JPH04241606A - Method for evaluating impedance control area of articulated force control manipulator - Google Patents

Abstract

PURPOSE:To stably control a target impedance without setting the target impedance to an unreasonable value by evaluating the realizable area of virtual impedances by paying special attention to virtual inertias. CONSTITUTION:To each parameter (inertia, efficient of viscosity (d), and modulus of elasticity (k)) of the target impedances of joints 1 and 2 against the external force moments applied to the joints 1 and 2, the target values of the aimed corresponding oscillation frequencies, damping coefficients, and virtual inertias are given. When the target values are given, step responses to the joints 1 and 2 are measured by variously changing the virtual inertias against real inertias while the oscillation frequencies and damping coefficients are fixed. Then actually realized virtual inertias are calculated from the periods and amplitudes of the responses and the relative degree of achievement is found against the target inertias.

Description

[Detailed description of the invention]

0001

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to an impedance control method for an articulated force control manipulator.

0002

[Prior Art] Conventionally, impedance control has been developed as a force control method for manipulators, for example, in the literature by Tate et al.
Journal of the Robotics Society of Japan vol. 7, no. 3, pp. 60
-71), it has been applied to tasks such as grasping and touching objects. The mechanical impedance of the manipulator's hand refers to the inertia, viscosity, and elasticity of that hand, and in contact work, stable force control can be achieved by setting the virtual inertia of the manipulator's hand to various values. It is characterized by what it can do. At that time, what kind of target impedance (target impedance refers to the target mechanical impedance achieved at the hand of the manipulator when executing impedance control) for the workpiece, target inertia, target viscosity, target consisting of elastic)
The big problem is how to set the virtual impedance (virtual impedance) to the manipulator's hands when impedance control is executed to perform tasks as flexibly as humans. (consisting of virtual inertia, virtual viscosity, and virtual elasticity), and in particular, it has been considered essential to be able to set virtual inertia in various ways.

On the other hand, there is a certain limit to the virtual impedance that can be achieved depending on the actuator's ability and the position and posture of the manipulator's hand, and if the target impedance is set beyond this limit, the control of the manipulator becomes unstable. There was a risk that it would happen. That is, (1) the posture of the manipulator greatly influences the value of virtual inertia that can be achieved at the end of the manipulator, and there is a certain limit to the target impedance that can actually be set. Now let M be the virtual inertia matrix of the manipulator's hand in the work coordinate system, and let I be the virtual inertia matrix on the joint space realized at each joint.

0004

[Math 1]

There is the following relationship. At this time, if the manipulator does not have redundant degrees of freedom,

[0006]

[Math 2]

[0007] Normally, a diagonal matrix M is set as the target inertia of the manipulator's hand in the work coordinate system based on the dynamic characteristics of the object and the work content. On the other hand, the Jacobian ann J changes depending on the posture of the manipulator, and furthermore, the real inertia on the joint space changes depending on the posture of the manipulator, so the control region of the matrix I of virtual inertia on the joint space defined from the actuator ability also changes. It fluctuates accordingly. Therefore, the area of virtual inertia that can actually be achieved at the tip of the manipulator changes depending on the posture of the arm. This is particularly noticeable in DD (direct drive) and low reduction ratio force control type manipulators, and it is difficult to perform stable control over a wide range with constant virtual inertia. ■In impedance control using the torque control method, it is generally difficult to accurately detect acceleration or external force used to control virtual inertia, and noise and calculation delays have a considerable impact on control characteristics. in this way,
The target virtual impedance, especially the range of virtual inertia settings that can actually be achieved, is greatly influenced by the position and posture of the manipulator's hand. Conventionally, among this virtual impedance, there are methods to evaluate the range in which stable control can be executed for other parameters (viscosity and elasticity) when the target inertia is fixed, but virtual impedance directly focuses on the virtual inertia. There is no evaluation method in the impedance area.

[0008]

[Problem to be Solved by the Invention] However, in the conventional technology, there is no evaluation method that focuses on virtual inertia in the virtual impedance that can actually be realized at the hand of the manipulator, and there is a risk that stable control cannot be executed. There was a problem. Therefore, when performing impedance control using a multi-joint force control manipulator, the present invention provides a method for controlling each joint's target impedance parameters (inertia, viscosity coefficient, elastic coefficient) in response to an external force moment applied to each joint. Give target values of vibration frequency fr, damping coefficient ζ, and virtual inertia i corresponding to
The step response of this joint is measured when the frequency fr and the damping coefficient ζ are fixed and the virtual inertia i relative to the real inertia is varied, and the actually realized virtual inertia is calculated from the period and amplitude of this response. , by finding the relative degree of achievement of this relative to the target inertia i, we can calculate the virtual impedance that can be achieved at each joint, relative to the target impedance of the manipulator hand that is dependent on the actuator's ability and the position and posture of the manipulator hand. To evaluate a region and perform impedance control using a manipulator in a stable manner without setting a target impedance to an unreasonable value.

[0009]

[Means for Solving the Problems] In order to achieve the above object, the present invention provides the following methods for each parameter (inertia i, viscosity coefficient d, elastic coefficient k) of the target impedance of each joint with respect to the external force moment applied to the joint. The target vibration frequency fr, the damping coefficient ζ, and the target value of the virtual inertia i corresponding to are given. At this time, the frequency fr and the damping coefficient ζ are fixed, and the virtual inertia i relative to the real inertia is varied and given.
Measure the step response regarding this joint. The actually achieved virtual inertia is calculated from the period and amplitude of this response, and the degree of achievement relative to the target inertia i is determined.

