CN105538341A - Robot calibration system and method based on incomplete end coordinate information - Google Patents
Robot calibration system and method based on incomplete end coordinate information Download PDFInfo
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Abstract
The invention relates to a robot calibration system and method based on incomplete end coordinate information and belongs to the field of robot calibration. A magnetic gauge stand of the robot calibration system based on the incomplete end coordinate information is mounted on a fixed platform by means of magnetic force; the magnetic gauge stand is also connected with a tie wire sensor by means of a connecting rod; an end of a tie wire of the tie wire sensor is mounted on a universal joint; a tilt angle sensor is attached on and moves along with the universal joint that is mounted on a robot; the tie wire sensor and the tile angle sensor are in connection communication with a computer via a tie wire sensor cable and a tilt angle sensor cable, respectively, while the robot is in connection communication via a robot cable; and the computer is used for acquiring a tie wire length of the tie wire sensor, an angle of the tilt angle sensor and a joint turn angle of the robot. The robot calibration system and method based on the incomplete end coordinate information have the advantages of improving the reliability and accuracy of structural parameter calculation, and improving the calibration efficiency while simplifying operation steps.
Description
Technical field
The present invention relates to a kind of Robot calibration system and method based on end olonomic coordinate information, belong to Robot calibration field.
Background technology
Along with robot is in the extensive utilization of industry-by-industry, industry has strict requirement to industrial robot repetitive positioning accuracy spatially and absolute fix precision when moving, because robot is a kind of multiple degrees of freedom equipment, there is the shortcoming that error accumulation is amplified in this version, the structural parameters error in joint at different levels can be amplified step by step, thus causes the precision of robot to reduce.
Demarcation is the effective ways eliminating robot architecture's parameter error, and robot calibration method conventional at present generally all will by fine measuring instruments such as laser tracker, laser interferometer, three coordinate measuring machines.
The common feature of above method is the coordinate value will measuring robot end, and required calibration facility cost is high, complex operation step, require that higher, data acquisition is wasted time and energy to the technical merit of operating personnel, is difficult to realize automation.
Summary of the invention
The invention provides a kind of Robot calibration system and method based on end olonomic coordinate information, to solve the problems such as existing equipment cost is high, complex operation step, positioning precision are low.
Technical scheme of the present invention is: a kind of Robot calibration system based on end olonomic coordinate information, comprises fixed platform 1, Magnetic gauge stand 2, connecting rod 3, stay wire sensor 4, obliquity sensor 5, universal joint 6, robot 7, stay wire sensor cable 8, robot cable 9, obliquity sensor cable 10, computer 11;
Described Magnetic gauge stand 2 is arranged in fixed platform 1 by magnetic force, Magnetic gauge stand 2 and stay wire sensor 4 are linked together by connecting rod 3, the end of stay wire sensor 4 bracing wire is arranged on universal joint 6, universal joint 6 posts obliquity sensor 5, obliquity sensor 5 moves with universal joint 6, and universal joint 6 is arranged in robot 7; Stay wire sensor 4, obliquity sensor 5 are respectively by stay wire sensor cable 8, obliquity sensor cable 10 and computer 11 connecting communication, and robot 7 is by robot cable 9 and computer 11 connecting communication; Bracing wire length, the angle of obliquity sensor 5, the joint rotation angle of robot 7 of stay wire sensor 4 is gathered by computer 11.
