CN107315357B - Approximate modeling method of rod-shaped flexible mechanism for adjusting attitude of chip star - Google Patents
Approximate modeling method of rod-shaped flexible mechanism for adjusting attitude of chip star Download PDFInfo
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Abstract
The invention discloses an approximate modeling method of a rod-shaped flexible mechanism for adjusting the attitude of a chip star, which comprises the steps of discretizing the bending deformation process of the rod-shaped flexible mechanism according to the equal deflection size and the small distance, gradually solving the configuration of a material corresponding to the deflection of each discrete point from the minimum deflection point, then correcting errors of the bending configuration of the material at the initial small deflection deformation position by utilizing interpolation correction, finally obtaining the bending deformation track of the rod-shaped flexible mechanism, being capable of calculating all track processes of the bending deformation of an intelligent piezoelectric material or a similar flexible material in a targeted manner, effectively correcting the errors in the bending deformation process, and being capable of rapidly and directly calling related data when the related data are required to be utilized, thereby greatly improving the calculation efficiency and the calculation speed.
Description
Technical Field
The invention belongs to the technical field of control of the attitude of a chip satellite, and relates to an approximate modeling method of a rod-shaped flexible mechanism for adjusting the attitude of the chip satellite.
Background
Once proposed, the chipstar has attracted much attention as one of the microminiature satellites. Thanks to the development of chip technology, tasks which can only be executed by a large-scale spacecraft in the past can be replaced by one or more small chipstars; compared with the traditional large-scale spacecraft, the chip star has great advantages in manufacturing and launching cost. Due to the limitations of size and mass, the traditional attitude determination and adjustment methods (such as momentum wheels and the like) cannot be applied to the chip satellite or are limited considerably, and a novel adjustment method is to connect the components of the chip satellite through a self-driven flexible rod mechanism, change the relative configuration of each component through the bending of a rod-shaped flexible mechanism, and change the attitude of the chip satellite or keep the attitude and orbit stable.
The research on the deformation process of flexible materials, which are flexible intelligent deformable materials (such as intelligent piezoelectric materials, etc.), is a popular research direction at present, and is receiving extensive attention and research. At present, the deformation configuration of the rod-shaped flexible mechanism is researched, and the rod-shaped flexible mechanism is generally considered to be an ultra-redundant hinged multi-rigid body. For the bending problem of the rod-shaped flexible mechanism part with known terminal point coordinates, a jacobian method, an analytical method, an Angle OPT method (Angle OPT) and a pull object line method (T curve method) are effective algorithms.
However, the above algorithms all have the problem of complicated calculation in the solving process, when the chipstar uses the rod-shaped flexible mechanism to adjust the attitude, the data in the bending deformation process is required, the time-varying bending configuration calculation can greatly increase the calculation workload, meanwhile, the chipstar is limited by the limitation of the size and the mass of the chipstar, the load capacity is limited, and the corresponding calculation performance is generally not enough to bear the calculation workload. Besides, when the bending deflection is small, the algorithm has the phenomenon that the relative calculation error is larger more or less.
Disclosure of Invention
Aiming at the defects in the prior art, the invention aims to provide an approximate modeling method of a rod-shaped flexible mechanism for adjusting the attitude of a chip star, which improves the calculation efficiency and the calculation precision in the process of adjusting and controlling the attitude of the chip star.
The technical scheme adopted by the invention for solving the technical problems is as follows:
an approximate modeling method of a rod-shaped flexible mechanism for adjusting the attitude of a chip star comprises the steps of firstly, selecting rods with unit length aiming at the possible maximum bending deflection of the rod-shaped flexible mechanism, discretizing the deflection at equal intervals from zero, and calculating to obtain the coordinates of the tail end points of the rod-shaped flexible mechanism corresponding to each discrete deflection point;
then, the rod-shaped flexible mechanism is approximately regarded as a hinge multi-rigid body with super redundancy, and the deformation structure state of the corresponding rod-shaped flexible mechanism is obtained by solving point by point from small to large;
then, aiming at the solving error of the initial small-deflection deformation moment, correcting by using an interpolation algorithm;
and finally, obtaining the bending deformation track with equal deflection intervals in the bending deformation process of the rod-shaped flexible mechanism.
Further, the discrete rod-shaped flexible mechanism terminal point coordinates corresponding to each deflection point are calculated by using an Euler method or a pseudo-rigid body method.
And further, solving point by point from small to large by using a pull object line method to obtain the deformation structure state of the corresponding rod-shaped flexible mechanism.
Further, when the bending configuration error of the initial small-deflection deformation is corrected, the three criteria are based;
①, the coordinates of the individual hinge points, i.e. the ordinate, increase in the transverse direction from the origin to the end of the lever;
② in the longitudinal direction, the coordinates of the respective hinge points should satisfy the interpolation function of the extrapolation method;
③ the distance between the two hinge points at the head and the tail of each rod piece and the length of the rod piece have the corresponding precision range.
