CN111470070B - Space non-cooperative target non-contact despun identification device and method - Google Patents

Space non-cooperative target non-contact despun identification device and method Download PDF

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CN111470070B
CN111470070B CN202010385707.4A CN202010385707A CN111470070B CN 111470070 B CN111470070 B CN 111470070B CN 202010385707 A CN202010385707 A CN 202010385707A CN 111470070 B CN111470070 B CN 111470070B
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cooperative target
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electromagnet
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CN111470070A (en
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赵成植
孟庆良
梁建勋
季洪鑫
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Tsinghua University
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    • B64—AIRCRAFT; AVIATION; COSMONAUTICS
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Abstract

The invention discloses a space non-cooperative target non-contact despun identification device and method. The device comprises a working spacecraft, an electromagnet rotating device and a mechanical arm; the fixed end of the mechanical arm is arranged on the working spacecraft, and the driving end of the mechanical arm is connected with the electromagnet rotating device; the working spacecraft controls the mechanical arm to drive the electromagnet rotating device, so that the distance between the electromagnet rotating device and a space non-cooperative target is within a preset range; the electromagnet rotating device is used for despinning the space non-cooperative target; the working spacecraft is used for acquiring an image of a space non-cooperative target, reacting force of the electromagnet rotating device on the space non-cooperative target, and determining parameters of the space non-cooperative target according to the image and the reacting force. By adopting the device and the method, the object is despuned by adopting the electromagnet under the condition of not contacting the non-cooperative object, and the object parameter can be identified.

Description

Space non-cooperative target non-contact despun identification device and method
Technical Field
The invention relates to the technical field of space dynamics and control, in particular to a space non-cooperative target non-contact racemization identification device and method.
Background
On-orbit service of non-cooperative targets (unknown flyers such as orbital refuse or uncontrolled known flyers such as rolling satellites) is a very challenging space mission, and capture of the non-cooperative targets is one of the most critical steps in the process of serving the non-cooperative targets, so that the technology can be applied to the fields of space refuse removal, space defense and the like. The identification technology for the kinetic parameters of the non-cooperative target object aims to reduce the unknown in the capture process so as to reduce the capture risk to the maximum extent.
There are many scholars studying parameter identification after a target is captured, and identification after capture, while relatively easy, still fails to overcome the risk of capture. There are also studies on the application of stimuli prior to capture, and stimuli to non-cooperative targets can be negative, i.e. slow the roll of non-cooperative targets while achieving the goal of de-rotation. The application of the excitation before capture can be divided into two categories, one being contact excitation, achieved by means of e.g. a decelerating brush, mechanical impulses, tethered robots. Another type is non-contact excitation, such as with gas impact, electrostatic force, ion beam, laser, electromagnetic force, and the like. Since space debris and non-cooperative satellites mostly contain aluminum alloy and titanium alloy parts, racemization or excitation by electromagnetic force has attracted the interest of some scholars. Some have proposed applying a magnetic field around a rotating conductive target, using eddy currents generated by its relative motion to dampen the motion of the target. Some scholars propose a method for racemization by using a superconducting coil, but the method is limited to theoretical analysis, and practical application needs a power supply and a cooling system and is difficult to realize. These studies are mainly focused on target racemization and no analysis in terms of parameter estimation is performed, so there is still a risk of capture.
Disclosure of Invention
The invention aims to provide a space non-cooperative target non-contact de-rotation identification device and a method, which can perform de-rotation operation on a target by adopting an electromagnet under the condition of not contacting the non-cooperative target and can identify target parameters.
In order to achieve the purpose, the invention provides the following scheme:
a racemization identification device, comprising:
the device comprises a working spacecraft, an electromagnet rotating device and a mechanical arm;
the fixed end of the mechanical arm is arranged on the working spacecraft, and the driving end of the mechanical arm is connected with the electromagnet rotating device; the working spacecraft controls the mechanical arm to drive the electromagnet rotating device, so that the distance between the electromagnet rotating device and a space non-cooperative target is in a preset range; the electromagnet rotating device is used for despinning the space non-cooperative target;
the working spacecraft is used for acquiring an image of the space non-cooperative target and a reaction force of the electromagnet rotating device on the space non-cooperative target, and determining parameters of the space non-cooperative target according to the image and the reaction force.