Based on a robot calibration method for end olonomic coordinate information, the concrete steps of described method are as follows:
Step1, obliquity sensor 5 to be attached on universal joint 6, and universal joint 6 to be arranged on robot 7 end;
Step2, stay wire sensor 4 to be arranged on Magnetic gauge stand 2 by connecting rod 3, and fixed magnetic gauge stand 2, the end of the bracing wire of stay wire sensor 4 with universal joint 6 is connected;
Step3, to power on, open obliquity sensor 5, stay wire sensor 4, robot 7, and robot 7 is moved to initial pose and meets count initialized variable v=0;
Step4, judge whether that data acquisition operates;
If data acquisition, goes to Step7, if not yet complete, go to Step4;
Step5, counting variable are from increasing 1:v=v+1;
Step6, gathered the joint rotation angle data of the bracing wire length of stay wire sensor 4, the angle-data of obliquity sensor 5 and robot 7 by computer 11;
Step7, the pose of conversion robot 7, the principle of conversion is: the corner converting each joint according to the size of joint order successively (as: moves successively according to joint principle from small to large, joint one transforms to 20 ° from 0 °, transform to 40 ° from 20 ° more next time, by that analogy, the angle in each conversion joint increases by 20 °, be increased to 340 ° always, namely the pose conversion in this joint is completed, also can move according to the method in all the other joints, make each joint sufficient movement of robot 7, user also can increase or reduce the number of transitions of pose, to obtain more data), wherein all joints number of transitions is t, often converts once just to turn back to step Step4 and judge,
T=v is made after Step8, data acquisition;
The calculating of continuous 2 i and the j distances of Step9, robot 7 end spaces:
After data acquisition completes, utilization collects data can continuous 2 i and the j distance l of calculating robot 7 end spaces
i,j, because the bracing wire of stay wire sensor 4 is vertical all the time with obliquity sensor 5 place plane, and obliquity sensor 5 together with bracing wire along with universal joint 6 moves, the angle that then obliquity sensor 5 gathers is the angle α of bracing wire and horizontal plane x-axis, with the angle β of y-axis: the angle calculation first by collecting obtains the direction vector of bracing wire, secondly the angle of the bracing wire in i position and the bracing wire in j position is calculated according to the direction vector of bracing wire, the angle of the bracing wire of last basis in i position and the bracing wire in j position and the bracing wire in i position and calculate the distance between robot 7 end i and robot 7 end j 2 at the length gauge of the bracing wire of j position,
The calculating of direction vector:
Direction vector in the bracing wire of i position:
Utilization orientation cosine cos α
i 2+ cos β
i 2+ cos γ
i 2=1, calculate angle γ
ithus determine the direction vector m of the bracing wire in i position, m=(cos α
i, cos β
i, cos γ
i);
The direction vector n of the bracing wire in j position is: n=(cos α
j, cos β
j, cos γ
j);
The angle of the bracing wire in i position and the bracing wire in j position
for:
The calculating of robot 7 end i and j distance between two points:
According to the cosine law
obtain the distance l of end between i and the j of 2, space
i,j; In formula, l
i, l
jrepresent when robot 7 terminal position is respectively i, j, the bracing wire length of stay wire sensor 4; α
i, β
i, γ
irepresent when robot 7 terminal position is i respectively, the angle of bracing wire and horizontal plane x-axis, and angle, and the angle of z-axis of y-axis; α
j, β
j, γ
jrepresent when robot 7 terminal position is j respectively, the angle of bracing wire and horizontal plane x-axis, and angle, and the angle of z-axis of y-axis;
Solving of Step10, robot 7 structural parameters to be calibrated:
Utilize the joint rotation angle data of the robot 7 collected, the distance l calculated
i,j, and the kinematical equation of robot 7 lists t equation, each equation form is:
Wherein,
Expression robot 7 terminal position is positioned at coordinate value during i, θ
i, 1, θ
i, 2..., θ
i,wexpression robot 7 terminal position is positioned at w joint rotation angle value during i, and q is robot 7 structure parameter vectors to be identified;
Step10, solve the equation group of t equation composition:
…
In superincumbent equation group, the structure parameter vectors q only having robot 7 to be identified is uncertain, utilizes nonlinear least square method to solve, obtains the exact value of structure parameter vectors q;
Step11, by structure parameter vectors q substitute into robot 7 kinematical equation in, checking calibration result validity, complete the demarcation of robot 7.
Operation principle of the present invention is: stay wire sensor 4, obliquity sensor 5, universal joint 6, robot 7 are coupled together, the joint rotation angle of the length of stay wire sensor 4, the angle of obliquity sensor 5 and robot 7 is gathered by computer 11, and the pose of robot 7 is changed according to joint order change, make to collect sufficient data; First according to the direction vector of the angle determination bracing wire collected, secondly calculate the angle of any twice bracing wire according to direction vector, last according to calculate angle and any bracing wire length gauge collected for twice calculate the distance of robot 7 end 2 in space.According to the end equation that it is unknown quantity that the distance of 2 and the kinematical equation of robot 7 obtain with robot 7 structural parameters in space of robot 7, solve the demarcation that namely this equation realizes robot.