The invention relates to an approximate modeling method of a bending deformation track of a rod-shaped flexible mechanism for adjusting the attitude of a chip star, which aims at the simulation problem of the bending deformation of flexible materials such as intelligent piezoelectric materials and the like, discretizes the bending deformation process according to the equal deflection size and the interval, determines the position of a bending tail end point by point according to the deflection size, gradually solves the configuration of the material corresponding to the deflection of each discrete point from the minimum deflection point by using a T curve method and other methods, and then corrects the material configuration of the initial small deflection deformation position by using interpolation correction based on the global configuration change, the whole track process of the bending deformation of the intelligent piezoelectric material or the similar flexible material can be calculated in a targeted manner, the error in the intelligent piezoelectric material or the similar flexible material can be effectively corrected, when the related data is needed to be utilized, the related data can be quickly and directly called, so that the calculation efficiency and the calculation speed are greatly improved.
Drawings
FIG. 1 is a simplified computational flow framework diagram of the algorithm;
FIG. 2 shows a set of calculations for the algorithm;
FIG. 3 is a block diagram of the calculation result data of the algorithm invoked;
Detailed Description
The invention is further illustrated by the following figures and examples.
Please refer to the simple computation flow diagram of the algorithm in fig. 1:
(1) aiming at the possible maximum bending deflection of the rod-shaped flexible mechanism, rods with unit length are selected, and the deflection process from zero to the maximum deflection is dispersed at equal intervals into a plurality of deflection value points (hundreds to thousands, which can be set according to the precision and the storage requirement) from zero to the maximum deflection.
(2) And calculating to obtain the corresponding rod-shaped flexible mechanism terminal point coordinates by using methods such as an Eulerian method, a pseudo-rigid body method and the like according to the deflection of each discrete deflection value point. Taking a pseudo-rigid body method as an example, the pseudo-rigid body method equivalently regards a flexible rod piece as a two-section rigid rod, the two sections of rigid rods are elastically hinged, and the sum of the lengths of the two sections of rigid rods is equal to the length of the flexible rod piece; corresponding to the bending of the flexible rod piece, the two sections of rigid rods equivalently deform in a mechanical structure, namely, the first section of rigid rod keeps horizontal and static, and the second section of rigid rod rotates around an elastic hinge point. Based on the theory, the final coordinate formula of the tail end point of the flexible rod is
py＝γl sinθ
px＝l[1-γ(1-cosθ)]
Wherein p isyThe longitudinal coordinate of the tail end point of the flexible rod and the bending deflection of the flexible rod are obtained; p is a radical ofxThat is, on the corresponding abscissa, γ is the proportion of the total length of the second rigid rod, which is an equivalent approximation, and has different corresponding values according to the bending power source (for example, γ is 0.7346 at a pure bending moment); l is the length of the flexible rod, and is the sum of the lengths of two equivalent and similar rigid rods, wherein the unit length is 1; theta is the rotation angle of the second section of rigid rod around the hinge point. In the calculation, the corresponding theta angle value can be calculated according to the deflection value, and then the abscissa of the terminal point of the corresponding flexible rod is calculated.
(3) The rod-shaped flexible mechanism is approximately regarded as a super-redundancy hinged multi-rigid body, the deformation structure state of the corresponding rod-shaped flexible mechanism is described through the coordinates of each hinged point, and the specific coordinates of each hinged point can be obtained by solving through an algorithm such as an object pulling line (namely a T curve) according to the coordinates of the tail end point of the rod, and the T curve method is taken as an example for simple explanation.
The basic principle of the T-curve is derived from the movement of a single rigid rod, i.e. if the speed direction of the rod tail end is always along the rod, the movement trajectory of the rod tail end is a pull line when the head end of the rod moves along a straight line. Taking the linear motion of the rod head end as the x axis and the position of the rod head end when the rod is perpendicular to the x axis as the origin, the coordinate of the rod tail end corresponding to the horizontal coordinate p of the rod head end is taken as
Wherein L is the length of the rod.
The T curve method of the multi-rigid rod is the application of the hinged series connection of the single rods, namely, a local coordinate system is established from the tail end to the rod one by one, and the tail end coordinate is updated by using the T curve method according to the change of the head end coordinate, wherein the head end coordinate of the tail end rod is transformed corresponding to the change of the tail end coordinate of the flexible rod from one deflection point to the next deflection point, and then the change of the tail end coordinate of each rod is the change of the head end coordinate of the next rod until the first rod. And if the tail end coordinate of the first rod in the global coordinate system deviates from the initial origin, integrally translating the deformed multi-rigid-body rod, so that the tail end coordinate of the first rod returns to the initial origin. And then, solving by using a T curve method again, wherein the head end coordinate of the tail end rod is transformed into the tail end coordinate of the flexible rod from the head end coordinate of the tail end rod after corresponding translation to the next deflection point. And repeating the steps until the tail end coordinate offset of the first rod meets the precision requirement. And finally obtaining the coordinates of each hinge point corresponding to the next deflection point. And (3) with the gradual increase of the deflection of the rod piece from zero, the coordinates of each hinge point corresponding to each deflection point can be finally obtained, and the bending configuration of the corresponding rod piece can be described.
