JP2772064B2 - Robot model identification device - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION [Object of the Invention] (Industrial application field) The present invention relates to a robot model identification device for identifying a physical parameter of a robot model, and more particularly, to a method for easily and accurately identifying a spring constant of a robot joint. It was made.

(Prior Art) In order to control a robot at a high level, an accurate physical model of the robot is set, various parameters of a motion equation representing the model are identified, and the robot is used by using the identified model. In order to perform the desired operation, the control constants of the robot controller must be identified.

As a general physical model identification method, for example, as shown in the following document 1, a robot is regarded as a rigid link mechanism,
Rigid body parameters such as inertia and friction of each axis are obtained by the following equation (1).

Document 1: Maeda "dynamic model and the identification of the robot arm" Journal of the Robotics Society of _{7-2, pp95-100 (1989) m ·} M + d · M + f · sgn (θ M) + g · sin (θ M) = u ... (1) θ _M: motor rotation angle u: input to the motor _M: 1 frequency value differential of theta _M (motor angular velocity) _M: 2 frequency value differential of theta _M (motor angular acceleration) m: moment of inertia m · _M: Axial inertial force term d: Viscous friction coefficient d ・_M : Axial viscous friction term f: Clone friction force f ・ sgn ( _M ): Coaxial Coulomb friction force term g: Gravity g ・ sin (θM): Axial Equation (1) above is an example for one axis, but for two or more axes, an interference term due to inertial force or the like is added thereto.

By the way, in a robot having a joint such as an industrial robot, a joint drive speed reducer often has low rigidity.

Conventionally, in the identification of a robot model having this type of low-rigidity joint, a spring constant as a joint stiffness parameter is determined by using a catalog value of a speed reducer manufacturer or a displacement when an external force is applied to the speed reducer. Or to calculate the spring constant.

(Problems to be Solved by the Invention) However, in the conventional method of obtaining the physical parameters of the joint stiffness by catalog values and actual measurements, the reliability of the catalog values cannot be said to be sufficient. In many cases, it is necessary to disassemble the robot joints, which is troublesome. Further, there is a problem that it is difficult to identify a friction coefficient or the like that is paired with a spring constant as a required joint stiffness on a model.

Accordingly, an object of the present invention is to provide a robot model identification device capable of identifying joint stiffness by calculation together with other physical parameters without using catalog values or direct measurement.

[Means for Solving the Problems] To solve the above problems, the present invention provides an identification signal generator that generates an identification signal, and a robot that outputs the identification signal generated by the generator. Robot model identification comprising: an input / output data memory for storing input / output signals as input in time series as time-series data; and an identification unit for identifying physical parameters of the robot model using the input / output signal data stored in the memory. In the apparatus, the robot model is represented by a motion equation including a spring constant as joint stiffness, a moment of inertia on a joint driving means side and a moment of inertia on a joint load side, and the identification unit includes the spring constant and the joint driving means side. And the moment of inertia on the joint load side.

In the above robot model identification device, the equation of motion has a friction coefficient or a damping coefficient each of which is paired with the spring constant, the moment of inertia on the joint driving means side, and the moment of inertia on the joint load side. It is preferable that the identification is performed including the coefficient or the damping coefficient.

Further, in the above-mentioned robot model identification device, when the robot has multiple axes, it is preferable to provide an acceleration sensor for each axis so as to avoid the influence of other axes from the detection values of the acceleration sensors.

(Action) In the robot model identification device of the present invention, a robot equation is set up with a motion equation including a spring constant as joint stiffness, an inertia moment on the inertial drive means side and an inertia moment on the joint load side, and the robot model is identified. By giving the signal, the spring constant, the moment of inertia on the joint driving means side, and the moment of inertia on the joint load side are obtained by calculation together with other parameters.

In addition to the spring constant and the moment of inertia on the joint driving means side and the joint load side, a friction coefficient or a damping coefficient such as a viscous friction coefficient can be obtained.

Further, the influence between the joints of the multi-joint robot can be removed from the detection value of the acceleration sensor provided for each axis.

(Embodiment) Hereinafter, an embodiment of the present invention will be described with reference to an example of a one-axis and two-axis robot that horizontally turns.

First, an example of one axis will be described. FIG. 1 is a block diagram of an identification device for identifying a single-axis robot model assuming a SCARA-type first axis, an ASEA-type, or a PUMA-type vertical articulated robot, and FIG. 2 is a model of the first-axis robot. 3 is a block diagram thereof, and FIG. 4 is a frequency response diagram thereof.

