JPH02224991A - Method for identifying moment of inertia of robot arm using machine resonance - Google Patents

Abstract

PURPOSE:To carry out the identification of the moment of inertia of a robot arm simply and with high accuracy by detecting motion which is generated by a motor with respect to an adjacent link by means of an acceleration pickup and applying the signal thereof to the joint motor of the adjacent link as normal feedback. CONSTITUTION:Motion that the joint motor 5 of a link 6 to be measured generates with respect to an adjacent link 3 is detected by an acceleration pickup 20, and applied to the joint motor 2 of the adjacent link 3 as normal feedback. As a result, the generation of coupled vibration is suppressed to obtain an accurate fixed value.

Description

[Detailed description of the invention] [Industrial application field] This article relates to a method for identifying the moment of inertia of a robot arm.

[Summary of the invention]

The present invention uses a dynamic characteristic model of a single motor load system to drive a joint motor to be measured in a moment of inertia identification method that utilizes the property that the resonance frequency changes when the mass of the load changes. By detecting the forced vibration generated by the motor in relation to the adjacent link using an acceleration pickup and applying the signal as positive feedback to the joint motor of the link, the influence of the achieved vibration generated by the forced vibration can be reduced. This is to obtain an accurate moment of inertia.

[Prior Art] In order to control industrial or research and development robots at high speed and with high precision, it is necessary to accurately identify the moment of inertia of a robot arm, and several methods have been used in the past.

Specifically, there were methods to calculate it based on drawings, methods to find it from the moment of inertia measuring device number, and methods to find it analytically by comparing the dynamic characteristic model of the robot arm with experimental results.

[Problem that the invention seeks to solve]

However, the method of calculating by calculation based on drawings assumes that the mechanical body is made with extremely high precision, and has the drawback that accurate values cannot be obtained for actual robots. Another disadvantage is that the calculation requires a lot of effort. Furthermore, this method cannot be taken if the user of the robot does not own the blueprints for the robot.

In addition, current moment of inertia measurement devices are suitable for measuring the moment of inertia of shaft-shaped parts with simple shapes.
It is difficult to apply to measuring mechanical bodies with complex shapes such as robot arms, and furthermore, expensive measuring equipment is required.
There were drawbacks such as. In addition, there is a method of analytically determining the moment of inertia using the law of conservation of energy (Transactions of the Society of Instrument and Control Engineers, Vol. 22-6, pp. 637-6).
43, 1987) has been proposed. However, this method does not give sufficient consideration to nonlinear elements such as the viscous friction coefficient and dynamic friction torque, and has the disadvantage that the moment of inertia of a mechanical body with large nonlinear elements such as a robot arm cannot be accurately identified.

Furthermore, as an identification method that is not affected by nonlinear elements, when the joint axes of the link other than the link to be measured are mechanically fixed and the joint motor of the link to be measured is driven, the robot arm is unloaded and loaded. A method has been proposed to calculate the moment of inertia of the link by focusing on the fact that the resonant frequency of the arm changes when the arm is held (Robot Society of Japan Paper Vol. 16, No. 4, pp. 282-291, 1
988), in this method, when measuring the moment of inertia of a robot arm as shown in Fig. 2, all joint motors other than the one to be measured are fixed, and a single motor load is measured isometrically as shown in Fig. 3(a). The moment of inertia is determined using the mechanical resonance model of the system.

Generally, the connection between the encoder and motor is much stronger than the connection between the motor load and can be considered as one unit.

However, with this method, if the joint axis that is not the target of measurement is not mechanically fixed sufficiently, the movement of the link to be measured will be transmitted to the adjacent joint axis, resulting in vibrations that will occur and the measurement accuracy will deteriorate. There was a phenomenon. Furthermore, this method requires modification of the jig or robot arm for fixing the joint axes, and there is a problem in that adding the jig or modification changes the moment of inertia of the object to be measured itself.

