CN112975971A - A kind of robot inertia force compensation method - Google Patents

A kind of robot inertia force compensation method Download PDF

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CN112975971A
CN112975971A CN202110226160.8A CN202110226160A CN112975971A CN 112975971 A CN112975971 A CN 112975971A CN 202110226160 A CN202110226160 A CN 202110226160A CN 112975971 A CN112975971 A CN 112975971A
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inert
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acceleration
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CN112975971B (en
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段晋军
戴振东
刘正权
郭策
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Nanjing University of Aeronautics and Astronautics
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Nanjing University of Aeronautics and Astronautics
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    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J9/00—Programme-controlled manipulators
    • B25J9/16—Programme controls
    • B25J9/1628—Programme controls characterised by the control loop
    • B25J9/1638—Programme controls characterised by the control loop compensation for arm bending/inertia, pay load weight/inertia

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Abstract

The invention discloses a robot inertia force compensation method, which comprises the following steps of obtaining acceleration, obtaining inertia force, and establishing mapping between the inertia force and the acceleration: finert＝[M]A, calculating an inertial force compensation parameter [ M]Let the compensating force Fcomp＝‑FinertCompensating the moment Tcomp＝‑TinertThe method is used for compensating the inertia force with load measurement, wherein the tail end of the robot makes linear motion, a linear motion track parameter equation is established, the form is concise, the implementation is convenient, the acceleration changes according to a sine rule, the measurement is efficient and concise, and the smooth and simple control of the motion is ensured; in addition, by measuring the inertial force FinertThe measured acceleration a is utilized to establish the mapping relation between the inertia force and the acceleration, so that the inertia force is accurately compensated, the real-time calculation efficiency is improved, the shape and the material of the end effector of the robot do not need to be measured, and the complexity and the calculation error of integral calculation of the rotational inertia are avoided.

Description

Robot inertia force compensation method
Technical Field
The invention relates to the technical field of robot processing, in particular to a robot inertia force compensation method.
Background
The processing precision of the robot is closely related to acceleration and deceleration motion control and dynamics control of the robot. At present, when an industrial robot is applied to industries such as machining and assembly, the contact force between a robot terminal tool or a workpiece and the external environment needs to be accurately sensed so as to ensure the flexibility of operation. In the existing application, a six-component sensor is usually selected, which can measure three-dimensional orthogonal force and three-dimensional orthogonal moment, three-dimensional orthogonal acceleration and three-dimensional orthogonal angular acceleration in any force system in space; under dynamic conditions, the moment measured by the robot end sensor comprises load gravity, load inertia force and external contact force applied to the load. In a closed-loop force control algorithm, a robot controller corrects the motion of the robot at the next moment according to the force feedback and the pose feedback of a sensor;
in the process of movement of the robot mechanical arm, an inertial mass effect can be generated, which is caused by acceleration generated by a load end (a clamp, an actuator, a sensor and the like) of the sensor; the inertia force can be generated under the influence of the acceleration, and the measurement value of the sensor can be directly influenced;
the traditional load end inertial mass is obtained by performing integral calculation by using a theoretical mechanics theory according to the rigid body shape and the material of a robot end actuator (including a sensor and a clamp), and when the overall shape of the actuator is more regular, the calculation result is higher in precision, but in general, the actuator is formed by assembling a plurality of different components, and the material of each component is also larger in difference, so that the calculation error of the inertial mass M of the actuator is larger; therefore, the inertia force error obtained by multiplying the acceleration value a measured by the sensor by M obtained by theoretical calculation is also large, so that a robot inertia force compensation method is urgently needed to solve the problem in order to meet the requirement of the measurement accuracy of the machining contact force.
Disclosure of Invention
The invention provides a robot inertial force compensation method which can eliminate the influence of load inertial force on a sensor measurement value so as to accurately analyze the external contact force applied to a load, and solves the problems in the prior art.