The invention has the beneficial effects as follows:
1, the stay wire sensor of vary in length is adopted, thus the space of robot becomes large when image data, the motion in each joint of robot is more abundant, provides the stronger Data support of robustness for structural parameters resolve proving operation is light more flexibly simultaneously.
2, robot end is in the distance of space point-to-point transmission, can accurately calculate according to the reading of stay wire sensor and obliquity sensor, improves reliability and precision that structural parameters resolve.
3, owing to not needing the coordinate value measuring robot end, because this simplify operating procedure and improve demarcation efficiency.
Accompanying drawing explanation
Fig. 1 is the pose figures of apparatus of the present invention in calibration process during image data;
Fig. 2 is the length of robot end of the present invention when pose i, j and angle schematic diagram;
Each label in figure: 1-fixed platform, 2-Magnetic gauge stand, 3-connecting rod, 4-stay wire sensor, 5-obliquity sensor, 6-universal joint, 7-robot, 8-stay wire sensor cable, 9-robot cable, 10-obliquity sensor cable, 11-computer.
Detailed description of the invention
Embodiment 1: as shown in Figure 1-2, based on a Robot calibration system for end olonomic coordinate information, comprise fixed platform 1, Magnetic gauge stand 2, connecting rod 3, stay wire sensor 4, obliquity sensor 5, universal joint 6, robot 7, stay wire sensor cable 8, robot cable 9, obliquity sensor cable 10, computer 11;
Described Magnetic gauge stand 2 is arranged in fixed platform 1 by magnetic force, Magnetic gauge stand 2 and stay wire sensor 4 are linked together by connecting rod 3, the end of stay wire sensor 4 bracing wire is arranged on universal joint 6, universal joint 6 posts obliquity sensor 5, obliquity sensor 5 moves with universal joint 6, and universal joint 6 is arranged in robot 7; Stay wire sensor 4, obliquity sensor 5 are respectively by stay wire sensor cable 8, obliquity sensor cable 10 and computer 11 connecting communication, and robot 7 is by robot cable 9 and computer 11 connecting communication; Bracing wire length, the angle of obliquity sensor 5, the joint rotation angle of robot 7 of stay wire sensor 4 is gathered by computer 11.
Based on a robot calibration method for end olonomic coordinate information, the concrete steps of described method are as follows:
Step1, obliquity sensor 5 to be attached on universal joint 6, and universal joint 6 to be arranged on robot 7 end;
Step2, stay wire sensor 4 to be arranged on Magnetic gauge stand 2 by connecting rod 3, and fixed magnetic gauge stand 2, the end of the bracing wire of stay wire sensor 4 with universal joint 6 is connected;
Step3, to power on, open obliquity sensor 5, stay wire sensor 4, robot 7, and robot 7 is moved to initial pose and meets count initialized variable v=0;
Step4, judge whether that data acquisition operates;
If data acquisition, goes to Step7, if not yet complete, go to Step4;
Step5, counting variable are from increasing 1:v=v+1;
Step6, gathered the joint rotation angle data of the bracing wire length of stay wire sensor 4, the angle-data of obliquity sensor 5 and robot 7 by computer 11;
The pose of Step7, conversion robot 7, the principle of conversion is: the corner converting each joint according to the size of joint order successively; Wherein all joints number of transitions is t, often converts once just to turn back to step Step4 and judge;
T=v is made after Step8, data acquisition;
The calculating of continuous 2 i and the j distances of Step9, robot 7 end spaces:
After data acquisition completes, utilization collects data can continuous 2 i and the j distance l of calculating robot 7 end spaces
i,j, because the bracing wire of stay wire sensor 4 is vertical all the time with obliquity sensor 5 place plane, and obliquity sensor 5 together with bracing wire along with universal joint 6 moves, the angle that then obliquity sensor 5 gathers is the angle α of bracing wire and horizontal plane x-axis, with the angle β of y-axis: the angle calculation first by collecting obtains the direction vector of bracing wire, secondly the angle of the bracing wire in i position and the bracing wire in j position is calculated according to the direction vector of bracing wire, the angle of the bracing wire of last basis in i position and the bracing wire in j position and the bracing wire in i position and calculate the distance between robot 7 end i and robot 7 end j 2 at the length gauge of the bracing wire of j position,