Optionally, the electromagnet rotating device specifically includes:
the device comprises a rotary table, a rotating shaft, a power supply device and a plurality of electromagnets;
the rotating shaft penetrates through the turntable and is connected with the driving end of the mechanical arm, and the rotating shaft is arranged in the middle of the turntable; the electromagnets are respectively arranged at the edges of the turnplate, and the turnplate is used for driving the electromagnets to rotate; the power supply device is sleeved on the outer side of the rotating shaft and used for providing electric energy for the electromagnet.
Optionally, the power supply device specifically includes:
an electric brush and a conductive ring;
the conducting ring is sleeved outside the rotating shaft, and the electric brush is sleeved outside the conducting ring; the electric brush is in sliding contact with the conducting ring, and the electric brush provides electric energy for the electromagnet when in sliding contact with the conducting ring.
Optionally, the electromagnet is a U-shaped electromagnet.
The invention also provides a racemization identification method, which is applied to the racemization identification device and comprises the following steps:
the working spacecraft controls the mechanical arm to drive the electromagnet rotating device, so that the distance between the electromagnet rotating device and a space non-cooperative target is within a preset range;
the working spacecraft acquires an image of the space non-cooperative target and the reaction force of the electromagnet rotating device on the space non-cooperative target;
and the working spacecraft determines the parameters of the space non-cooperative target according to the image and the reaction force.
Optionally, the acquiring, by the working spacecraft, an image of a space non-cooperative target specifically includes:
the working spacecraft acquires a first image and a second image; the first image is an image of the space non-cooperative target obtained by the working spacecraft before the despinning operation of the electromagnet rotating device on the space non-cooperative target is carried out; and the second image is an image of the space non-cooperative target obtained by the working spacecraft after the racemization operation of the space non-cooperative target is carried out by the electromagnet rotating device.
Optionally, the determining, by the operating spacecraft, the parameter of the space non-cooperative target according to the image and the reaction force specifically includes:
and determining the mass and the moment of inertia of the space non-cooperative target according to the image and the reaction force.
Optionally, the method for determining the quality of the spatial non-cooperative target specifically includes:
the working spacecraft determines the initial rotation angular speed of the space non-cooperative target according to the first image;
the working spacecraft determines the rotation angular speed of the space non-cooperative target according to the second image;
integrating the reaction force with time to obtain impulse force applied to the space non-cooperative target;
and determining the quality of the space non-cooperative target according to the impulse force applied to the space non-cooperative target and the difference value between the despinning angular velocity and the initial rotational angular velocity.
Compared with the prior art, the invention has the beneficial effects that:
the invention provides a space non-cooperative target non-contact racemization identification device and a method, which can achieve the aim of decelerating the target without contacting the target, and reduce the possibility of dangerous phenomena caused by contact under the condition that the space non-cooperative target has higher speed in space; the despun operation can be realized only by the magnetic conductor without a device such as a magnet on a space non-cooperative target. The invention can avoid the problem that the permanent magnet acts with the internal components of the working spacecraft to cause failure in the mode of the electromagnet, and the electromagnet is electrified only during operation, thereby greatly enhancing the safety. In addition, the parameters of the space non-cooperative target can be determined according to the acquired image of the space non-cooperative target and the reaction force of the electromagnet rotating device on the space non-cooperative target, the problem that the target parameters cannot be estimated only by despinning the target in the prior art is solved, and the risk of capturing the target is greatly reduced by identifying the target parameters.
The U-shaped electromagnet rotating device can obtain stronger force action under the condition of consuming the same energy compared with a single electromagnet, namely, the device can consume less energy under the condition of achieving the same force action compared with the traditional electromagnet, thereby saving the energy and reducing the aerospace cost.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings needed to be used in the embodiments will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings without inventive exercise.