In order to achieve the purpose, the invention provides the following technical scheme: a robot inertial force compensation method, comprising:
s1, obtaining acceleration, including planning the robotThe tail end moves linearly, the starting point and the end point of the tail end are determined, and a motion trail parameter equation is established as
Figure BDA0002956314690000021
Sampling all time step points in the linear motion, and calculating the acceleration a (t) of all the time step points;
s2, obtaining an inertia force, comprising:
a. method for obtaining sensor three-dimensional force F by using no-load motion of robotmeas＝(Fx，Fy，Fz) And three-way moment Tmeas＝(Tx，Ty，Tz)；
b. Identifying the gravity magnitude G and the centroid position C ═ C (C) by using a gravity compensation algorithmx,Cy,Cz)；
c. Decomposing gravity and gravity moment along the sensor coordinate system to obtain G '═ G'x,G′y,G′z) And T ═ T'x,T′y,T′z)；
d. Measuring a sensor value F in a sensor coordinate systemmeasAnd TmeasRespectively subtracting the gravity value G 'and the gravity moment T' to obtain an inertia force FinertAnd moment of inertia Tinert；
S3, establishing a mapping between inertia force and acceleration: finert＝[M]A, calculating an inertial force compensation parameter [ M]；
S4, make the compensation force Fcomp＝-FinertCompensating the moment Tcomp＝-TinertAnd the method is used for compensating the inertia force with load measurement.
Preferably, in step S1, the starting point Ps of the linear motion of the robot end is determined as (x)s,ys,zs) And end point Pe ═ xe,ye,ze) The straight-line distance between two points is
Figure BDA0002956314690000022
The total time of the linear motion of the tail end of the robot is T, wherein all points on the linear segment between the two points are positioned on the robot to doIn the space.
Preferably, in step S1, the trajectory parameter equation S is subjected to isoparameter sampling on t, and the acceleration a (t) is calculated as:
a. sampling parameters of the straight line s (t) to obtain discrete parameters
Figure BDA0002956314690000031
And a sequence of discrete points
Figure BDA0002956314690000032
Figure BDA0002956314690000033
Wherein A is 2 pi L/T2，ω＝2π/T；
b. Computing a sequence of velocity discrete points
Figure BDA0002956314690000034
Deriving t by the linear equation s (t):
Figure BDA0002956314690000035
wherein at each time sampling point tiIn the above-mentioned manner,
Figure BDA0002956314690000036
c. calculating acceleration discrete point sequences
Figure BDA0002956314690000037
Deriving t by the velocity equation v (t):
Figure BDA0002956314690000038
wherein at each time sampling point tiIn the above-mentioned manner,
Figure BDA0002956314690000039
preferably, in step S2, the robot performs idle motion, that is, only the end effector of the robot moves along the above-mentioned linear track, and does not need to contact with the real workpiece, so as to ensure that the sensor measurement value only includes gravity and inertia force.
Preferably, in step S2, when the gravity and the moment of gravity are resolved along the sensor coordinate system, the direction of the gravity of the robot end effector does not coincide with the Z direction of the sensor coordinate system, and the gravity is projected in three directions of the sensor coordinate system according to the posture of the robot end effector.
Preferably, in step S2, FmeasAnd TmeasRespectively subtracting the gravity value G 'and the gravity moment T', and specifically:
Finert_x＝Fmeas_x-G′x；
Finert_y＝Fmeas_y-G′y；
Finert_z＝Fmeas_z-G′z；
Tinert_x＝Tmeas_x-T′x；
Tinert_y＝Tmeas_y-T′y；
Tinert_z＝Tmeas_z-T′z。
preferably, in step S3, the discrete series of measurements are formed by a least squares method
Figure BDA0002956314690000041
And
Figure BDA0002956314690000042
fitting to obtain an inertia force compensation parameter M, wherein M is mass corresponding to translational motion, M is rotational motion, and M is rotational inertia, and in the F ═ Ma, when R is>(n +1), the least squares method is an over-determined equation whose solution is: m ═ aTa)-1aTF, wherein the dimension of F is [ R ]]Dimension of a [ R ]]And R is the number of rows of data.
Compared with the prior art, the invention has the beneficial effects that:
in the invention, the tail end of the robot makes linear motion, and a linear motion track parameter equation is established, so that the method has a simple form and is convenient to implement, and meanwhile, the acceleration sine law changes, the measurement is efficient and simple, and the smooth motion is ensured and is simple and controlled; in addition, by measuring the inertial force FinertThe measured acceleration a is utilized to establish the mapping relation between the inertia force and the acceleration, so that the inertia force is accurately compensated, the real-time calculation efficiency is improved, the shape and the material of the end effector of the robot are not required to be measured, the complexity and the calculation error of integral calculation of the rotational inertia are avoided, the influence of the action of the load inertia force on the measurement value of the sensor is eliminated, and the external contact force applied to the load is accurately analyzed.
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The accompanying drawings, which are included to provide a further understanding of the invention and are incorporated in and constitute a part of this specification, illustrate embodiments of the invention and together with the description serve to explain the principles of the invention and not to limit the invention.