[Means for Solving the Problems] In order to solve the above problems, the present invention drives a joint motor to be measured, and uses an acceleration pickup to detect forced vibrations generated by the motor in relation to adjacent links. We decided to detect the signal and apply it as positive feedback to the joint motor of the adjacent link.

[Effect] As mentioned above, by detecting the motion generated by the joint motor of the link to be measured relative to the adjacent link using an acceleration pickup and applying it as positive feedback to the joint motor wall of the adjacent link, the rapid vibration is occurrence is suppressed and accurate identification values can be obtained. The principle of this action is shown in Figure 3 (b
). In FIG. 2, the second joint axis 1
Let us find the moment of inertia for 5. During measurement, the first joint shaft 14 is fixed and the second joint shaft 15 is fixed.
The joint motor 5 is driven. Since the stiffness of the joint is generally much lower than that of the link, the link mechanism shown in Fig. 2 is modeled as a plurality of spring-mass systems as shown in Fig. 3(b). If the second joint motor 5 is driven when the joint shaft 14 of is not sufficiently fixed,
The vibration is transmitted to the first spring element 25 of the first joint shaft 14, and the achieved vibration is generated.

According to the present invention, an acceleration pickup is attached to the first link 3 to detect the movement of the second joint motor 5, and the signal is positively fed back to the first joint motor 2, so that the first joint axis 14 is Move synchronously with the movement of link 3,
By making the displacement of the first spring element 25 of the first joint shaft 14 minute, rapid vibration can be suppressed and the moment of inertia can be accurately identified. Furthermore, since there is no need to modify the robot arm or use special jigs, measurements can be performed easily and at low cost.

[Example] The contents of the present invention will be explained based on the drawings. FIG. 2 is an external view of a robot generally called a SCARA type robot, which has three joints in the horizontal direction and one joint in the vertical direction. Let us find the moment of inertia of this robot with respect to the horizontal rotation joint. FIG. 3(b) is a model of the above-mentioned SCARA type robot. Here, the third joint axis 16 is the robot tip axis, and since we are considering an unloaded state, it is added to the mass m2 of the second link 6 as a mere mass in the model. In the figure, 01 is the displacement of the 1st joint axis, k3 is the spring constant of the 1st spring element, B1 is the viscous friction coefficient of the 1st spring element, ml is the mass of the 1st link, and 1 is the circumference of the center of gravity of the 1st link. moment of inertia, d
l is the length of the first link, and S is the position of the center of gravity of the first link. Further, fcl is the Coulomb friction torque of the first joint axis, and D is the viscous friction coefficient of the second joint axis.

Here, the spring element is specifically generated by a gear component, which is used in most robots as a speed reducer. When the equation of motion is derived from this model, it becomes Equation (1).

=J,, (B2) θ -2m2 d+ B2 -m2 d+ B2 5 J12 (B2 ) θ +m2d + 32 S + J +□ (B2 ) B2 sin B2 × 01 B2 1 n B2 × B1 θ+fe+ + J 2 □θ2 1nθ2 ×θ〒 ... (1) + D 2 B2 +'fc2 In equation (1), the effective inertia Jll of the first and second joint axes 14.15, J22, the first and second joint axes 14.1
The mutual inertia J1° between 5 is given by the following formula.

Jl, (B2)20+2βcos θ2J, 2(B2
)=γ+βcos B2... (2) J2゜(
B2)=J2□=γ However, a, β, and γ are coefficients determined by the following equation.

a=I+ +m+ S+"+I2+m2fd+"+S+
”) β=m2al B2 ・= (3
) γ: ■2 + m2 S 2 Therefore, once α, β, and γ are determined, the moment of inertia of each joint axis can be determined according to equation (2).

When considering a single system (load to mortal encoder), it is modeled as shown in FIG. 3(a). load 2
9, the motor 28, and the encoder 27 each have a moment of inertia J, , J, J, and are connected by a shaft having a spring constant and a viscosity coefficient shown in the figure. Generally, the moment of inertia of an encoder is sufficiently smaller than the moment of inertia of a load or a motor. Also, the viscosity coefficient of the shaft can be considered to be almost zero, and the connection between the motor and encoder is much stronger than the connection between the motor and load, and Kffl-)K
It can be considered as -1. Under this approximation, the resonant frequency is derived as follows.