FIG. 1 is a schematic diagram of a non-contact de-rotation identification apparatus for a spatial non-cooperative target according to an embodiment of the present invention;
FIG. 2 is a diagram of a non-contact de-rotation identification apparatus for a spatial non-cooperative target according to an embodiment of the present invention;
FIG. 3 is a schematic view of an electromagnet rotating apparatus according to an embodiment of the present invention;
FIG. 4 is a view showing a structure of an electromagnet rotating device according to an embodiment of the present invention;
FIG. 5 is a flowchart illustrating a non-contact de-rotation identification method for a spatial non-cooperative target according to an embodiment of the present invention;
FIG. 6 is a schematic diagram illustrating changes in angular velocity of a spatially non-cooperative target in an embodiment of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The invention aims to provide a space non-cooperative target non-contact de-rotation identification device and a method, which can perform de-rotation operation on a target by adopting an electromagnet under the condition of not contacting the non-cooperative target and can identify target parameters.
In order to make the aforementioned objects, features and advantages of the present invention comprehensible, embodiments accompanied with figures are described in further detail below.
Examples
As shown in fig. 1-4, a non-contact de-rotation identification device for a spatial non-cooperative target includes: the device comprises a working spacecraft 1, an electromagnet rotating device 3 and a mechanical arm 2.
The fixed end of the mechanical arm 2 is arranged on the working spacecraft 1, and the driving end of the mechanical arm 2 is connected with the electromagnet rotating device 3; the working spacecraft 1 controls the mechanical arm 2 to drive the electromagnet rotating device 3, so that the distance between the electromagnet rotating device 3 and the space non-cooperative target 4 is in a preset range (the distance between the tail end of the mechanical arm 2 and the space non-cooperative target is controlled to be 450 mm); the electromagnet rotating device 3 is used for despinning the space non-cooperative target 4; the working spacecraft 1 is used for acquiring an image of the space non-cooperative target 4 and the reaction force of the electromagnet rotating device 3 on the space non-cooperative target 4, and determining the parameters of the space non-cooperative target 4 according to the image and the reaction force.
The electromagnet rotating device 3 includes: the rotary table comprises a rotary table 9, a rotating shaft 7, a power supply device and four U-shaped electromagnets 5. The rotating shaft 7 penetrates through the turntable and is connected with the driving end of the mechanical arm 2, and the rotating shaft 7 is arranged in the middle of the turntable; the four electromagnets 5 are arranged at the edge of the turntable at equal intervals, and the turntable is used for driving the electromagnets 5 to rotate; the power supply device is sleeved on the outer side of the rotating shaft 7 and used for providing electric energy for the electromagnet 5. The power supply device includes: a brush 6 and a conductive ring 8. The conducting ring 8 is sleeved outside the rotating shaft 7, and the electric brush 6 is sleeved outside the conducting ring 8; the brush 6 is in sliding contact with the conductive ring 8, and the brush 6 supplies electric energy to the electromagnet 5 when in sliding contact with the conductive ring 8.
The racemization principle is that metal is put into a changing magnetic field, induced electromotive force can be generated in the metal, the electromotive force can generate large current because the resistance of the metal is small, and the current-carrying metal moves in the magnetic field and generates interaction force.
Fig. 5 is a flowchart of a non-contact despinning identification method for a spatial non-cooperative target in an embodiment of the present invention, fig. 6 is a schematic diagram of angular velocity variation of the spatial non-cooperative target in the embodiment of the present invention, in fig. 6, an abscissa represents time, and an ordinate represents angular velocity, and as the despinning time increases, the angular velocity decreases first and then tends to be stable. As shown in fig. 5-6, a method for identifying a non-contact despun of a spatial non-cooperative target is applied to a non-contact despun identification apparatus of a spatial non-cooperative target, and the method includes:
step 101: the working spacecraft controls the mechanical arm to drive the electromagnet rotating device, so that the distance between the electromagnet rotating device and the space non-cooperative target is within a preset range.
Step 102: the working spacecraft obtains the image of the space non-cooperative target and the reaction force of the electromagnet rotating device on the space non-cooperative target.
Step 102, specifically comprising:
the working spacecraft acquires a first image and a second image; the first image is an image of the space non-cooperative target obtained by the working spacecraft before the despinning operation of the space non-cooperative target is carried out by the electromagnet rotating device; and the second image is an image of the space non-cooperative target obtained by the working spacecraft after the electromagnetic rotating device performs despinning operation on the space non-cooperative target.
Step 103: and the working spacecraft determines the parameters of the space non-cooperative target according to the image and the reaction force. The parameters of the spatial non-cooperative target include a mass and a moment of inertia of the spatial non-cooperative target.