In the drawings:
FIG. 1 is a general flowchart of a robot inertial force compensation method;
FIG. 2 is a graph of displacement versus time for a straight line trajectory;
FIG. 3 is a graph of velocity versus time for a straight-line trajectory;
FIG. 4 is a graph of acceleration versus time for a straight line trajectory.
Detailed Description
The preferred embodiments of the present invention will be described in conjunction with the accompanying drawings, and it will be understood that they are described herein for the purpose of illustration and explanation and not limitation.
Example (b): as shown in fig. 1, a robot inertial force compensation method for accurately compensating an inertial force by measuring the inertial force and using a measured acceleration to establish a mapping relationship between the inertial force and the acceleration, includes:
s1, obtaining the acceleration, including planning the end of the robot to do linear motion, anddetermining the starting point and the end point of the motion track, and establishing a motion track parameter equation of
Figure BDA0002956314690000051
Sampling all time step points in the linear motion, and calculating the acceleration a (t) of all the time step points;
first, the starting point Ps of the linear motion of the robot end is determined as (x)s,ys,zs) And end point Pe ═ xe,ye,ze) Calculating the linear distance between the two
Figure BDA0002956314690000052
Determining the total linear motion time of the tail end of the robot as T, wherein the distance between the two points is equal to the distance between the two points and is located in the robot working space, in the embodiment, L is 0.8m, and T is 8 s;
performing equal parameter sampling on t by using a track parameter equation s, and calculating an acceleration a (t) specifically as follows:
a. as shown in FIG. 1, for the displacement curve, the parameter sampling is performed on the straight line s (t) to obtain the discrete parameter
Figure BDA0002956314690000053
And a sequence of discrete points
Figure BDA0002956314690000054
Figure BDA0002956314690000055
Wherein A is 2 pi L/T2，ω＝2π/T；
b. As shown in FIG. 3, a velocity discrete point sequence is calculated for the velocity profile
Figure BDA0002956314690000056
Deriving t by the linear equation s (t):
Figure BDA0002956314690000057
wherein at each time sampling point tiIn the above-mentioned manner,
Figure BDA0002956314690000061
c. as shown in FIG. 4, a sequence of acceleration discrete points is calculated for the acceleration curve
Figure BDA0002956314690000062
Deriving t by the velocity equation v (t):
Figure BDA0002956314690000063
wherein at each time sampling point tiIn the above-mentioned manner,
Figure BDA0002956314690000064
s2, obtaining an inertia force, comprising:
a. method for obtaining sensor three-dimensional force F by using no-load motion of robotmeas＝(Fx，Fy，Fz) And three-way moment Tmeas＝(Tx，Ty，Tz) (ii) a In order to ensure that the measured value of the sensor only contains gravity and inertia force, the robot does no-load motion, namely, the tail end of the robot only moves along the linear track without contacting with a real workpiece;
b. identifying the gravity magnitude G and the centroid position C ═ C (C) by using a gravity compensation algorithmx,Cy,Cz) Wherein the Gravity Compensation algorithm adopts an algorithm disclosed in the document Bias Estimation and Gravity Compensation For Force-Torque Sensors;
c. decomposing gravity and gravity moment along the sensor coordinate system to obtain G '═ G'x,G′y,G′z) And T ═ T'x,T′y,T′z)；
When the gravity and the gravity moment are decomposed along a sensor coordinate system, wherein the gravity direction of the robot end effector is inconsistent with the Z direction of the sensor coordinate system, and the gravity is projected to three directions of the sensor coordinate system according to the posture of the robot end effector;
d. measuring a sensor value F in a sensor coordinate systemmeasAnd TmeasRespectively subtracting the gravity value G 'and the gravity moment T' to obtain an inertia force FinertAnd moment of inertia TinertThe method specifically comprises the following steps:
Finert_x＝Fmeas_x-G′x；
Finert_y＝Fmeas_y-G′y；
Finert_z＝Fmeas_z-G′z；
Tinert_x＝Tmeas_x-T′x；
Tinert_y＝Tmeas_y-T′y；
Tinert_z＝Tmeas_z-T′z。
s3, establishing a mapping between inertia force and acceleration: finert＝[M]A, calculating an inertial force compensation parameter [ M]；
Wherein, in step S3, the discrete sequence of measurement values is determined by the least squares method
Figure BDA0002956314690000071
And
Figure BDA0002956314690000072
fitting to obtain an inertia force compensation parameter M, wherein M is mass corresponding to translational motion, M is rotational motion, and M is rotational inertia, and in the F ═ Ma, when R is>(n +1), the least squares method is an over-determined equation whose solution is: m ═ aTa)-1aTF, wherein the dimension of F is [ R ]]Dimension of a [ R ]]R is the number of rows of data;
s4, make the compensation force Fcomp＝-FinertCompensating the moment Tcomp＝-TinertFor compensation of inertial forces with load measurement, improving the calculation for implementing compensationEfficiency.
