claim 1, wherein the identification equation objective function is established by: rope residual error functions of all the measuring points are superposed together to obtain an objective function f, and a least square problem g is constructed by using the objective function foptThe calculation formula is as follows:
f＝[ξ1 T … ξk T]T，
7. the method for calibrating the kinematics of the cable parallel robot based on the pulley kinematics as recited in claim 1,
the system identification matrix H is obtained as follows: the target function f is subjected to partial derivation on each element in x and y to obtain deltaxAnd deltayThe relationship between them is:
the identification matrix H can be obtained as:
8. the method of claim 1, wherein calibrating the measurement poses comprises selecting a number of measurement poses and obtaining distribution coordinates of the given number of measurement poses within the working space.
9. The method for calibrating the kinematics of the cable parallel robot based on the pulley kinematics as claimed in claim 1, wherein the method comprises the steps of determining whether the precision requirement is met by a geometric parameter precision determination method and a terminal error precision determination method, wherein the geometric precision determination method is used for calculating the error between the geometric parameter obtained by the current calibration and the geometric parameter obtained by the previous calibration and determining whether the error is within a given error limit; the terminal error precision judging method is to calculate the terminal error of the measuring point after the current round of calibration, compare the terminal error with the terminal error of the measuring point after the previous round of calibration and judge whether the error change is within the given limit.
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