Equation (4) clearly shows that when the mass of the load changes, f
, , the value of f2 changes. The above-mentioned α, β, and γ are determined using the properties of this mechanical resonance. Hereinafter, f1 will be referred to as the notch frequency. When a new load m is applied to the tip of the robot arm in the model shown in Figure 3(b), the equation of motion (1)
is modified as follows.

J,, (θri=J, +(B2) +Im+m(d+”+
d2 +2al d2CO6θ2) Jl. (B2)=J, 2(B2)+Im+m (d2
"+d+ d2 cos θ2 )". From equation (6), γ is determined as equation (7).

The effective inertia of the first and second articulation axes 14.15 and the mutual inertia between the first and second articulation axes 14.15 are changed by. Actually apply a load to the robot tip to find the resonant frequency, and use this equation (5) and the above equation (4) to calculate α,
Calculate β and γ. First, the first joint shaft 14 is fixed, and the notch frequency of the second joint shaft 15 is measured when no load is applied and when a load is applied. This notch frequency is calculated using equations (4) and (5).
Therefore, the following formula is obtained.

f +2+ = (k2/γ)”2/2πfm+z+=
(k2 /fy+ 1 m+md2") "2/
2x...(6) Here, f 1+ is the notch frequency in the case of no load, f
M+21 is the notch frequency when a load is applied. Also, the spring constant of 2 for the second joint axis 15 does not change depending on the presence or absence of a load or the posture of the arm... (7) Next, set the second joint axis 15 to 02=0, that is, the arm is extended straight. Notch frequencies f n+ , fmN+ of the first joint shaft 14 when fixed in the state, no load and load applied
Measure. Furthermore, the second joint axis 15 is set at another angle θ2, and the notch frequency f (+B) in a no-load state is determined.

However, θ2≠0.

These f n+ , fmn+, f (Ill, θ2
From equations (4) and (5), β becomes the following equation.

f+? ++ (f +?1 f mn+) further α
is the following formula.

f'(B-f2N+...(9) Thus α,
By determining β and γ and substituting these values into equation (2), the moment of inertia of each joint axis has been identified.

In this identification method, instead of identifying the physical parameters of the inertial term such as mass, link length, and center of gravity position individually, α, β,
It is obtained as a group indicated by γ, which has the advantage of preventing the accumulation of errors and further reducing the time and cost required for identification. If an attempt is made to fix the joint axes mechanically during actual measurements, it will be necessary to modify the robot or use a special jig, and there is a high possibility that rapid vibration will occur. FIG. 4 shows a comparison of the notch frequency of the second joint shaft 15 between the case where the achieved vibration does not exist and the case where the achieved vibration exists. The angle θ2 of the second joint axis 15 is plotted on the horizontal axis, and the change in the notch frequency of the second joint axis 15 under load and under no load is shown. It can be seen that the notch frequency changes greatly depending on the presence of the achieved vibration. Furthermore, even if you try to achieve this electrically by applying a high-gain position servo to the joint axis to be fixed instead of mechanically fixing it, it will not have any effect because the spring element of the joint axis exists outside the servo loop in the first place. .

FIG. 1 is a configuration diagram of a measuring device according to the present invention. In the present invention, the frequency of the second joint axis 15 is increased by driving the first joint motor 2 along the movement of the first link 3 so that the spring element interposed therein does not act. This eliminates the influence of rapid vibration caused by the vibration of the first link 3 when measuring characteristics. The vibration of the first link 3 may be measured by attaching an acceleration pickup 20.

The above can be described theoretically as follows. Regarding the part of the first joint shaft 14 in FIG. 1, FIG. 3 (
Considering the model a), the equation of motion is written in Laplace transform form as follows.

iKt = (JfflS”+DfflS+Kml
/N2) θm-, /N・θ1T, 5+s= (
J+s2+D+s+Km+)θ, -Kffi, /N-θ
.

