JPS63121904A - State space converting function filter - Google Patents

Abstract

PURPOSE:To estimate parameters only with angle and velocity without using acceleration neither taking the inverse matrix of an inertial matrix by using specific state space converting function filters. CONSTITUTION:(s+mu)<-1> filters 12a-12c are so constituted that the output of a function device 10 is inputted to a part of these filters and an input having no parameters to a controlled system is directly inputted to another part, and mu(s+mu)<-1> filters 11a-11c are so constituted that the output of the function part 10 is inputted to a part of these filters and the output of a detecting means which detects the extent of motion of the controlled system 6 is directly inputted to another part. Outputs from (s+mu)<-1> filters 12a-12c and mu(s+mu)<-1> filter 11a-11c are inputted to an estimating or adjusting device. Thus, an acceleration term is eliminated to obtain terms up to speed, and parameters are processed as they are linear, thus facilitating estimating parameters.

Description

DETAILED DESCRIPTION OF THE INVENTION (1) Purpose of the Invention Industrial Field of Application The present invention is directed to a vertically articulated robot manipulator, etc., which is rich in interference and nonlinearity, and in which the inertia term is affected by acceleration. This is a target that includes some unknown parameters, and is related to adaptive control or estimation of parameters used for control, and the entire parameter is estimated by the first-order derivatives without using acceleration, that is, the second-order derivatives. This is related to the configuration of the filter that enables this.

In devices such as a vertical multi-joint robot arm, where each joint interferes with each other and the load changes, such as when grasping and releasing an object, the control characteristics may deteriorate if the gain is kept fixed as in the conventional PID control method. This causes problems such as vibration and inability to perform precise movements.

For objects that interfere with each other in this way, non-interference control that cancels out the interfering terms and makes each axis independent is effective.

However, in this case, correct values for each arm's inertia, gravity, center of gravity, etc. are required.

Furthermore, if one controller is to be applied to several types of vertically articulated robot arms, it is necessary to find and adjust parameters each time.

Even in such a case, if the parameters are adapted while being estimated, troublesome adjustments can be eliminated, but this requires means for estimating the parameters.

A method for estimating such parameters is the least squares method, but in order to estimate it, it is possible to replace the parameters linearly or in a summarized form. must be linear.

Furthermore, in those using conventional filters, there are limitations such as the fact that the acceleration parameter cannot be changed.

Description of the Prior Art Conventionally, it has generally been possible to accurately measure speed using measuring means such as a tachometer, but acceleration tends to include noise. When attached to a joint, there are many problems such as the influence of gravity appearing in the acceleration, which must be corrected depending on the posture.

Furthermore, in the past, filters have been used for adaptive control to estimate parameters without requiring acceleration, but in that case the equation of motion is d=Aχ+Bu... (Equation 1) However, χ=[χ7. χ2. ......, χN] A:NXN
Matrix u' = [w + u2. +++ ++
+luncoB: NXM matrix ■ indicates transposition.

It must be in the form , and forms that include parameters for the highest order differential value are not handled.

For example, in the case of a two-joint arm of an articulated robot manipulator shown in FIG. 2, the equation of motion as a characteristic of the arm to be controlled is shown as follows.

......(Formula 2) However, al= (m7+ m2) d, 2+ m2d22a2
= m2 ci, z clause = m2 d! d2, l, = < mH+ m2) g dtaE” m2
g d2 In other words, in Fig. 2, the first arm 3 rotates around the first joint 1, and the second arm 4 rotates around the second intersection 2, and the mass of each arm is Tip 2
and 5, the distance between the first joint 1 and the second joint 2 is a mountain, the distance between the second joint 2 and the tip 5 of the second arm 4 is d2, and the distance between the first joint 1 and the second joint 2 is d2, and 3 is the concentrated mass of m7 + the concentrated mass of the second arm 4 is the slope, the rotation angle of the first arm 3 is shown in white, and the rotation angle of the second arm 4 is shown in the figure.

Also, al, a2. a3. a4. a5 is a parameter. In the above equation, the matrix on the left side that includes [δ, a] is the inertia matrix, the first term on the right side is the centrifugal force, Coriolis, the second term is the gravity term, and the third term is the input torque to each arm. .

In the above, if θl and θ2 are measurable, and input u7. If u2 is known, the parameters of slope to slope can be estimated by applying the least squares method to the formula summarized for each parameter in the upper equation of Equation 2 above. As a practical matter, that measurement is difficult.