The calculating of direction vector:
Direction vector in the bracing wire of i position:
Utilization orientation cosine cos α
i 2+ cos β
i 2+ cos γ
i 2=1, calculate angle γ
ithus determine the direction vector m of the bracing wire in i position, m=(cos α
i, cos β
i, cos γ
i);
The direction vector n of the bracing wire in j position is: n=(cos α
j, cos β
j, cos γ
j);
The angle of the bracing wire in i position and the bracing wire in j position
for:
The calculating of robot 7 end i and j distance between two points:
According to the cosine law
obtain the distance l of end between i and the j of 2, space
i,j; In formula, l
i, l
jrepresent when robot 7 terminal position is respectively i, j, the bracing wire length of stay wire sensor 4; α
i, β
i, γ
irepresent when robot 7 terminal position is i respectively, the angle of bracing wire and horizontal plane x-axis, and angle, and the angle of z-axis of y-axis; α
j, β
j, γ
jrepresent when robot 7 terminal position is j respectively, the angle of bracing wire and horizontal plane x-axis, and angle, and the angle of z-axis of y-axis;
Solving of Step10, robot 7 structural parameters to be calibrated:
Utilize the joint rotation angle data of the robot 7 collected, the distance l calculated
i,j, and the kinematical equation of robot 7 lists t equation, each equation form is:
Wherein,
Expression robot 7 terminal position is positioned at coordinate value during i, θ
i, 1, θ
i, 2..., θ
i,wexpression robot 7 terminal position is positioned at w joint rotation angle value during i, and q is robot 7 structure parameter vectors to be identified;
Step10, solve the equation group of t equation composition:
…
In superincumbent equation group, the structure parameter vectors q only having robot 7 to be identified is uncertain, utilizes nonlinear least square method to solve, obtains the exact value of structure parameter vectors q;
Step11, by structure parameter vectors q substitute into robot 7 kinematical equation in, checking calibration result validity, complete the demarcation of robot 7.
Embodiment 2: as shown in Figure 1-2, based on a Robot calibration system for end olonomic coordinate information, comprise fixed platform 1, Magnetic gauge stand 2, connecting rod 3, stay wire sensor 4, obliquity sensor 5, universal joint 6, robot 7, stay wire sensor cable 8, robot cable 9, obliquity sensor cable 10, computer 11;
Described Magnetic gauge stand 2 is arranged in fixed platform 1 by magnetic force, Magnetic gauge stand 2 and stay wire sensor 4 are linked together by connecting rod 3, the end of stay wire sensor 4 bracing wire is arranged on universal joint 6, universal joint 6 posts obliquity sensor 5, obliquity sensor 5 moves with universal joint 6, and universal joint 6 is arranged in robot 7; Stay wire sensor 4, obliquity sensor 5 are respectively by stay wire sensor cable 8, obliquity sensor cable 10 and computer 11 connecting communication, and robot 7 is by robot cable 9 and computer 11 connecting communication; Bracing wire length, the angle of obliquity sensor 5, the joint rotation angle of robot 7 of stay wire sensor 4 is gathered by computer 11.
Embodiment 3: as shown in Figure 1-2, a kind of robot calibration method based on end olonomic coordinate information, the concrete steps of described method are as follows:
Step1, obliquity sensor 5 to be attached on universal joint 6, and universal joint 6 to be arranged on robot 7 end;
Step2, stay wire sensor 4 to be arranged on Magnetic gauge stand 2 by connecting rod 3, and fixed magnetic gauge stand 2, the end of the bracing wire of stay wire sensor 4 with universal joint 6 is connected;
Step3, to power on, open obliquity sensor 5, stay wire sensor 4, robot 7, and robot 7 is moved to initial pose and meets count initialized variable v=0;
Step4, judge whether that data acquisition operates;
If data acquisition, goes to Step7, if not yet complete, go to Step4;
Step5, counting variable are from increasing 1:v=v+1;
Step6, gathered the joint rotation angle data of the bracing wire length of stay wire sensor 4, the angle-data of obliquity sensor 5 and robot 7 by computer 11;
The pose of Step7, conversion robot 7, the principle of conversion is: the corner converting each joint according to the size of joint order successively; Wherein all joints number of transitions is t, often converts once just to turn back to step Step4 and judge;
T=v is made after Step8, data acquisition;
The calculating of continuous 2 i and the j distances of Step9, robot 7 end spaces:
After data acquisition completes, utilization collects data can continuous 2 i and the j distance l of calculating robot 7 end spaces
i,j, because the bracing wire of stay wire sensor 4 is vertical all the time with obliquity sensor 5 place plane, and obliquity sensor 5 together with bracing wire along with universal joint 6 moves, the angle that then obliquity sensor 5 gathers is the angle α of bracing wire and horizontal plane x-axis, with the angle β of y-axis: the angle calculation first by collecting obtains the direction vector of bracing wire, secondly the angle of the bracing wire in i position and the bracing wire in j position is calculated according to the direction vector of bracing wire, the angle of the bracing wire of last basis in i position and the bracing wire in j position and the bracing wire in i position and calculate the distance between robot 7 end i and robot 7 end j 2 at the length gauge of the bracing wire of j position,
The calculating of direction vector:
Direction vector in the bracing wire of i position:
Utilization orientation cosine cos α
i 2+ cos β
i 2+ cos γ
i 2=1, calculate angle γ
ithus determine the direction vector m of the bracing wire in i position, m=(cos α
i, cos β
i, cos γ
i);
The direction vector n of the bracing wire in j position is: n=(cos α
j, cos β
j, cos γ
j);
The angle of the bracing wire in i position and the bracing wire in j position
for:
The calculating of robot 7 end i and j distance between two points:
According to the cosine law
obtain the distance l of end between i and the j of 2, space
i,j; In formula, l
i, l
jrepresent when robot 7 terminal position is respectively i, j, the bracing wire length of stay wire sensor 4; α
i, β
i, γ
irepresent when robot 7 terminal position is i respectively, the angle of bracing wire and horizontal plane x-axis, and angle, and the angle of z-axis of y-axis; α
j, β
j, γ
jrepresent when robot 7 terminal position is j respectively, the angle of bracing wire and horizontal plane x-axis, and angle, and the angle of z-axis of y-axis;
Solving of Step10, robot 7 structural parameters to be calibrated:
Utilize the joint rotation angle data of the robot 7 collected, the distance l calculated
i,j, and the kinematical equation of robot 7 lists t equation, each equation form is:
Wherein,
Expression robot 7 terminal position is positioned at coordinate value during i, θ
i, 1, θ
i, 2..., θ
i,wexpression robot 7 terminal position is positioned at w joint rotation angle value during i, and q is robot 7 structure parameter vectors to be identified;
Step10, solve the equation group of t equation composition:
…
In superincumbent equation group, the structure parameter vectors q only having robot 7 to be identified is uncertain, utilizes nonlinear least square method to solve, obtains the exact value of structure parameter vectors q;
Step11, by structure parameter vectors q substitute into robot 7 kinematical equation in, checking calibration result validity, complete the demarcation of robot 7.
By reference to the accompanying drawings the specific embodiment of the present invention is explained in detail above, but the present invention is not limited to above-mentioned embodiment, in the ken that those of ordinary skill in the art possess, various change can also be made under the prerequisite not departing from present inventive concept.
Claims (2)
1. based on a Robot calibration system for end olonomic coordinate information, it is characterized in that: comprise fixed platform (1), Magnetic gauge stand (2), connecting rod (3), stay wire sensor (4), obliquity sensor (5), universal joint (6), robot (7), stay wire sensor cable (8), robot cable (9), obliquity sensor cable (10), computer (11);
Described Magnetic gauge stand (2) is arranged in fixed platform (1) by magnetic force, Magnetic gauge stand (2) and stay wire sensor (4) are linked together by connecting rod (3), the end of stay wire sensor (4) bracing wire is arranged on universal joint (6), universal joint (6) posts obliquity sensor (5), obliquity sensor (5) moves with universal joint (6), and universal joint (6) is arranged in robot (7); Stay wire sensor (4), obliquity sensor (5) are respectively by stay wire sensor cable (8), obliquity sensor cable (10) and computer (11) connecting communication, and robot (7) is by robot cable (9) and computer (11) connecting communication; Bracing wire length, the angle of obliquity sensor (5), the joint rotation angle of robot (7) of stay wire sensor (4) is gathered by computer (11).