0010

[Operation] With the above means, it is possible to evaluate the realizable range of virtual impedance that changes depending on the actuator's ability and the manipulator's posture, paying particular attention to virtual inertia. It is now possible to perform stably without setting the impedance to an unreasonable value.

[0011]

[Examples] Specific examples of the present invention will be described below. When performing impedance control using a multi-joint force control manipulator, the range of virtual impedance that can be achieved at each joint is evaluated as follows. That is, for each parameter (inertia i, viscosity coefficient d, elastic coefficient k) of the target impedance of a joint in response to an external force moment applied to the joint, the corresponding target vibration frequency fr, damping coefficient ζ, and virtual inertia are determined. Give the target value of i. At this time, the frequency fr and the damping coefficient ζ are fixed, the virtual inertia i with respect to the real inertia is varied, and the step response regarding this joint is measured. The actually created virtual inertia is calculated from the period and amplitude of this response, and the degree of achievement of this relative to the target inertia i is determined. External force moment τ
If the parameters of the target impedance of a certain joint with respect to i are inertia ii, viscosity coefficient di, and elastic coefficient ki, then the equation of motion for this joint is ideally expressed by the following equation by impedance control.

0012

[Math 3]

However, in reality, the following system is realized which includes errors due to the actuator's ability and the manipulator's posture at that time.

[0014]

[Math 4]

The target impedance achieved by this actual system will be evaluated using the following procedure. First, the relational expression between the frequency fr and the damping coefficient ζ when each parameter of the virtual impedance set as a target is given the step response of the system;

[0016]

[Math 5]

Set using [0017]. That is, the frequency fri and the damping coefficient ζi are fixed to certain values, and only the virtual inertia ii is varied and set. These frequencies f
The target viscosity coefficient di and elastic coefficient ki can be calculated inversely from ri, the damping coefficient ζi, and the virtual inertia ii, and these can be given to the control system as the target impedance.

[0018]

[Math 6]

Next, the angular amplitude and period are measured from the step response to this system, and the damping coefficient ζ0 and vibration frequency fr0 of the system are calculated. The calculation uses the following relational expression for damped vibration of a system with viscous friction and solid friction.

[0020]

[Math 7]

However, Xi (i=1, 2, . . . ) is the total amplitude, and Ai represents the deflection of the virtual spring due to solid friction. Therefore, the parameter to be sought, iei, can be calculated using the following relational expression.

[0022]

[Math. 8]

Here, it is assumed that the elastic coefficient k can be controlled almost accurately since it is a position servo.

[0024]

[Math. 9]

[0025] It was set as ∧. From this result, the target inertia ii
The relative degree of achievement of the actual virtual inertia ii with respect to

[0026]

[Math. 10]

It is evaluated as follows. By the above procedure, the virtual impedance that can be realized in each joint at the hand position and posture of a certain manipulator can be calculated by its virtual inertia ii
The evaluation focuses on the following. A more specific explanation will be given by taking the manipulator shown in FIG. 1 as an example. This manipulator has a total of two degrees of freedom, one degree of freedom for the shoulder and one degree of freedom for the elbow. Each joint is equipped with a torque-controlled actuator. This actuator is compact with an integrated reduction gear, and applies torque feedback using the signal from the torque sensor at the output end, achieving good linearity of torque command/output as shown in Figure 2. . The reduction ratio was set to 1:40. The control system of this actuator is greatly affected by the dynamic characteristics of the arm, and conventional techniques have not been able to evaluate whether accurate impedance control can be executed. FIG. 3 shows experimental results regarding the elbow joint 3 in the schematic diagram of FIG. 1. Set the frequency to 1
．． 5, 2.0, and 3.0 Hz, the damping coefficient was fixed at 0.2, and the target inertia was given from 20% to 180% of the actual inertia. The vertical axis represents the degree of relative achievement of the realized virtual inertia with respect to the target inertia. 60% to 180% for low frequency (1.5HZ), high frequency (3.0HZ)
For the target inertia between 100% and 160%, it was confirmed that virtual inertia with a relative error of within 10% could be achieved. It is obvious that virtual inertia can be similarly achieved for other joints (shoulder 1 and wrist 5), so the explanation will be omitted.

[0028]

As described above, according to the present invention, the range of virtual impedance that can be realized in each joint of a multi-joint force control manipulator can be evaluated with particular attention to virtual inertia. This makes it possible to evaluate the possible range of virtual impedance that changes depending on the actuator's ability and the manipulator's posture, and to stabilize the target impedance without setting it to an unreasonable value when performing impedance control using the manipulator. It became possible to control the

[Brief explanation of the drawing]

FIG. 1 is a schematic diagram of the vertical articulated force control manipulator used in the experiment.

FIG. 2 is a graph showing torque command/output characteristics of an actuator.

FIG. 3 is a graph showing experimental results of the relative degree of achievement of virtual inertia actually achieved with respect to target inertia.

[Explanation of symbols]

1 Shoulder joint 2 Upper arm 3 Elbow joint 4 Lower arm 5 Wrist

Claims (1)

[Claims] 1. A method for evaluating the range of virtual impedance that can be achieved at each joint when performing impedance control using a multi-joint force control manipulator, the method comprising: For each parameter (inertia, viscosity, elasticity) of the target impedance of the joint for a certain external force moment on the joint,
The corresponding target values of vibration frequency fr, damping coefficient ζ, and virtual inertia i are given, and the frequency fr and damping coefficient ζ are fixed, and the virtual inertia i relative to the real inertia is varied. Measure the step response of A method for evaluating the impedance control area of an articulated force control manipulator that evaluates the virtual impedance area that can be realized at the joints.