Keywords

1 Introduction

The bilateral servo control technology was first proposed by Masato Kishiri of Hitachi Corporation in 1963, to achieve true remote operation between master and slave robotic arms [1]. Subsequently, INOUE, Lee and Andriot et al. pushed bilateral servo control technology to new heights [2,3,4,5,6,7,8,9,10]. Although various improved bilateral servo control strategies emerged later, they can be generally classified into four categories: powerless feedback type, position symmetry type, force position synthesis type, and force feedback position type [11]. The force feedback position type is an improvement of the force position comprehensive type, which is easier to achieve [12], has high stability, and is suitable for force telepresence robot systems.

The inverse kinematics solution is the foundation of robot control, but the 3T redundant degree of freedom parallel robot cannot obtain accurate analytical solutions. In order to achieve control, the inverse kinematics results of a non redundant 3D translational parallel robot are used for control, and then the control algorithm is used for real-time correction to eliminate accumulated errors, achieving relatively accurate position control of a 3T redundant degree of freedom parallel robot.

A force feedback position type bilateral servo control strategy with position difference compensation was designed for the working condition of using a 3T redundant degree of freedom parallel robot as a remote control handle. The master slave hand force feedback position bilateral servo control experiment and force feedback position bilateral servo control experiment with position difference compensation were conducted on the experimental platform. The experimental results showed that, This method can effectively reduce the error accumulation caused by using non redundant inverse kinematics methods to solve redundant parallel robots, maintain good position following performance of the master–slave robot, and improve the transparency of force displacement control in the master–slave remote control robot system.

2 Mechanism Design

The overall structure of the 3T redundant parallel robot is shown in Fig. 1, and the range of motion of the driving pair and the length of the connecting rod are shown in Table 1.

Fig. 1
A schematic diagram of a 3 T redundant degree of freedom parallel robot, displaying various components and mechanisms labeled from 1 to 11. A circular platform forms the top part, with three arms connecting it to the base structure. The base structure contains mechanical components, including gears, levers, and supports.

Design schematic diagram of a 3T redundant degree of freedom parallel robot

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Table 1 Range of motion and connecting rod parameters of the motion pair
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In the Fig. 1, 1—handle; 2—Three dimensional force sensor; 3—Mobile platform; 4—Connection head; 5—Short pole; 6—Long pole; 7—Drive rod; 8—Rotating drive components; 9—Linear drive components; 10—Guide rail plate; 11—Fixed platform.

3 Bilateral Servo Control Strategy

The inverse kinematics of a 3T redundant degree of freedom parallel robot can only be solved offline, which increases the difficulty of controlling the slave hand. So a force feedback with position difference compensation—position bilateral servo control strategy—was proposed, using the inverse kinematics solution method of non redundant parallel robots to calculate the driving amount. Then, through position difference compensation, the consistency of motion between the master and slave hands was achieved. The principle of the force feedback position bilateral servo control strategy with position difference compensation is shown in Fig. 2.

Fig. 2
A schematic of the control strategy flows through solve spatial pose, q m s, encoder, master, rotating motor, displacement sensor, operator, F h, F f, q m, master and slave controllers, 3 D force sensors, environment, delta F s, delta e x, q s s, q s, and F s.

Schematic diagram of control strategy

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In the Fig. 2, Fh is the operating force, Ff is the feedback force, Fs is the environmental contact force, F0 is the set threshold, qm is the actual angular displacement of the main hand rotating motor, qms is the actual angular displacement of the main hand linear motor, qmd is the driving angular displacement of the main hand motor, qs is the actual angular displacement of the slave hand rotating motor, qss is the actual angular displacement of the slave hand linear motor, qsd is the driving angular displacement of the slave hand rotating motor qbs and the driving angular displacement of the linear motor qsz, Xm is the spatial pose of the main manual platform center, and Xs is the spatial pose of the manual platform center, ΔEX is the difference information between the master and slave hands, ΔFs is the difference between the environmental contact force Fs and the threshold F0.

When there is no contact between the hand and the environment, qmd is the driving angular displacement qmz of the main hand linear motor; When the hand comes into contact with the environment, qmd includes both the driving angular displacement qbm of the rotating motor and the driving angular displacement qmz of the main hand linear motor; ΔEX includes not only the position difference eX between the master and slave hands, but also the position difference eXm between the master hand and the previous moment, as well as the position difference eXs between the slave hand and the previous moment, as well as the difference eXms between eXm and eXs.