Finally, it should be noted that: although the present invention has been described in detail with reference to the foregoing embodiments, it will be apparent to those skilled in the art that changes may be made in the embodiments and/or equivalents thereof without departing from the spirit and scope of the invention. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims (7)

1.一种机器人惯性力补偿方法，其特征在于，包括：1. a robot inertia force compensation method, is characterized in that, comprises: S1、获得加速度，包括规划机器人末端做直线运动，并确定其起点和终点，建立运动轨迹参数方程为
Figure FDA0002956314680000011
对直线运动中所有时间步长点采样，计算得到所有时间步长点的加速度a(t)；S1. Obtaining the acceleration, including planning the end of the robot to move in a straight line, and determining its starting point and end point, and establishing the parameter equation of the motion trajectory as
Figure FDA0002956314680000011
Sampling all time-step points in linear motion, and calculate the acceleration a(t) of all time-step points; S2、获得惯性力，包括：S2. Obtain inertial force, including: a、利用机器人空载运动获得传感器三向力Fmeas＝(Fx，Fy，Fz)和三向力矩Tmeas＝(Tx，Ty，Tz)；a. Obtain the sensor three-way force F meas = (F x , F y , F z ) and the three-way moment T meas = (T x , Ty , T z ) by using the no-load motion of the robot; b、利用重力补偿算法辨识重力大小G和质心位置C＝(Cx,Cy,Cz)；b. Use gravity compensation algorithm to identify gravity magnitude G and centroid position C=(C x , C y , C z ); c、将重力和重力矩沿传感器坐标系分解，得到G′＝(G′x,G′y,G′z)和T′＝(T′x,T′y,T′z)；c. Decompose gravity and gravitational moment along the sensor coordinate system to obtain G′=(G′ x , G′ y , G′ z ) and T′=(T′ x , T′ y , T′ z ); d、在传感器坐标系中将传感器测量值Fmeas和Tmeas分别减去重力值G′和重力矩T′得到惯性力为Finert和惯性力矩Tinert；d. In the sensor coordinate system, the sensor measurement values F meas and T meas are respectively subtracted from the gravity value G′ and the gravity moment T′ to obtain the inertial force as F inert and inertia moment T inert ; S3、建立惯性力和加速度之间的映射：Finert＝[M]·a，计算惯性力补偿参数[M]；S3. Establish the mapping between inertial force and acceleration: F inert = [M]·a, calculate the inertial force compensation parameter [M]; S4、令补偿力Fcomp＝-Finert，补偿力矩Tcomp＝-Tinert，用于带负载测量的惯性力补偿。S4. Let the compensation force F comp =-F inert , and the compensation torque T comp =-T inert , for inertia force compensation with load measurement. 2.根据权利要求1所述的一种机器人惯性力补偿方法，其特征在于：在步骤S1中，确定机器人末端直线运动的起点Ps＝(xs,ys,zs)和终点Pe＝(xe,ye,ze)，两点之间直线距离为
Figure FDA0002956314680000012
机器人末端直线运动总时间为T，其中，两点之间的直线段上所有点均位于机器人工作空间内。2. a kind of robot inertia force compensation method according to claim 1 is characterized in that: in step S1, determine the starting point Ps=(x s , y s , z s ) and end point Pe=( x e , y e , z e ), the straight-line distance between the two points is
Figure FDA0002956314680000012
The total time of the linear motion of the robot end is T, in which all points on the straight line segment between the two points are located in the robot workspace. 3.根据权利要求2所述的一种机器人惯性力补偿方法，其特征在于：在步骤S1中，将轨迹参数方程s对t进行等参采样，并计算加速度a(t)具体为：3. a kind of robot inertia force compensation method according to claim 2 is characterized in that: in step S1, the trajectory parameter equation s is carried out isoparametric sampling to t, and the calculation acceleration a (t) is specifically: a、对直线s(t)进行参数采样，得到离散后的参数
Figure FDA0002956314680000013
和离散点序列
Figure FDA0002956314680000014
a. Sampling the parameters of the straight line s(t) to obtain the discrete parameters
Figure FDA0002956314680000013
and discrete point sequence
