CN108995829B - Platform on-orbit calibration method - Google Patents
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Abstract
A platform on-orbit calibration method, in particular to a six-degree-of-freedom Gough-Stewart platform on-orbit calibration method, reduces the load triaxial attitude coupling coefficient of an actuator of an active pointing hyperstatic platform by compensating the actuator force coefficient of the active pointing hyperstatic platform. The method comprises the following steps: according to the three-axis attitude and the three-axis main inertia of the load whole subjected to normalization processing, determining a resultant moment normalization result actually suffered by the three axes of the mass center of the load whole; and according to the translation displacement of the load mass center subjected to normalization processing, normalizing the three-axis actual acting force of the load mass center. And performing iterative computation to give an optimal solution of the force coefficient of the actuator according to the translational displacement of the load mass center subjected to normalization processing and the three-axis actual acting force of the load mass center subjected to normalization processing. Compensating driving current of the active directional hyperstatic actuator according to the identified actuator force coefficient, realizing load triaxial attitude decoupling of the active directional hyperstatic platform, and reducing triaxial attitude coupling coefficient.
Description
Technical Field
The invention belongs to the field of spacecraft attitude control, and relates to a platform on-orbit calibration method.
Background
At present, the optical load of the spacecraft points at high precision and the kinematics parameters of which the control can not be accurate are high in stability. And because the counter electromotive force coefficients of the motors in the actuators are different, the output forces of the motors are different under the same input condition. This allows significant coupling of the three-axis attitude of the load. Therefore, the force coefficient of an actuator for decoupling the load attitude is required to be calibrated, and the load triaxial attitude coupling coefficient is reduced.
The single actuator force coefficient calibration method has the following defects:
1. in the existing hyperstatic platform load high-precision control, the force coefficient calibration of a single actuator is usually only carried out, and the centralized calibration of the force coefficients of a plurality of actuators cannot be realized;
2. the existing calibration technology needs to obtain the load mass center attitude and the mass center translational displacement simultaneously in the calibration process of a plurality of actuators. When the translational displacement of the load mass center cannot be obtained, the existing calibration method is difficult to realize the accurate calibration of the force coefficients of a plurality of actuators.
3. The active directional hyperstatic platform formed by a plurality of actuators has a platform configuration error which directly influences the three-axis attitude error of the load. Single actuator force coefficient calibration method in prior art does not calibrate load centroid Jacobian matrix JpThe load attitude error caused by configuration deviation, namely the Jacobian matrix J of the centroid of the load can not be solvedpThe difference between the actual value and the theoretical design causes the load attitude deviation problem.
Disclosure of Invention
The technical problem solved by the invention is as follows: the method overcomes the defects of the prior art, can greatly reduce the load triaxial attitude coupling coefficient, and provides a technical basis for high-precision pointing, high-stability control and rapid and stable control of the optical load of the spacecraft.
The technical solution of the invention is as follows:
a platform on-orbit calibration method comprises the following steps:
1) taking all the loads carried by the platform as a whole, and solving the mass center of the whole asDetermining the resultant moment normalization result tau actually suffered by the three shafts of the load equivalent mass center according to the three-shaft attitude and the three-shaft main inertia of the load equivalent mass centerreal，norm(ii) a According to the translational displacement r of the equivalent center of mass of the loadpDetermining the load equivalent mass center three-axis actual acting force normalization result Freal，norm；
2) Iteratively correcting the force normalization result according to the resultant moment normalization result and the resultant moment expected value taur＝[τ1τ2τ3]Finding the optimal solution, tau, with the force normalization result approaching 01，τ2，τ3Respectively obtaining expected values of moments of a rolling shaft, a pitching shaft and a yawing shaft of the load equivalent mass center;
3) and determining the force coefficient of the actuator according to the optimal solution of the acting force normalization result approaching to 0 and the resultant moment normalization result, and finishing calibration.
Normalizing the result according to the resultant moment and the resultant moment expected value taur＝[τ1τ2τ3]The method for finding the optimal solution of the acting force normalization result approaching 0 specifically comprises the following steps:
21) determining an index function J according to a resultant moment normalization result and an acting force normalization resultreal；
22) Judgment index function JrealWhether the absolute value is less than the critical value, if so, the index function JrealDetermining the normalized result of the acting force as the optimal solution; if not, entering step 23); the critical value is less than 10-3。
23) Iteratively correcting the action force normalization result, and repeating the step 22) until an optimal solution of the action force normalization result is obtained.