Step 103, specifically comprising:
and determining the mass and the moment of inertia of the space non-cooperative target according to the image and the reaction force.
The method for determining the quality of the space non-cooperative target specifically comprises the following steps:
and the working spacecraft determines the initial rotation angular speed of the space non-cooperative target according to the first image. And the working spacecraft determines the despun rotation angular speed of the space non-cooperative target according to the second image.
Specifically, the working spacecraft acquires a point cloud image of a space non-cooperative target through a ToF (Time of Flight) camera to perform attitude estimation. Because the non-cooperative target is in an uncontrolled rotation state, images shot at different moments are partially overlapped and partially different, but the two point cloud images can be overlapped to the maximum extent through translation and rotation, and thus the angular speed can be determined.
Reaction force FsThe time t is subjected to integral operation to obtain impulse i borne by the space non-cooperative targetforce. The impulse formula is as follows:
Figure BDA0002483842990000061
in the formula, t0As the initial time, Δ t is the time of racemization.
And determining the quality of the space non-cooperative target according to the impulse force applied to the space non-cooperative target and the difference value between the despinning angular velocity and the initial rotational angular velocity. The mass calculation formula is as follows:
Figure BDA0002483842990000062
Figure BDA0002483842990000063
in the formula (I), the compound is shown in the specification,
Figure BDA0002483842990000064
for angular velocity differences, the superscript T is the transposed symbol, vcm (1)For despin angular velocity of rotation, vcm (0)For the purpose of the initial angular velocity of rotation,
Figure BDA0002483842990000065
representing the mass estimate, Δ iforceIndicating the amount of change in impulse.
The method for determining the main inertia moment of the space non-cooperative target specifically comprises the following steps:
Figure BDA0002483842990000071
in the formula itorqueIs a forceMoment-induced impulse, MsThe torque, t, measured for the torque sensor of the working spacecraft0Denotes the initial time and Δ t denotes the racemization time.
The angular momentum of the spatially non-cooperative target with respect to the center of mass is Lrotate。
The change in angular momentum is Δ Lrotate＝T(qp)(1)Λωp (1)-T(qp)(0)Λωp (0)
Wherein, T (q)p) Is a quaternion qpOf the rotation matrix qpFor the common meaning of robot kinematics, Λ is the moment of inertia about the center of mass, Λ ═ diag (I)1，I2，I3)，I1、I2、I3The components of the moment of inertia, ω, in the x-, y-and z-axes of the principal moment of inertia, respectivelyp (1)And ωp (0)Post-change and pre-change angular velocities, respectively.
The change in angular momentum can be rewritten as:
Figure BDA0002483842990000072
wherein the content of the first and second substances,
Figure BDA0002483842990000073
in the formula, omegapRepresenting the angular velocity matrix, ωpx，ωpy，ωpzRepresenting three components of angular velocity in the x-axis, y-axis and z-axis,
Figure BDA0002483842990000074
the normalized principal moment of inertia is represented,
Figure BDA0002483842990000075
the moment of inertia components of the x, y and z axes of the normalized principal moment of inertia, respectively.
Let K be | | | xlI and
Figure BDA0002483842990000076
the ratio of (a) to (b),
Figure BDA0002483842990000077
||xli represents a double vertical inline vector xlThe superscript (1) indicates a period of racemization and the superscript (0) indicates the preschedulation.
Can be calculated
Figure BDA0002483842990000079
The estimated value of the angular momentum is
Figure BDA0002483842990000081
Wherein the content of the first and second substances,
Figure BDA0002483842990000082
is a vector from the origin to the centroid after a certain amount of time of derotation,
Figure BDA0002483842990000083
representing the vector from the origin to the centroid of the despin front.
The optimal solution of the magnitude of the principal moment of inertia is
Figure BDA0002483842990000084
pinertiaFor the complete inertial parameter, pinertia＝[m，BΔrx，BΔry，BΔrz，I1，I2，I3，Δq1，Δq2，Δq3]Wherein m is mass, r is relative position vector, I1 is x-axis rotational inertia, I2 is y-axis rotational inertia, 13 is z-axis rotational inertia,BΔrx，BΔry，BΔrzthe x-axis component, the y-axis component and the z-axis component of the position vector representing the principal coordinate system of inertia relative to the reference coordinate system, Δ q1，Δq2，Δq3The method is used for representing the change of the offset of the x axis, the change of the offset of the y axis and the change of the offset of the z axis of the inertial main coordinate system relative to the reference coordinate system.
