Technical Information

# E-3 Sensor-less compliance control for assembly robots

In recent years, requirements for automation of assembly work on the production line have increased remarkably on the worldwide market. The most of assembly work involves contacting with parts, such as interlocking and pressing of parts. On such applications, the robot arm is required to softly touch the part under the flexible control. Under technical collaboration with Toshiba Corp. R&D Center, Toshiba Machine Co., Ltd. has developed the sensorless compliance technology which detects external force exerted on the robot arm to flexibly control the arm without using 6-axis force torque sensors.

[Platform]
E. Control and mechatronics technologies
[Applications]
Vertical multi-joint robot

[Technical points]

• Detection of external force exerted on the robot arm to flexibly control the arm without using sensors.
• Aiming at expanding the robot application range and enhancing the system productivity with the low-priced force control technology.
• Three fundamental technologies:
1. Processing estimating external force
2. Calculation of dynamic equation
3. Processing of compliance model compensation value

## 1. Introduction

The compliance control is the technology for flexibly controlling the arm by detecting external force exerted on the robot hand by means of a commercially available 6-axis force torque sensor. This sensor is expensive and sensitive to shocks, however, and is not used frequently at job sites. The sensor-less compliance control is the technology for executing compliance control by estimating external force imposed on the robot hand based on each axis torque value without using any 6-axis force torque sensor. This function has been developed to intend expanding the robot application range and enhancing the system productivity with the low-priced force control technology.

## 2. Descriptions on function

Fig. 1 Control Block Diagram

The sensor-less compliance control is consisted of the three fundamental technologies ([1], [2] and [3]) as shown in Fig 1)
In the Fig. 1 above, fe represents the estimated external force (N), Δr signifies the compensation value (mm), θR the target angle (rad), u the electric current command value (A), τe the estimated torque (Nm), τr the actual drive torque (Nm), Δτ the error torque (Nm), J the Jacobian matrix and JT the transposed Jacobian matrix.

Fig. 2 Comparison of force torque sensor value and estimated external force on the Z-axis direction

[1] Processing estimating external force

The process will generate the external force (fe) that exerted on the arm end, instead of using the 6-axis force torque sensor, using the error torque (Δτ) which occurs when external force is exerted on the arm. The following is the transformation formula from Δτ to fe as shown in below. (1)

fe = (JT)-1 · Δτ
= (JT)-1 · (τr - τe) (1)

From the formula above, it is important to calculate the highly accurate estimate torque (fe), in order to exactly estimate the external force (fe) high-accuracy calculation of the estimated torque τe is very important.
Fig. 2 shows the comparison of the force torque sensor value and estimated external force when the force is exerted on the Z axis ± directions of the hand while the robot is standing still.
The estimated result is good in the range of ±25 to 75 (N), and you can see that it is enough estimated accuracy to detect the contact force during interlocking and pressing of parts.

[2] Calculation of dynamic equation

The estimated torque (τe) is figured out with accuracy by real-time simulation of various physical phenomena (friction, inertia, gravity, etc.) which generates in the arm and joint by using the dynamic equation.

Fig. 3 Compliance model and integral compensation

[3] Processing of compliance model compensation value

Δrc (mm) for the hand position is figured out from external force fe (N) and deviation Δf of target force value fd (N). By adding this value to the present path data, tool-center-point can be controlled flexibly as if the springs and dampers were mounted. It is also possible to adjust the arm behavior at the time of contact by changing spring constant K and damper constant D. In Fig. 3, M signifies the mass contact, Kc the compliance control gain, KI the integral compensation gain and s the Laplace operator.

Fig. 4 Effects of integral compensation

Because the distance up to the part with which the robot comes into contact cannot be grasped beforehand at actual pressing and fitting work, approach motion to the part is necessary until the robot contacts it.
Then, we added the integral compensation at the latter stage of the compliance model (Fig. 3). Thus, compensation value Δr can be increased at a constant rate in a direction where the deviation of force is eliminated, and the contact motion as shown above becomes possible. (Fig. 4)

## 3. Application cases

Fig. 5 Pin insertion and screw tightening

[1] Pin insertion

Fig. 5 exemplifies the pin insertion (maximum clearance = 0.221mm, chamfering of hole = C1.0, depth of insertion = 30mm, center shift value ≈ 3mm). As the pressing force can be specified separately for each direction, like pressing with predetermined force in the red arrow-marked direction and making external force 0 (N) in the blue arrow-marked direction, it is easy to insert a pin into the hole position while getting it to fit the hole position.

[2] Screw clamping

When the robot screw clamps with an electric screw driver, a passive compliance unit (i.e., unit combining spring and slide mechanisms) is normally mounted between the driver and robot to absorb a position error. According to this method, however, the absorbable range is limited, and adjustment of the screw tightening start position, feed rate, etc. are necessary. Then, the screws were tighten by moving down the driver from above each screw tightening point under the compliance control (i.e., pressing with constant force only in the screw tightening direction). Due to the pressing force control, excessive pressing could be prevented, no screws were missing and stable screw tightening could be done successfully.

## 4. Conclusion

This sensor-less compliance control is implemented at the optional function of vertical articulated robot, TV Series. In the future, we will apply this function to the job requiring compensation of a configuration error and other diversified jobs on the production line to further improve the accuracy.
This function can also detect external force exerted on the arm in addition to the tool-center-point. We are determined to promote the further development of "Direct Teaching function" which workers can imposes the force on the robot arm to guide and teach.