The index function JrealThe method specifically comprises the following steps:
Freal,norm(n)＝[FrealxFrealyFrealz]，
τreal,norm＝[τrealxτrealyτrealz]，
τr＝[τ1τ2τ3]，
Freal,norm(0)＝Freal，norm，
wherein, the lower foot marks realx, realy and realz respectively represent the components on the rolling axis, the pitching axis and the yawing axis of the equivalent center of mass of the load, and tau1，τ2，τ3Roll axis, pitch axis and yaw axis torque expectation values, n being 0,1, 2.
The method for iteratively correcting the force normalization result specifically comprises the following steps:
wherein k isrealAnd updating the coefficient for the acting force normalization result, wherein the value range is (-1, 1), and t is time.
The platform is a six-degree-of-freedom Gough-Stewart platform;
the step 3) determines that the actuator force coefficient α is [ α ]1… α6]The specific method comprises the following steps:
wherein, βijElement of the ith row and jth column of the β matrix, β ═ J (J)p T)-1,JpIs a Jacobian matrix of equivalent center of mass of the load, when βi,3+kWhen equal to 0, αi＝1，i＝1，2，...，6，j＝1,2,...,6，k＝1,2,3。
Step 1) determining the resultant moment normalization result tau actually suffered by the three axes of the equivalent center of mass of the loadreal，normThe method specifically comprises the following steps:
τreal，norm＝k2·θpnorm·Ipnorm，
wherein, thetap＝[θpx,θpy,θpz]For the load equivalent centroid three-axis coupling attitude measurement, Ipx,Ipy,IpzRespectively are main inertia measured values of a rolling axis, a pitching axis and a yawing axis of the equivalent center of mass of the load, k2The load equivalent mass center rotation stiffness coefficient is obtained according to the stiffness of the platform actuator.
Step 1) determining an acting force normalization result Freal，normThe method specifically comprises the following steps:
Freal，norm＝(k1·rpnorm)·m，
wherein r ispx,rpy,rpzDesigned values of translational displacement r of load equivalent centroid roll axis, pitch axis and yaw axispx,rpy,rpzThe value ranges of (1) and (0.1) are all (-0.1); m is the load mass, k1The rigidity coefficient of the load equivalent mass center three-axis translational displacement is obtained according to the rigidity of the platform actuator.
Compared with the prior art, the invention has the beneficial effects that:
1) the calibration model of the 6 actuator force coefficients α is established, the optimal solution of the load centroid acting force is solved by establishing an index function, the concentrated calibration of the plurality of actuator force coefficients is realized, the inconsistent unification of the plurality of actuator force coefficients is realized, and the identification calibration of the plurality of actuator force coefficients is realized.
2) According to the method, the translation displacement of the load mass center is not required to be measured, the optimal solution of the three-axis load mass center acting force is searched in an iteration mode by setting the initial value of the translation displacement of the load mass center, and the error between the actual value and the expected value of the three-axis load mass center acting force is minimized. On the basis, the optimal solution of the force coefficient of the actuator is obtained, and the calibration precision of the force coefficient of the actuator is improved.
3) The three-axis attitude of the load comprises a Jacobian matrix J due to the centroid of the loadpAnd load attitude deviation caused by configuration deviation. According to the invention, the Jacobian matrix J of the centroid of the load can be compensated by measuring the three-axis attitude of the loadpAnd load attitude errors caused by configuration deviations.
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FIG. 1 is a flow chart of the method of the present invention.
Detailed Description
The invention adopts the flow shown in FIG. 1 to complete the calibration method of the force coefficient of the load attitude decoupling actuator of the active pointing hyperstatic platform.
1) Taking all loads carried by the platform as a whole, solving the mass center of the whole as a load equivalent mass center, and determining a resultant moment normalization result tau actually received by three shafts of the load equivalent mass center according to the three-shaft attitude and the three-shaft main inertia of the load equivalent mass centerreal，norm(ii) a According to the translational displacement r of the equivalent center of mass of the loadpDetermining the load equivalent mass center three-axis actual acting force normalization result Freal，norm；
2) Iteratively correcting the force normalization result according to the resultant moment normalization result and the resultant moment expected value taur＝[τ1τ2τ3]Finding the optimal solution, tau, with the force normalization result approaching 01，τ2，τ3Respectively obtaining expected values of moments of a rolling shaft, a pitching shaft and a yawing shaft of the load equivalent mass center;
3) and determining the force coefficient of the actuator according to the optimal solution of the acting force normalization result approaching to 0 and the resultant moment normalization result, and finishing calibration.