If a conventional filter is used in this case, it becomes necessary to multiply the inertia matrix of θ by an inverse matrix from the left on both sides. However, az(aI+283CO3θ2)
-(a2+a3 Cogθ2)', the linearity with respect to the parameters is lost as in the original equation, and there is a problem that the parameters cannot be estimated.

(2) Structure of the Invention Means and Effects for Solving the Problems As described above, the present invention is intended to control objects that interfere with each other, such as a vertically articulated robot arm, by adjusting the parameters of the control object. When it becomes necessary to estimate
If the acceleration coefficient includes a parameter and is inverted so that a conventional filter can be used, linearity with respect to the parameter disappears, whereas it remains linear with respect to the parameter and the required state As an amount, 1
The present invention attempts to solve the above-mentioned problems by converting the equation using the next derivative, that is, the measured value up to the velocity. By applying -1-, which is a first-order filter, -1- changes a kind of space S
This is an action filter that converts s0μ, eliminates the acceleration term and uses the term up to velocity, and processes the parameters as they are linear, making it easy to estimate the parameters.

That is, the spatial state transformation effect filter of the present invention first includes a plurality of function vectors that constitute a function applied to a parameter,
For example, in the case of a multi-jointed robot arm, the inputs are joint angles and joint angular velocities, as well as inputs to the servo system to be controlled that correspond to the torque that moves the joints, and these input state values are used to restore the original state. configuring a plurality of function values that output function values depending on the parameters of the equation of motion, using the output of the function values and input to the controlled object as input, and using the state value of the number of parameters + 1 as output,
Each state value has the output of a transformed function on parameters and one known transformed function without parameters, and said transformation may be configured in a small number, It is constructed based on these.

According to the state space conversion action filter of the present invention having such a configuration, it is possible to estimate the parameters of the controlled object including parameters in the acceleration term, which was not possible with conventional filters, and it is also possible to measure the controlled object. Since it is sufficient to measure up to speed, it is a very effective means for a multi-input controlled object where the unknown parameter is a coefficient of a function including acceleration.

EXAMPLES Below, the present invention will be explained in detail based on examples.
The figure shows the two-joint arm of the multi-joint robot manipulator as described above, and FIG. 1 shows the configuration of an embodiment in which the present invention is applied to the two-joint arm shown in FIG. It shows.

In the figure, 6 is a controlled object configured as a servo system of a two-joint arm, and Equation 2 shown by 6 shows its equation of motion. u7. u2 is an input to the servo system of the two joints to be controlled, and the inputs ul and u2 change the acceleration of each arm 3, 4, thereby changing the position and speed of each arm.

The angle θ of the arm 3 changes depending on the human power ul and u2
l, the angular velocity at, and the angular velocity 4 of the arm 4 are detected as electrical signals by a measuring means 9 installed at each joint, such as an encoder or a tachometer.

The angle ψ thus detected as an electrical signal.

The life and angular velocity -1r02 are input directly to the filter 11, input to the filter 11 via a function unit 10 such as sin and cos, and input to the filter 12 via the function unit 10. There are things to do,
Furthermore, there are devices in which the input to the controlled object is input directly to the filter 12.

In the above, each of the function units 10 is composed of a plurality of units, and in the example shown in FIG. 1, the function unit 10σ is cos
2 c by combination with C2, adder, and multiplier
It constitutes osθ2·δl + CO5θ2·sec2. The function unit 10b constitutes −sinθl, and the function unit 10c
constitutes -5in (θl+02).

Similarly, the filter 11 is composed of a plurality of filters 12a, 11b, 11c and an adder, and the filter 12 is composed of a plurality of filters 12a, 12a, 12b, and 12C, which are -1/(s+μ). ing. This filter can be constructed using conventional techniques.

The input is converted by a combination of these function units, filters, adders, and multipliers, and the filter output ψI is the output of the converted function.

ψ2. ψ3. ψ4. ψ5. It is configured to output ψ6, and its output is configured to be an output indicating the state value of the parameter +1.

With the above configuration, the output from the function unit 10, the input from the measuring means, and the input from the input to the controlled object are
When passed through the filters shown in , the outputs of the filters 11 and 12 become the outputs of the transformed functions for estimating the unknown parameters.

Here, it will be explained that the filter output ψ6 configured in FIG. 1 is a state quantity for estimating the parameters included in the equation of motion shown by 6.

In the two-joint arm shown in this example, the unknown parameter is (C7+ 2 :ay CO8θ2)θ1+ (a2+
ay C03 (92) θ2=a3 S f n θ
x (l12'+ 2 el 62) C4
sin θ.