(4) And finally, aiming at the solving error of the initial small-deflection deformation moment, carrying out fitting correction by using an interpolation algorithm (extrapolation method).
For the bending problem of the flexible rod, in order to obtain a good simulation configuration by a T curve method, on one hand, more rods for approximate super-redundancy hinged multi-rigid bodies are needed, on the other hand, the step length of gradual increase of the deflection of the tail end of the rod from zero needs to be smaller, otherwise, a configuration distortion phenomenon (generally distortion is approximate to S shape) occurs, besides the calculated amount is increased, the problem of solving errors during initial small-deflection deformation is caused, namely, the approximate hinged multi-rigid bodies reach the accuracy requirement without integral deformation due to the fact that the deflection of the tail end of the rod is too small, so that the head end and the tail end of the integral multi-rigid-body rods of the rods meet the accuracy requirement, and a relatively large error exists at a middle hinge point on the configuration.
Finally, the bending deformation track with equal deflection intervals in the bending deformation process of the rod-shaped flexible mechanism shown in figure 2 is obtained. Wherein, the rod-shaped flexible mechanism is approximately represented by 20 sections of hinged multi-rigid-body rod pieces, and the number of the rod pieces in actual operation can be adjusted according to the requirements of calculation efficiency and calculation precision.
Please refer to fig. 3 for data acquisition in the subsequent simulation or control application process of attitude adjustment of the satellite. On the one hand, the bending track of the equal deflection interval of the rod-shaped flexible mechanism is determined according to the actual length of the rod-shaped flexible mechanism, and on the other hand, the coordinates of the end points of the equal time interval are determined according to the time-varying track of the end points of the rod-shaped flexible mechanism. And then, searching whether data corresponding to the coordinates of the terminal points exist in the bending track with the equal deflection spacing, if so, directly calling the corresponding data, otherwise, calling data corresponding to a plurality of nearby terminal coordinate points, and obtaining bending configuration data corresponding to the coordinates of the terminal points to be solved by utilizing a spline interpolation equal-section interpolation algorithm. Finally, the data is integrated, i.e. the time-varying bending trajectory of the actual rod-like flexible mechanism can be determined for subsequent calculation needs.
The foregoing is a more detailed description of the invention and it is not intended that the invention be limited to the specific embodiments described herein, but that various modifications, alterations, substitutions and equivalents will be apparent to those skilled in the art without departing from the spirit of the invention, and are intended to be within the scope of the invention as defined by the appended claims.
Claims (4)
1. An approximate modeling method of a rod-shaped flexible mechanism for adjusting the attitude of a chip star is characterized by comprising the following steps of:
firstly, aiming at the maximum bending deflection of the rod-shaped flexible mechanism, selecting a rod with a unit length, carrying out equal-interval discretization on the bending deflection from zero to the maximum bending deflection, and calculating to obtain the coordinates of the tail end point of the rod-shaped flexible mechanism corresponding to each discretized deflection point;
then, the rod-shaped flexible mechanism is approximately regarded as a hinge multi-rigid body with super redundancy, and the deformation structure state of the corresponding rod-shaped flexible mechanism is obtained by solving point by point from small to large;
then, aiming at the solving error of the initial small-deflection deformation moment, correcting by using an interpolation algorithm;
and finally, obtaining the bending deformation track with equal deflection intervals in the bending deformation process of the rod-shaped flexible mechanism.
2. The approximate modeling method for a rod-like flexible mechanism for attitude adjustment of a chip star according to claim 1, characterized in that: and calculating the discrete rod-shaped flexible mechanism terminal point coordinates corresponding to each deflection point by using an Euler method or a pseudo-rigid body method.
3. The approximate modeling method for a rod-like flexible mechanism for attitude adjustment of a chip star according to claim 1, characterized in that: and solving point by point from small to large by using a pull object line method to obtain the deformation structure state of the corresponding rod-shaped flexible mechanism.
4. The approximate modeling method for a rod-like flexible mechanism for attitude adjustment of a chip star according to claim 1, characterized in that: aiming at the solving error of the initial small-deflection deformation moment, when the correction is carried out by utilizing an interpolation algorithm, the method is based on the following three criteria:
① are oriented in the transverse direction, starting from the origin and going to the end of the bar, the ordinate of each hinge point gradually increasing;
② in the longitudinal direction, the abscissa of each hinge point should satisfy the interpolation function of the extrapolation method;
③ the distance between the two hinge points at the head and the tail of each rod piece and the length of the rod piece have the corresponding precision range.
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