Normalizing the result according to the resultant moment and the resultant moment expected value taur＝[τ1τ2τ3]The method for finding the optimal solution of the acting force normalization result approaching 0 specifically comprises the following steps:
21) normalizing the result and the acting force according to the resultant momentDetermining an index function J from the resultsreal；
22) Judgment index function JrealWhether the absolute value is less than the critical value, if so, the index function JrealDetermining the normalized result of the acting force as the optimal solution; if not, entering step 23);
23) iteratively correcting the action force normalization result, and repeating the step 22) until an optimal solution of the action force normalization result is obtained.
The specific method comprises the following steps:
(1) establishing a kinematics model of the translational displacement of the actuator and the load mass center generalized displacement, which specifically comprises the following steps:
δL＝Jp[rpθp]T
where δ L is the displacement of the actuator, rpIs the translational displacement of the center of mass of the load, thetap＝[θpx,θpy,θpz]Three-axis coupled attitude measurements of the load. J. the design is a squarepIs a load centroid Jacobian matrix.
(2) The establishment of actuator output force, actuator force coefficient α and load mass center generalized force dynamics model specifically comprises the following steps:
wherein f isr＝[fr1,…,fr6,]TThe expected output force of the six actuators; frealIs the three-axis actual acting force of the load centroid, taurealThe resultant moment actually suffered by the three axes of the load mass center.
(3) Expected output force and actual output force model of actuator
Constructing a force coefficient calibration model of the active pointing hyperstatic actuator by utilizing a kinematic equation of the displacement of the active pointing hyperstatic actuator and the load mass center, the output force of the actuator, the resultant force borne by the load mass center and a moment equation; wherein, the load coupling attitude measurement is used as the first input quantity of the calibration model, and the initial value F of the load translation control force is usedrealFor calibrating second input quantity of model(ii) a The force coefficient of the actuator is the output quantity of the calibration model; the actuator kinematic relationship reflects the relationship between the force, moment of the load and the actuator force, expressed as:
wherein, FrThe expected force of the load mass center is obtained, and F is obtained because the hyperstatic platform only carries out load attitude controlr≡0；τr＝[τ1τ2τ3]，τ1，τ2，τ3Roll axis, pitch axis and yaw axis moment expectation values of the load centroid, respectively. f. ofr＝[fr1,…,fr6,]TThe expected output force of the six actuators; j. the design is a squarepIs a load centroid Jacobian matrix.
The model of the expected value and the actual output force of the actuator is represented as:
freal＝αfr
wherein f isrealFor the actual output force of each actuator, α ═ α1… α6]Is the ratio coefficient of the actual output to the desired output force of the actuator.
(4) Load attitude testing and coupling coefficient calculation
Carrying out load three-axis attitude measurement of the active pointing hyperstatic platform to obtain a load three-axis attitude coupling measurement value thetap＝[θpx,θpy,θpz]And calculating the three-axis attitude coupling coefficient of the load as
γij＝θj/θi
In the above formula, γijRepresenting the attitude coupling coefficient of the ith axis attitude maneuver to the jth axis; thetaiRepresenting the measured attitude of the ith shaft during maneuvering; thetajRepresenting the attitude component of the j-th axis coupling. The results of the three-axis attitude coupling coefficient test of the load are shown in the following table.
(5) Load attitude and load three-axis inertia normalization
The three-axis attitude and inertia normalization of the load is carried out according to the following formula, and the result is
Wherein, Ip＝[Ipx,Ipy,Ipz]Is the three-axis principal inertia of the load; the results of the normalized test are shown in the table below.
Three-axis attitude normalization array theta through load equivalent centroidpnormLoad-equivalent triaxial main inertia normalization array IpnormDetermining the resultant moment normalization result tau actually suffered by the three axes of the equivalent center of mass of the loadreal，norm：
τreal，norm＝k2·θpnorm·Ipnorm，
Wherein, thetap＝[θpx,θpy,θpz]For the load equivalent centroid three-axis coupling attitude measurement, Ipx,Ipy,IpzRespectively are main inertia measured values of a rolling axis, a pitching axis and a yawing axis of the equivalent center of mass of the load, k2The load equivalent mass center rotation stiffness coefficient is obtained according to the stiffness of the platform actuator.