The principles and embodiments of the present invention have been described herein using specific examples, which are provided only to help understand the method and the core concept of the present invention; meanwhile, for a person skilled in the art, according to the idea of the present invention, the specific embodiments and the application range may be changed. In summary, this summary should not be construed to limit the present invention.

Claims (5)

1. A despin identification device, comprising:
the device comprises a working spacecraft, an electromagnet rotating device and a mechanical arm;
the fixed end of the mechanical arm is arranged on the working spacecraft, and the driving end of the mechanical arm is connected with the electromagnet rotating device; the working spacecraft controls the mechanical arm to drive the electromagnet rotating device, so that the distance between the electromagnet rotating device and a space non-cooperative target is in a preset range; the electromagnet rotating device is used for despinning the space non-cooperative target;
the working spacecraft is used for acquiring an image of the space non-cooperative target and a reaction force of the electromagnet rotating device on the space non-cooperative target, and determining parameters of the space non-cooperative target according to the image and the reaction force;
the working spacecraft acquiring the image of the space non-cooperative target specifically comprises the following steps:
the working spacecraft acquires a first image and a second image; the first image is an image of the space non-cooperative target obtained by the working spacecraft before the despinning operation of the electromagnet rotating device on the space non-cooperative target is carried out; the second image is an image of the space non-cooperative target obtained by the working spacecraft after the despinning operation of the electromagnet rotating device on the space non-cooperative target is carried out;
the working spacecraft determines the parameters of the space non-cooperative target according to the image and the reaction force, and specifically comprises the following steps:
determining the mass and the moment of inertia of the space non-cooperative target according to the image and the reaction force;
the method for determining the quality of the space non-cooperative target specifically comprises the following steps:
the working spacecraft determines the initial rotation angular speed of the space non-cooperative target according to the first image;
the working spacecraft determines the rotation angular speed of the space non-cooperative target according to the second image;
integrating the reaction force with time to obtain impulse force applied to the space non-cooperative target; the impulse force is calculated by the following formula:
Figure FDA0003276081700000011
wherein, t0Is the initial time, and delta t is the racemization time;
determining the quality of the space non-cooperative target according to the impulse force applied to the space non-cooperative target and the difference value between the despun rotation angular velocity and the initial rotation angular velocity; the method specifically comprises the following steps:
calculating the quality of the spatial non-cooperative target by adopting the following formula:
Figure FDA0003276081700000021
Figure FDA0003276081700000022
wherein the content of the first and second substances,
Figure FDA0003276081700000023
for angular velocity differences, the superscript T is the transposed symbol, vcm (1)Is a rotation angle speed of rotationDegree, vcm (0)For the purpose of the initial angular velocity of rotation,
Figure FDA0003276081700000024
for the quality estimation, Δ iforceIs the impulse variation;
calculating the moment of inertia of the spatially non-cooperative target using the following formula:
Figure FDA0003276081700000025
wherein the content of the first and second substances,
Figure FDA0003276081700000026
is the optimal solution of the magnitude of the main inertia moment, and K is | | xlI and
Figure FDA0003276081700000027
ratio of (a) | | xlI is a double vertical linear inner vector xlThe die of (a) is used,
Figure FDA0003276081700000028
Figure FDA0003276081700000029
Figure FDA00032760817000000210
is a normalized primary moment of inertia,
Figure FDA00032760817000000211
the rotational inertia components of the x-axis, the y-axis and the z-axis of the normalized principal moment of inertia, respectively;
Figure FDA00032760817000000212
Figure FDA00032760817000000213
is an estimate of the angular momentum,
Figure FDA00032760817000000214
ro,cm (1)for vectors from origin to centroid after derotation of a set time, ro,cm (0)Vector from origin to centroid for despin, T (q)p) Is a four-element qpOf the rotation matrix qpThe upper corner mark (1) represents racemization setting time, and the upper corner mark (0) represents racemization front.