When the hand comes into contact with the environment, the environmental force Fs received from the hand suddenly increases, instantly exceeding the threshold F0. The slave controller controls the slave motor and linear motor to immediately stop rotating, and then determines the displacement, speed, and direction of the retraction based on the size and direction of Fs, completes the retraction command, and transmits the retraction command to the master controller; Then continue to determine the size of Fs and F0. If Fs is greater than F0 at this time, continue to retreat and transmit retreat commands to the main controller; If Fs is less than F0 at this time, terminate the rollback and transmit the rollback commands, and return to the master hand to control the operation of the slave hand.

In the retraction state, the main controller first controls the relay to turn on, causing the main hand to turn on the motor, and then executes the retraction task according to the retraction command. At this point, the operator will feel the direction of the feedback force and feedback force, and immediately stop the forward operation. After waiting for the retraction task to be completed, according to the direction of the feedback force, operate the main hand handle to keep the secondary hand handle away from the elastic contact position, avoid obstacles, and complete the operation task.

The spatial postures of the center point of the master–slave manual platform are Xm and Xs, respectively. The spatial postures of the previous moment are Xm − 1 and Xs − 1, respectively. Therefore, the position difference eXm and eXs between the master–slave manual platform and the previous moment are

$$ e_{Xm} = X_{m} - X_{m - 1} $$
(1)
$$ e_{Xs} = X_{s} - X_{s - 1} $$
(2)

The difference eX between the spatial pose of the center point of the master–slave manual platform and the difference eXms between eXm and eXs are

$$ e_{X} = X_{m} - X_{s} $$
(3)
$$ e_{Xms} = e_{Xm} - e_{Xs} $$
(4)

Difference between hand force and threshold

$$ \Delta F_{s} = F_{s} - F_{0} $$
(5)

When there is no contact between the hands and the environment, ΔFs is less than 0; When in contact with the environment from the hand, ΔFs is greater than 0.

4 Testing and Verification

The experimental platform of the assembled bilateral servo control system is shown in Fig. 3.

Fig. 3
A photo of a cluttered desk in a room. The desk is covered with various items, including electronic equipment, tangled cables, a metal frame, and a metallic box.

Bilateral servo control test platform

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The initial position is set as the initial position of the linear motor by placing the nut sleeve of the main slave hand on the outermost end of the lead screw (θi = 157 mm), The top of the drive lever is located at the lowest point (θi2 = 65°) serves as the initial angular displacement of the rotating motor. Respectively apply the force feedback position bidirectional servo control strategy and the force feedback position bidirectional servo control strategy with position difference compensation to control the slave hand to follow the master hand’s movement. From the hand handle, first reach near the rubber ball, and then make elastic contact with the rubber ball. After the operator feels the feedback force, detach the rubber ball from the hand handle and walk around the rubber ball for half a circle. Finally, the master slave operating handle returns to its initial position. Used to detect the master–slave following performance and obstacle avoidance performance of redundant isomorphic master–slave control systems.

Collect angular displacement data of 12 motors and substitute the angular displacement data into the forward kinematics solution formula to obtain the displacement curve of the center of the master slave robot’s moving platform. The results are shown in Fig. 4.

Fig. 4
Two 3-D graphs of Z per millimeters versus y per millimeters and x per millimeters. On the left graph, master (40, 320, 60) has the highest estimated value. On the right graph, slave and master (negative 40, 320, 60) has the highest estimated value.

Spatial displacement following curve

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Comparing Fig. 4a, b, it can be seen that both control strategies can achieve simple obstacle avoidance capabilities. Regardless of whether elastic contact occurs or not, the tracking error of the control strategy without position difference compensation is greater than that of the control strategy with position difference compensation, so the tracking performance of the control strategy with position difference compensation is better.

5 Conclusion

Based on the above research, the following conclusions can be drawn.

  1. (1)

    The force feedback position bidirectional servo control strategy with position difference compensation can solve the control problem caused by the inability of 3T redundant parallel robots to solve inverse kinematics online;

  2. (2)

    Compared to the force feedback position bidirectional servo control strategy, the force feedback position bidirectional servo control strategy with position difference compensation is more suitable for the bidirectional servo control system of 3T redundant degree of freedom parallel robots.