C5S! Since all are included in n (θ!+θ2) + u7, it can be seen that the above equation can be used to estimate all parameters. That is, the following equation is the equation for estimation.

C7C7+ a2e2 + ay [2CO3θ2et
+cos C2112-sinθ2<j'i+ 21
jt 42> ] + 24Sinθ.

+a5S! n (θl+02) u7=0 where,
It should be noted that only one U has no parameters. In this embodiment, it is ul, but it does not necessarily have to be u7, and only one such term is sufficient.

Also, in the above equation, θ1. e2 is included. In this formula −
Multiplying yo to the whole results in the following.

S tenμ Note that S means S of Laplace transform.

C71-ne+a2''-a+a3(''-50μs10μs10μX 2 CO5C2g, 10-upper-cos 532g2S
10μ' 11-[sinθ2 (C2'+ 20t'e2)
] lS ten μ + a4 ” S!nθ7+a5-1-sin (θ
l+θ2) S, 10 μs 11−u7=0 S0 μ Parameter al”” The reason why C5 was placed before −1- is because the parameter S0 μ is constant.

In the above equation, if we focus on a certain term (il and tide), -1
- As a characteristic of S0μ L fcχ), g=f(χ) ーー50μ
There is a relationship of s0μ×(t(χ)n+μf(χ) mustache).

This relationship is calculated by multiplying both sides by S0μ, and then S is differentiated from this. 1...

θshi=δL −−”−e L L = 1.
2S0μ s0μ = 1-(2cosI92-θl) S0μ = 2 cosθ281--upper-(-2sin e2-
t92θlS+μ +2μcO3e2θI) -1-(cos glue S0μ = cos 02(j2--1-(-sin e2-02
+S0μ μcos 02j12) Therefore, -11-i.

S0μ ψ2=A--L-δ2 S0μ S1μ ψ4=-tech-sinθl S0μ ψ5-" Sin (θI102) S0μ ψ6=-upper-u7 S0μ Then, the original formula becomes a, ψ, + a2ψ2+ a, ψ7+a i ψ4+ a5
It is converted as ψ5− ψ6=0.

As shown in the example of FIG. 1, the conversion filter 7 described above can be constituted by a function unit, a filter 1, a filter 4, an adder, and a multiplier.

The transformation described above results in a change in the state space while remaining linear with respect to the parameters.

Therefore, in the case of the two-joint arm as the control target shown in Figs. 1 and 2, the equation of motion (
The unknown parameter al''EL; in Equation 2) can be estimated by applying the method of least squares to ψI to ψ6 as the above-mentioned converted outputs.

That is, in the above equation of the least squares method, if −U−ψ6 is set, then it can be obtained, and it can be obtained as the parameter estimated value path ~ center by the least squares parameter adjuster 8 shown in FIG. can.

Further, the necessary state values are θl, θ2 . It can be seen that .delta.l and .delta.2, and .theta.I and .theta.2 are unnecessary.

In the above embodiment, the function unit, adder, multiplier, filter, etc. were explained as fixed electric circuit elements, but these are
It can also be easily constructed using a computer program.

Furthermore, the field of application is not limited to the above-described embodiments, but can be widely applied to control objects such as process control that are expressed by second-order differential equations.

(3) Effects of the Invention As is clear from the above explanation, the state space transformation filter according to the present invention can: It is possible to obtain state values for estimating parameters using only .

Therefore, it is effective for use as an input to a parameter adjuster in adaptive control or as an input for estimating parameters.

[Brief explanation of the drawing]

FIG. 2 shows a two-joint arm of an articulated robot manipulator, and FIG. 1 shows the configuration of an embodiment in which the present invention is applied to the two-joint arm shown in FIG. be. In the figure, 1......First joint 2...Second joint and tip of the first arm 3...First arm 4 ......Second arm 5...Tip part 6 of second arm...
...Controlled object 7...State space transformation filter 8.
... Least squares parameter adjuster 9 ...
...Measurement means 10...Function device

Claims (1)

[Claims] A filter that can be used in a parameter estimator that estimates parameters of a controlled object or a control parameter adjuster such as adaptive control, the filter comprising at least the following:
1/( s + μ) and μ
/(s+μ), and the filters are 1/(s+μ).
+μ) One part of the filter takes the output of the function unit as input, the other part takes the input without parameters to the controlled object as direct input, and the other part of the filter μ/(s+μ) takes the function The output of the detector is input, and the other part is configured to directly input the output of the detection means for detecting the momentum of the controlled object.
+μ) as an input to the estimator or adjuster.