2. based on a robot calibration method for end olonomic coordinate information, it is characterized in that: the concrete steps of described method are as follows:
Step1, obliquity sensor (5) to be attached on universal joint (6), and universal joint (6) is arranged on robot (7) end;
Step2, stay wire sensor (4) is arranged on Magnetic gauge stand (2) by connecting rod (3), and fixed magnetic gauge stand (2), the end of the bracing wire of stay wire sensor (4) with universal joint (6) is connected;
Step3, to power on, open obliquity sensor (5), stay wire sensor (4), robot (7), and robot (7) is moved to initial pose and meets count initialized variable v=0;
Step4, judge whether that data acquisition operates;
If data acquisition, goes to Step7, if not yet complete, go to Step4;
Step5, counting variable are from increasing 1:v=v+1;
Step6, the bracing wire length being gathered stay wire sensor (4) by computer (11), the angle-data of obliquity sensor (5) and the joint rotation angle data of robot (7);
The pose of Step7, conversion robot (7), the principle of conversion is: the corner converting each joint according to the size of joint order successively; Wherein all joints number of transitions is t, often converts once just to turn back to step Step4 and judge;
T=v is made after Step8, data acquisition;
The calculating of Step9, continuous 2 i and the j distances of robot (7) end spaces:
After data acquisition completes, utilization collects data and gets final product continuous 2 i and the j distance l of calculating robot (7) end spaces
i,j, because the bracing wire of stay wire sensor (4) is vertical all the time with obliquity sensor (5) place plane, and obliquity sensor (5) together with bracing wire along with universal joint (6) motion, the angle that then obliquity sensor (5) gathers is the angle α of bracing wire and horizontal plane x-axis, with the angle β of y-axis: the angle calculation first by collecting obtains the direction vector of bracing wire, secondly the angle of the bracing wire in i position and the bracing wire in j position is calculated according to the direction vector of bracing wire, the angle of the bracing wire of last basis in i position and the bracing wire in j position and the bracing wire in i position and calculate the distance between robot (7) end i and robot (7) end j 2 at the length gauge of the bracing wire of j position,
The calculating of direction vector:
Direction vector in the bracing wire of i position:
Utilization orientation cosine cos α
i 2+ cos β
i 2+ cos γ
i 2=1, calculate angle γ
ithus determine the direction vector m of the bracing wire in i position, m=(cos α
i, cos β
i, cos γ
i);
The direction vector n of the bracing wire in j position is: n=(cos α
j, cos β
j, cos γ
j);
The angle of the bracing wire in i position and the bracing wire in j position
for:
The calculating of robot (7) end i and j distance between two points:
According to the cosine law
obtain the distance l of end between i and the j of 2, space
i,j; In formula, l
i, l
jrepresent when robot (7) terminal position is respectively i, j, the bracing wire length of stay wire sensor (4); α
i, β
i, γ
irepresent when robot (7) terminal position is i respectively, the angle of bracing wire and horizontal plane x-axis, and angle, and the angle of z-axis of y-axis; α
j, β
j, γ
jrepresent when robot (7) terminal position is j respectively, the angle of bracing wire and horizontal plane x-axis, and angle, and the angle of z-axis of y-axis;
Solving of Step10, robot to be calibrated (7) structural parameters:
Utilize the joint rotation angle data of the robot (7) collected, the distance l calculated
i,j, and the kinematical equation of robot (7) lists t equation, each equation form is:
Wherein,
expression robot (7) terminal position is positioned at coordinate value during i, θ
i, 1, θ
i, 2..., θ
i,wexpression robot (7) terminal position is positioned at w joint rotation angle value during i, and q is robot (7) structure parameter vectors to be identified;
expression robot (7) terminal position is positioned at coordinate value during j, θ
j, 1, θ
j, 2..., θ
j,wexpression robot (7) terminal position is positioned at w joint rotation angle value during j;
Step10, solve the equation group of t equation composition:
…
In superincumbent equation group, the structure parameter vectors q only having robot (7) to be identified is uncertain, utilizes nonlinear least square method to solve, obtains the exact value of structure parameter vectors q;
Step11, by structure parameter vectors q substitute into robot (7) kinematical equation in, checking calibration result validity, complete the demarcation of robot (7).
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CN115096264A (en) * | 2022-07-25 | 2022-09-23 | 昆明理工大学 | Novel omnidirectional tilt angle sensor and use method thereof |
CN115096264B (en) * | 2022-07-25 | 2023-01-13 | 昆明理工大学 | Novel omnidirectional tilt angle sensor and use method thereof |
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