Figure FDA0002956314680000014
Figure FDA0002956314680000015
Figure FDA0002956314680000015
 其中，A＝2πL/T2，ω＝2π/T；Among them, A=2πL/T 2 , ω=2π/T; b、计算速度离散点序列
Figure FDA0002956314680000021
通过直线方程s(t)对t求导：b. Calculate velocity discrete point sequence
Figure FDA0002956314680000021
Derivative for t by the straight line equation s(t):
Figure FDA0002956314680000022
Figure FDA0002956314680000022
 其中，在每个时间采样点ti上，
Figure FDA0002956314680000023
Among them, at each time sampling point t i ,
Figure FDA0002956314680000023
 c、计算加速度离散点序列
Figure FDA0002956314680000024
通过速度方程v(t)对t求导：c. Calculate the acceleration discrete point sequence
Figure FDA0002956314680000024
Derivative for t by the velocity equation v(t):
Figure FDA0002956314680000025
Figure FDA0002956314680000025
 其中，在每个时间采样点ti上，
Figure FDA0002956314680000026
Among them, at each time sampling point t i ,
Figure FDA0002956314680000026
 4.根据权利要求1所述的一种机器人惯性力补偿方法，其特征在于：在步骤S2中，机器人做空载运动，即机器人末端只有执行器沿上述直线轨迹运动，不需要与真实的工件接触，确保传感器测量值只包含重力和惯性力。4. a kind of robot inertia force compensation method according to claim 1 is characterized in that: in step S2, the robot does no-load motion, that is, the robot end only has the actuator to move along the above-mentioned linear trajectory, and does not need to be connected with the real workpiece Contact, make sure that the sensor measurements contain only gravitational and inertial forces. 5.根据权利要求1所述的一种机器人惯性力补偿方法，其特征在于：在步骤S2中，将重力和重力矩沿传感器坐标系分解时，机器人末端执行器的重力方向与传感器随体坐标系的Z方向不一致，根据机器人末端执行器的姿态将重力对传感器坐标系的三个方向进行投影。5. a kind of robot inertial force compensation method according to claim 1 is characterized in that: in step S2, when decomposing gravity and gravity moment along the sensor coordinate system, the gravity direction of the robot end effector and the sensor body coordinate The Z direction of the system is inconsistent, and the gravity is projected to the three directions of the sensor coordinate system according to the posture of the robot end effector. 6.根据权利要求1所述的一种机器人惯性力补偿方法，其特征在于：在步骤S2中，Fmeas和Tmeas分别减去重力值G′和重力矩T′，具体为：6. A kind of robot inertia force compensation method according to claim 1, is characterized in that: in step S2, F meas and T meas deduct gravity value G' and gravity moment T' respectively, specifically: Finert_x＝Fmeas_x-G′x；F inert_x =F meas_x -G'x; Finert_y＝Fmeas_y-G′y；F inert_y =F meas_y -G'y; Finert_z＝Fmeas_z-G′z；F inert_z =F meas_z -G'z; Tinert_x＝Tmeas_x-T′x；T inert_x =T meas_x -T'x; Tinert_y＝Tmeas_y-T′y；T inert_y =T meas_y -T'y; Tinert_z＝Tmeas_z-T′z。 Tinert_z =T meas_z -T' z . 7.根据权利要求1所述的一种机器人惯性力补偿方法，其特征在于：在步骤S3中，通过最小二乘法，由测量值的离散序列
Figure FDA0002956314680000031
和
Figure FDA0002956314680000032
拟合得到惯性力补偿参数M，其中，对应于平动运动，M为质量，对应于转动运动，M为转动惯量，在F＝Ma中，当R>(n+1)时，最小二乘法为超定方程，其解为：M＝(aTa)-1aTF，其中，F的维数为[R]，a的维数[R]，R为数据的行数。7. The method for compensating inertial force of a robot according to claim 1, characterized in that: in step S3, by the least squares method, a discrete sequence of measured values
Figure FDA0002956314680000031
and
Figure FDA0002956314680000032
The inertial force compensation parameter M is obtained by fitting, wherein, corresponding to translational motion, M is mass, corresponding to rotational motion, M is moment of inertia, in F=Ma, when R>(n+1), the least squares method is an overdetermined equation, and its solution is: M=(a T a) -1 a T F, where the dimension of F is [R], the dimension of a is [R], and R is the number of rows of data.
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