Determining a force normalization result Freal，normThe method specifically comprises the following steps:
Freal，norm＝(k1·rpnorm)·m，
wherein r ispx,rpy,rpzDesigned values of translational displacement r of load equivalent centroid roll axis, pitch axis and yaw axispx,rpy,rpzThe value ranges of (1) and (0.1) are all (-0.1); m is the load mass, k1The rigidity coefficient of the load equivalent mass center three-axis translational displacement is obtained according to the rigidity of the platform actuator.
(6) Taking the maneuvering of a certain axis of the load as an example, a calibration model is constructed as follows:
wherein, β ═ J (J)p T)-1，βijElement of i row and j column of β matrix when βi4When equal to 0, αiWhen β is equal to 1i4When not equal to 0, then have
Freal,norm＝[FrealxFrealyFrealz]，
τreal,norm＝[τrealxτrealyτrealz]，
τr＝[τ1τ2τ3]And k is 1,2 and 3 are respectively expected values of the moment of the roll axis, the moment of the pitch axis and the moment of the yaw axis of the load centroid.
(7) Taking x-axis maneuvering as an example, the resultant force of the loads in the x and y directions is 0, i.e., Frealx＝0，FrealyConstructing a load z-axis resultant force F as 0realzThe model for the actuator force coefficient α is:
λi＝(βi4τrealx+βi5τrealy+βi6τrealz)/βi4
γi＝βi3/βi4
the actuator force coefficient α is then denoted as FrealzThe function is, in order,
(8) calculating an index function Jreal(ii) a Let initial FrealAnd (5) calculating the Euclidean norm of the composite force and moment output by the motor of the actuator and the expected force and moment of the load.
Freal,norm(n)＝[FrealxFrealyFrealz]，
τreal,norm＝[τrealxτrealyτrealz]，
τr＝[τ1τ2τ3]，
Freal,norm(0)＝Freal，norm，
Wherein, the lower foot marks realx, realy and realz respectively represent the components on the rolling axis, the pitching axis and the yawing axis of the equivalent center of mass of the load, and tau1，τ2，τ3Roll axis, pitch axis and yaw axis torque expectation values, n being 0,1, 2.
(9) For the index function JrealDerivation and judgment of the index function JrealThe trend of the derivative of (c). If the absolute value of the derivative meets the threshold, i.e. the indicator function JrealAbsolute value of derivative < 10-3Judging that the actuator force coefficient identification result meets the requirement and quitting; if not, entering the next step;
(10) resultant force F for updating three-axis actual acting force of load mass centerreal,norm：
Freal,norm(0)＝Freal，norm，
Wherein k isrealFor load centroid triaxial force normalization result Freal,normUpdating the coefficient, wherein the optimal value range is (-1, 1); k is a positive integer and t is time.
(11) Taking x-axis maneuver as an example for illustration, F is calculated by iterationrealz-0.1590. The power coefficient identification results are shown in the following table:
| item(s) | α1 | α2 | α3 | α4 | α5 | α6 |
| Value of | 1.0385 | 1.0391 | 0.7823 | 0.7823 | 1.0461 | 1.0450 |
(12) And (5) solidifying the actuator force compensation coefficient obtained in the step (11) in a load DSP controller, and performing actuator compensation control to realize load triaxial attitude decoupling control. The actuator force compensation coefficient is calculated as:
kfi＝1/αi
the results of the actuator force compensation coefficient test are shown in the following table.
| Item(s) | kf1 | kf2 | kf3 | kf4 | kf5 | kf6 |
| Value of | 0.9629 | 0.9624 | 1.2782 | 1.2800 | 0.9559 | 0.9569 |
(13) And (5) carrying out a load triaxial attitude test on the actuator force compensation coefficient obtained in the step (12), wherein the test result of the load triaxial attitude coupling coefficient is as shown in the following table.
| Item | Before calibration | After calibration |
| Coupling coefficient of load X to Y axis | 8.22％ | 0.50％ |
| Coupling coefficient of load X to Z axis | 0.48％ | 0.28％ |
| Coupling coefficient of load Y to X axis | 7.65％ | 0.29％ |
| Coupling coefficient of load Y to Z axis | 0.85％ | 0.84％ |
| Z-to-X axis coupling coefficient of load | 1.0％ | 0.73％ |
| Load Z-to-Y axis coupling coefficient | 0.5％ | 0.35％ |
Those skilled in the art will appreciate that those matters not described in detail in the present specification are well known in the art.