... (10) However, as mentioned above, Bffl,, B, are almost zero,
Think of the motor and encoder as one. 1 is the motor current, K is the torque constant, N is the reduction ratio, and T6□ is a disturbance for assuming the torque exerted on the first link 3 by the reaction force of the forced vibration of the second joint shaft 15. Further, the viscoelastic coefficient of the motor is D□, and the viscoelastic coefficient of the load is Dl.

Here, 1=Kv(K, s2θ1+KcS θ,) −
Apply the feedback in (11). KV, ni, ni,
is the feedback gain. Then, the disturbance T0. The transfer functions from Sθi to sei are as follows.

... (12) However, D(sl=JIJ+nS"+(Jl (Dm-KtKJ
sl+JmD+) S2+(JIKffll/N2
+ DI(Dm −KtKvKsl”JmKmKff
llKtKVKl/N)+S+KffllDl/N2+
ni, FD□-ni, ni, ni, l ・
... (13). From the above equation, if the speed deviation is set as se, then se = sθm/N-se... (14) Therefore, K, = NJ, /, Kv, K, = D, /,
- If (15) can be selected, the speed deviation can be made constant to zero in response to the input of the disturbance T dim in the ideal state. In other words, the first joint motor 2 can be moved together with the movement of the first link 3.
The spring element interposed here no longer acts as a low rigidity. Therefore, since no mechanical resonance occurs regarding the first joint axis, this does not affect the frequency characteristics of the second joint axis as rapid vibrations.

However, the denominator polynomial D (s) in this case is D(S)・
(Jls + 01) (Jms2+ Km+/N”)
・= (16), and stability becomes a problem because D (s) has an unstable pole, but stability can be ensured by applying damping to the signal in equation (11) by passing it through an appropriate filter. Ru.

FIG. 1 is a configuration diagram of a measuring device according to the present invention. The second joint axis is vibrated by the frequency analyzer 13, and the output of the second encoder 4 is subjected to F/V conversion and is taken into the frequency analyzer 13 again as a speed signal to measure the notch frequency.

An acceleration pickup 20 is attached to the first link 3, which detects the motion of the second joint axis as an acceleration signal, and passes the signal through a filter 22 to the first joint motor 2 of the first joint axis.
Please leave positive feedback. Further, the speed signal obtained from the first encoder 1 is also positively fed back to the first joint motor 2. When a servo system is configured for the first joint axis in this way, the first joint axis is controlled to move in synchronization with the movement of the second joint axis transmitted via the first link 3, The first joint axis and the first
The displacement of the spring element between the links 3 can be suppressed to an extremely small value, the notch frequency can be determined with high accuracy, and the accuracy of identifying the moment of inertia can be improved.

[Effects of the Invention] As described above, according to the present invention, high accuracy and simple operation can be achieved without requiring modification of the robot or special jigs, and without being affected by nonlinear elements such as viscous friction coefficient and dynamic friction torque. Therefore, the moment of inertia of the robot arm can be identified.

[Brief explanation of the drawing]

Figure 1 is a configuration diagram of a moment of inertia measuring device according to the present invention, Figure 2 is an external view of a SCARA robot, and Figure 3 (a).
is a diagram showing a model of a single load-mortal encoder system, Figure 3 (b) is a diagram showing a model of a multiple load-morph system, and Figure 4 is a diagram showing the influence of coupled vibration on the notch frequency. be. that's all

Claims (1)

[Claims] When measuring the moment of inertia of a robot arm, all joint motors other than the joint motor to be measured are fixed, and the moment of inertia of the robot arm is determined using a mechanical resonance model, considering it as a single motor-load system. In the moment of inertia identification method, the joint motor to be measured is driven, the motion that the motor generates with respect to the adjacent link is detected by an acceleration pickup, and the signal is applied as positive feedback to the joint motor of the adjacent link. A method for identifying the moment of inertia of a robot arm using mechanical resonance.