Advanced impedance control of haptic joystick for effective mobile robot handling

This paper proposes optimized structure of 6 D.O.F. haptic joystick and tele-operated mobile robot system based on haptic interfaces. Kinematic analysis of specially designed 6 D.O.F. haptic joystick derives the coordinate of end effect. The designed haptic joystick transfers operator’s moving command to mobile platform with force controlled coordinate information. Attached ultra-sonic sensors detect nearby obstacles including walls and retransfer the distance between mobile platform and obstacles to the haptic joystick. Attained real-time displacement information controls DC motors between links supporting the handle for effective user handling. Practical simulations and real experiments verified proposed impedance control and its tele-operation system of intelligent haptic joystick.


Introduction
Recently, social needs for the tele-operation have been raised sharply in the field of industry and disaster environment to avoid unexpected blind accident.Teleoperation means communication between master-slave devices from a distance.It is necessary to provide realtime feedback and to develop optimized haptic device for precise tele-operation.
Serial mechanism haptic joystick has universally been used in the industry.Serial mechanism has simple structure and wide workspace, while it has relatively low durability and accuracy.Contrastively, parallel mechanism suits with precise work and force applied to actuator disperse into parallel links.But it is difficult to control in real-time.According to above characteristics, suggested 6 D.O.F haptic joystick designed as combination of serial and parallel mechanisms.The blended mechanism complements each other's defects.Also, end-effect of haptic joystick freely generates movement of 6 D.O.F. for commend parameters.
Ultra-sonic sensors attached to mobile platform detect obstacles and retransfer distance data between the mobile platform and obstacles to haptic joystick.DC motors between links supporting the handle generate virtual impedance, which transfer the distance data to user.
Advanced haptic joystick model is applicable to the industry which requires accurate works in specific environment.In this paper, kinematic of specially designed 6 D.O.F.haptic joystick is analyzed for the coordinate of end effect and simple experiment is preceded using mobile robot as a basic research before it is applied to the industrial robot.

Structure Analysis of The 6 D.O.F. Haptic Joystick
The structure of this device is combination of 3 manipulators which has serial joint in parallel as shown in Fig. 1 Each of the serial manipulator has 3 D.O.F. that composed of 2 active joints, 1 passive joint and 1 spherical joint.Degree of freedom of 6 D.O.F.serial•parallel mechanism is proved by Gruebler's equation.

Kinematic Analysis
The upper platform of hybrid manipulator has been attached between the handle of the joystick and the 3 serial manipulators.When we hold the points generated by the connecting between the upper plate and the serial manipulators as vertices and connect them, we can make the shape of a triangle.The desired end effect is located at the center of this triangle.According to the specially designed manipulator's structural characteristics, kinematic relationship of each parameter can be derived from decoupled analysis of serial manipulator and upper platform.

Relative coordinate for kinematic analysis in parallel mechanism
The relationship between i P and li P obtained using the relative coordinates in Fig. 2 -(c) is shown in Eq. ( 3) and ui P is derived as Eq.(4).

Kinematic analysis of the haptic joystick
The coordinate of serial manipulator is as shown in fig. 5 Each of 3 serial manipulators is composed of two links.The position vector li P obtained by Denavit-Hartenberg notation.is shown in Eq. (5).

Impedance control
Impedance control is the interaction between the manipulator and the environment.Using the analogy to electrical impedance where impedance is the ratio of voltage output to current input, mechanical impedance is the ratio of force output to motion input.In other words, the mechanical impedance is the force resisting to the direction of the applied force.Impedance in a teleoperation system does not appear immediately in the slave device, but through the master device that controls the slave device.The user can acquire the implied information about environment through the master device's impedance information, and instructs the master device to control the slave device based on this information The lowes-order term in any impedance is the static relation between output force and input displacement, a stiffness.If, in common with much of the current work on robot control, we assume actuators capable of generation commanded forces, act T , sensors capable of observing actuator position, , and a purely kinematic relation between actuator position and end-point position, ( ) X L , it is straightforward to design a feedback control law to implement in actuator coordinates a desired relation between end-point (interface) force, int F , and position, X .Defining the desired equilibrium position for the end-point in the absence of environmental forces (the virtual position) as 0 X , a general form for the desired force-position relation is : Compute the Jacobian, ( ) From the principal of virtual work : int ( ) The required relation in actuator coordinates is 0 ( ) ( )

Simulation
Simulation was performed to verify the workspace of the constructed haptic joystick.Kinematically, both link1 and link2 were chosen equal to 19 cm.Table 1 shows the constraint limits of the angles shown in Fig. 3.

Experiment environment
Fig. 4 is a tele-operation system using a haptic joystick and a mobile robot.The haptic joystick and the mobile robot exchange the data through the bluetooth module.The haptic joystick generates a virtual impedance based on the distance information received through the mobile robot attached ultrasonic sensors and transmits it to the user.The experiment was performed in an environment where obstacles were installed in the traveling path as shown in Fig. 5.

Experiment result
The Fig. 6 is the graph about the relative distance between the mobile robot and the obstacle recognized by the ultrasonic sensor, and the graph in Fig. 5 is the result of the impedance value generated in the joystick.The previous result is the output of the sensor attached to the right side among the three ultrasonic sensors attached the mobile robot, and the other sensors also present the same performance.In graph 6, the ultrasonic sensor outputs a value of 0 if it does not detect any obstacle within 20 cm.Otherwise, the closer to the obstacles, it output the lower value.The impedance value of the graph 7 is maintained at a value of 5 in the normal state, and a higher impedance value is output as the distance from the obstacle becomes closer.

Conclusion
Experimental results show that the impedance value properly changes according to the output value of the sensor, but it is difficult to obtain accurate data due to communication problems such as time delay in data transmission.Therefore, we will focus on this issue in developing a haptic joystick for improved performance.

Fig. 2 -
Fig. 2 -(a) shows the coordinate relationship for the kinematic analysis.Set the reference coordinate system {B} (Base frame) on the center of lower platform and set the coordinate system of end-effector {M} (Moving frame) on the upper platform.When define the position change between these 2 coordinates as vector d P , it means position of the {M} based on {B}.Define the coordinate of upper platform corner based on {B} as