2. The racemization identification device according to claim 1, wherein the electromagnet rotating device specifically comprises:
the device comprises a rotary table, a rotating shaft, a power supply device and a plurality of electromagnets;
the rotating shaft penetrates through the turntable and is connected with the driving end of the mechanical arm, and the rotating shaft is arranged in the middle of the turntable; the electromagnets are respectively arranged at the edges of the turnplate, and the turnplate is used for driving the electromagnets to rotate; the power supply device is sleeved on the outer side of the rotating shaft and used for providing electric energy for the electromagnet.
3. The racemization identification device according to claim 2, wherein the power supply device specifically comprises:
an electric brush and a conductive ring;
the conducting ring is sleeved outside the rotating shaft, and the electric brush is sleeved outside the conducting ring; the electric brush is in sliding contact with the conducting ring, and the electric brush provides electric energy for the electromagnet when in sliding contact with the conducting ring.
4. The racemization identification device according to claim 3, wherein the electromagnet is a U-shaped electromagnet.
5. A racemization recognition method applied to the racemization recognition device according to any one of claims 1 to 4, wherein the method comprises the following steps:
the working spacecraft controls the mechanical arm to drive the electromagnet rotating device, so that the distance between the electromagnet rotating device and a space non-cooperative target is within a preset range;
the working spacecraft acquires an image of the space non-cooperative target and the reaction force of the electromagnet rotating device on the space non-cooperative target;
the working spacecraft acquiring the image of the space non-cooperative target specifically comprises the following steps:
the working spacecraft acquires a first image and a second image; the first image is an image of the space non-cooperative target obtained by the working spacecraft before the despinning operation of the electromagnet rotating device on the space non-cooperative target is carried out; the second image is an image of the space non-cooperative target obtained by the working spacecraft after the despinning operation of the electromagnet rotating device on the space non-cooperative target is carried out;
the working spacecraft determines the parameters of the space non-cooperative target according to the image and the reaction force; the method specifically comprises the following steps:
determining the mass and the moment of inertia of the space non-cooperative target according to the image and the reaction force;
the method for determining the quality of the space non-cooperative target specifically comprises the following steps:
the working spacecraft determines the initial rotation angular speed of the space non-cooperative target according to the first image;
the working spacecraft determines the rotation angular speed of the space non-cooperative target according to the second image;
integrating the reaction force with time to obtain impulse force applied to the space non-cooperative target; the impulse force is calculated by the following formula:
Figure FDA0003276081700000041
wherein, t0Is the initial time, and delta t is the racemization time;
determining the quality of the space non-cooperative target according to the impulse force applied to the space non-cooperative target and the difference value between the despun rotation angular velocity and the initial rotation angular velocity; the method specifically comprises the following steps:
calculating the quality of the spatial non-cooperative target by adopting the following formula:
Figure FDA0003276081700000042
Figure FDA0003276081700000043
wherein the content of the first and second substances,
Figure FDA0003276081700000044
for angular velocity differences, the superscript T is the transposed symbol, vcm (1)For despin angular velocity of rotation, vcm (0)For the purpose of the initial angular velocity of rotation,
Figure FDA0003276081700000045
for the quality estimation, Δ iforceIs the impulse variation;
calculating the moment of inertia of the spatially non-cooperative target using the following formula:
Figure FDA0003276081700000046
wherein the content of the first and second substances,
Figure FDA0003276081700000047
is the optimal solution of the magnitude of the main inertia moment, and K is | | xlI and
Figure FDA0003276081700000048
ratio of (a) | | xlI is a double vertical linear inner vector xlThe die of (a) is used,
Figure FDA0003276081700000049
Figure FDA00032760817000000410
Figure FDA00032760817000000411
is a normalized primary moment of inertia,
Figure FDA00032760817000000412
the rotational inertia components of the x-axis, the y-axis and the z-axis of the normalized principal moment of inertia, respectively;
Figure FDA00032760817000000413
Figure FDA00032760817000000414
is an estimate of the angular momentum,
Figure FDA00032760817000000415
ro,cm (1)for vectors from origin to centroid after derotation of a set time, ro,cm (0)Vector from origin to centroid for despin, T (q)p) Is a four-element qpOf the rotation matrix qpThe upper corner mark (1) represents racemization setting time, and the upper corner mark (0) represents racemization front.
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