Claims (3)
1. A platform on-orbit calibration method is characterized by comprising the following steps:
1) taking all loads carried by the platform as a whole, solving the mass center of the whole as a load equivalent mass center, and determining a resultant moment normalization result tau actually received by three shafts of the load equivalent mass center according to the three-shaft attitude and the three-shaft main inertia of the load equivalent mass centerreal，norm(ii) a According to the translational displacement r of the equivalent center of mass of the loadpDetermining the load equivalent mass center three-axis actual acting force normalization result Freal，norm(ii) a The three axes are a rolling axis, a pitching axis and a yawing axis of the load equivalent mass center;
2) iteratively correcting the force normalization result according to the resultant moment normalization result and the resultant moment expected value taur＝[τ1τ2τ3]Finding the optimal solution, tau, with the force normalization result approaching 01，τ2，τ3Respectively obtaining expected values of moments of a rolling shaft, a pitching shaft and a yawing shaft of the load equivalent mass center;
3) determining the force coefficient of the actuator according to the optimal solution of the force normalization result approaching 0 and the resultant moment normalization result, and completing calibration;
normalizing the result according to the resultant moment and the resultant moment expected value taur＝[τ1τ2τ3]The method for finding the optimal solution of the acting force normalization result approaching 0 specifically comprises the following steps:
21) determining an index function J according to a resultant moment normalization result and an acting force normalization resultreal；
22) Judgment index function JrealWhether the absolute value is less than the critical value, if so, the index function JrealDetermining the normalized result of the acting force as the optimal solution; if not, entering step 23);
23) iteratively correcting the acting force normalization result, and repeating the step 22) until an optimal solution of the acting force normalization result is obtained;
the index function JrealThe method specifically comprises the following steps:
Freal,norm(n)＝[FrealxFrealyFrealz]，
τreal,norm＝[τrealxτrealyτrealz]，
τr＝[τ1τ2τ3]，
Freal,norm(0)＝Freal，norm，
wherein, the lower foot marks realx, realy and realz respectively represent the components on the rolling axis, the pitching axis and the yawing axis of the equivalent center of mass of the load, and tau1，τ2，τ3The method comprises the following steps of (1) respectively obtaining expected values of moments of a rolling shaft, a pitching shaft and a yawing shaft of a load equivalent mass center, wherein n is 0,1 and 2;
step 1) determining the resultant moment normalization result tau actually suffered by the three axes of the equivalent center of mass of the loadreal，normThe method specifically comprises the following steps:
τreal，norm＝k2·θpnorm·Ιpnorm,
wherein, thetap＝[θpx,θpy,θpz]For the load equivalent centroid three-axis coupling attitude measurement, Ipx,Ipy,IpzRespectively are main inertia measured values of a rolling axis, a pitching axis and a yawing axis of the equivalent center of mass of the load, k2The load equivalent mass center rotation stiffness coefficient is obtained according to the stiffness of the platform actuator;
said step 1) determining the forceNormalized result Freal，normThe method specifically comprises the following steps:
Freal，norm＝(k1·rpnorm)·m，
wherein r ispx,rpy,rpzDesigned values of translational displacement r of load equivalent centroid roll axis, pitch axis and yaw axispx,rpy,rpzThe value ranges of (1) and (0.1) are all (-0.1); m is the load mass, k1The rigidity coefficient of the translational displacement of the three axes of the load equivalent mass center is obtained according to the rigidity of the platform actuator;
the critical value is less than 10-3。
2. A calibration method according to claim 1, wherein the method for iteratively correcting the force normalization result specifically comprises:
wherein k isrealAnd updating the coefficient for the acting force normalization result, wherein the value range is (-1, 1), and t is time.
3. A calibration method according to claim 2, characterized in that:
the platform is a six-degree-of-freedom Gough-Stewart platform;
the step 3) determines that the actuator force coefficient α is [ α ]1… α6]The specific method comprises the following steps:
wherein, βijElement of the ith row and jth column of the β matrix, β ═ J (J)p T)-1，JpIs a Jacobian matrix of equivalent center of mass of the load, when βi,3+kWhen equal to 0, αi＝1，i＝1，2，...，6，j＝1,2,...,6，k＝1,2,3。
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