In FIG. 1, an identification device according to the present embodiment includes an identification signal generator 1 that generates an identification high-frequency signal including a wide frequency component such as an M-sequence code signal, and an identification signal (input to a one-axis robot 2). It comprises an input / output data memory 3 for storing data of a motor input (u) and an output signal (motor rotation angular velocity) _M of the robot 2 in time series, and a physical parameter identification unit 4. The identification unit 4 solves various equations relating to a motion equation including a spring constant as a joint stiffness stored in the storage unit 5, and calculates various physical parameters.

In FIG. 2, the model 2A of the one-axis robot 2 is
An angle sensor 6 with the motor 7 for detecting the rotation angle theta _M, indicated by the arms 9 which is rotated by an angle theta _A via reduction gear 8.

FIG. 3 shows a control diagram of the model 2A.
In the figure, the meaning of each code is shown below.

θ _M : Motor angle θ _A : Arm angle θ _s : Torsion angle M _M : Armature inertia moment D _M : Motor friction coefficient N: Gear ratio K _G : Spring constant D _G : Spring element damping coefficient D _A : Drive section friction Coefficient M _A- arm inertia moment If there is Coulomb friction force or gravity,
Identify and compensate by the method shown in pp. 203-208. To summarize the block diagram, the transfer function from the torque command u to the motor angular velocity output _M is given by the following cubic expressions (2) to (9).

_{a 0 D M + D A /} N 2 ... (3) a 1 = M M + M A / N 2 + (D G D A / N 2 + D M D A + D M D G) / K G ... (4) a 2 _{= (M M D + M D} D G + M A D M + M A D G / N 2) K G ... (5) a 3 = M M M A / K G ... (6) b 0 = 1 ... (7) b 1 = (D _A + D _G ) / K _G (8) b ₂ = M _A / K _G (9) Here, the values of a ₀ , a ₁ , a ₂ , a ₃ , b ₁ , and b ₂ are given. If possible, 6
A simultaneous equation for two physical parameters (N is known) can be solved.

In order to identify the equation (2), ARMA of the following equations (10) to (12) is applied to the robot input / output data sampled at period T.
(Auto Regressive Moving Averrage) Set the model.

C (z ^-1 ) _M (k) = D (z ^-1 ) u (k) + e (k)
^{... (10) C (z -1} ) = 1 + c 1 z -1 + ... c n z -n ... (11) D (z -1) = d 1 z -1 + ... + d n z -n ... (12) Therefore, c and d are obtained by applying the least squares method, and then
The impulse response is calculated by the following equation (13),
(14) can be obtained.

Reference 2: Shigemasa, "Computer-Assisted System Identification", Measurement and Control, 28-4, pp. 337-343, 1989. Also, as shown in Reference 2 above, using Hankel matrices composed of impulse responses Minimum realization, degree 3
Is obtained, and then converted to a continuous-time state equation to obtain the transfer function of equation (2).

FIG. 4 shows a frequency response diagram. In the figure, L
(10) is the frequency response of the gain of C (z ^-1 ) / D (z ^-1 ) obtained from equation (10), and L (2) is obtained from equation (2). 2 shows the frequency response after fitting in 2. Concerning the phase and gain responses indicated by the dashed line and the solid line, the convex portions and the concave portions appearing in the vicinity of 10 ¹ to 10 ² [Hz] show spring characteristics, respectively.
Note that it is sufficient that the fitting be performed at a frequency of 10 ² [Hz] or less including the portion affected by the spring constant in the figure.

_GP (z- ¹ ) = C (z- ¹ ) obtained from the equations (10) to (12).
Comparing the frequency response obtained by substituting z ^-1 = e ^-jwT for / D / (z ^-1 ), the values agree well up to 100 [Hz] required for spring constant identification. G _P (z ⁻¹ ) indicates a pulse transfer function from u to _M.

The _M -G _p (z ^-1) u above, it is possible to identify the spring element damping coefficient D _G serving as the spring constant K _G and a pair therewith along with other parameters. Also, by determining the control constants of the robot controller using the obtained parameters, the robot can be operated at high speed,
Advanced control such as high-precision positioning can be performed with low vibration.

Here, the spring constant K _G in this embodiment, since including the damping coefficient D _G are model identification, model and actual and are in agreement, it is possible to set the control constants for higher accuracy, a high degree of Control becomes possible.

Next, an example of a horizontally rotating 2-axis robot will be described, assuming the first and second axes of a horizontal rotating robot (SCARA type) and the second and third axes of a vertical articulated robot. However, it is assumed that the fixed frictional force and gravity are identified by the method of Reference Document 1 and are subtracted from the motor input (identification signal).

FIG. 5 is a block diagram showing a configuration example of a model identification device for such a two-axis robot. The difference from FIG. 1 is that an acceleration sensor 10 is added to an arm other than the axis to be identified, and the arm angular acceleration data _2A is taken into the input / output data memory 3. The physical parameter identification unit 11 identifies various parameters with reference to the formula storage unit 12 including the spring constant. The reason why the acceleration sensor is provided is that in the case of two axes, there is interference due to inertial force or the like between the first and second axes, and it is necessary to remove this.

For example, even if an input is applied to only one axis in order to obtain a physical parameter for one axis, two axes operate, and the effect is superimposed on the input / output data for one axis. This phenomenon is
Expression (2) is expressed as follows using the transfer function G (s) of one axis alone.

_{M1 = G (s) · u} 1 + G d2 (s) · θ A2 ... (15) u 1: 1 axis motor input _M1: 1 axis of the motor rotation angular speed _A2: arm angular acceleration of the second shaft (motor angular acceleration G _d2 (s): Disturbance given by axis 2 to axis 1, from _A2
A transfer function of a _M1 Therefore, as input u ₁ and _A2, given the two inputs and one output ARMA model as follows to output _{θ M1, M1 = G p (} z -1) · u 1 + G pd2 (Z ⁻¹ ) · _A2 (16)

Here, G _p and G _pd2 are pulse transfer functions. This (1
6) G _p and G _pd2 is obtained by applying the least squares method with two inputs and one output which indicated Tsugiki the literature (3) in the formula.

Using the obtained G _p (C _p (z ⁻¹ ) / D _p (z ⁻¹ )), the equation (1)
Equations (2) are obtained from (0) to (14), and one-axis physical parameters can be obtained in the same manner as the method shown for the one-axis robot.

Reference 3: Takayoshi Nakamizo “Signal Analysis and System Identification” Corona (1988) As described above, according to the identification device of this example, the robot is actually operated by the identification input signal generated by the identification signal generator 1. The input / output data and the output data of the acceleration sensor 10 previously added to the robot are subjected to curve fitting of the transfer function after obtaining the frequency response by the physical parameter identification unit 11 to derive a simultaneous equation of unknown physical parameters. By solving, it is possible to identify physical parameters such as stiffness, inertia, and friction, including the spring constant and various quantities related thereto. Therefore, the physical parameters including the joint stiffness can be diverted from the catalog values of the reducer,
The spring constant can be obtained without measuring the spring constant by measuring the displacement by applying an external force to the speed reducer. It is also possible to identify a viscous friction coefficient or the like that is paired with a spring constant that is difficult to measure.

[Effects of the Invention] As described above in detail, according to the present invention, the physical parameters including the joint stiffness required when using the control method in consideration of the inertia stiffness can be diverted from the catalog values of the reduction gear. The spring constant can be obtained without measuring the spring constant by measuring the displacement by applying an external force to the speed reducer. It is also possible to identify a viscous friction coefficient or the like that is paired with a spring constant that is difficult to measure.

[Brief description of the drawings]

Each of the drawings shows an embodiment of the present invention, FIG. 1 is a block diagram of an identification device for a one-axis robot, FIG. 2 is an explanatory diagram of a model of a one-axis robot, FIG. FIG. 4 is an identified frequency response diagram, and FIG. 5 is a block diagram of an identification device for a two-axis robot. 1 ... Signal generator for identification 2 ... 1-axis robot 3 ... I / O data memory 4,11 ... Physical parameter identification unit 5,12 ... Formulas including spring constant 10 ... Acceleration sensor

Claims (3)

(57) [Claims] An identification signal generator for generating an identification signal, an input / output data memory for storing input / output signals when the identification signal generated by the generator is input to a robot as time-series data, and A robot model identification device including an identification unit that identifies a physical parameter of a robot model using input / output signal data stored in the memory, wherein the robot model has a spring constant as joint rigidity;
It is expressed by the equation of motion including the moment of inertia of the joint driving means and the moment of inertia of the joint load, and the identification unit includes the spring constant, the moment of inertia of the joint driving means, and the moment of inertia of the joint load. A robot model identification device characterized by identifying. 2. A robot model identification apparatus according to claim 1, wherein said equation of motion is a friction coefficient or damping paired with said spring constant, said inertia moment on said joint drive means side, and said inertia moment on said joint load side. A robot model identification device having a coefficient, and identifying the robot model including the friction coefficient or the damping coefficient. 3. The robot model identification device according to claim 1, wherein when the robot has multiple axes, an acceleration sensor is provided for each axis, and the influence of another axis is avoided from the detection value of the acceleration sensor. Robot model identification device.