Model-based impedance control for serial robots teleoperation.

Hancu, Olimpiu ; Maties, Vistrian ; Balan, Radu 等

1. INTRODUCTION

The mechatronic approaches in the design of products and processes involve modeling, simulation and testing of the system viewed like an "undivided whole". It means a synergetic integration of system components and a functional integration by the software with all algorithms from control through adaptation to supervision, fault diagnosis, fault tolerance and human/machine operation. The interaction with environment is an important feature of mechatronic systems for industrial tasks like machining, manipulating and assembling. Using integrated simulation environments, a mechatronic design approach will be developed to optimize the behavior of a teleoperated serial manipulator in terms like precision, flexibility and adaptability to environment. For tasks which involve interaction with environment, difficulties arise when both the position and force of end-effector are to be controlled simultaneously. The literature reports two broad approaches for the control of robots executing constrained motion: hybrid (force/position) control and impedance control. In hybrid control, the end-effector force is explicitly controlled in selected directions and the end-effector position is controlled in the remaining directions. This issue was first addressed by hybrid position/force control (Raibert & Craig, 1981), where the task space is divided in two subspaces, each of which is either position or force controlled. Impedance control allows a conceptual separation of constrained and unconstrained directions, but within one single control law, and without the stability problems of hybrid control. In impedance control (Hogan, 1985; Kazerooni et al., 1986), a prescribed static or dynamic relation is sought to be maintained between the end-effector force and position. Field and Stepanenko (1993) have outlined an alternative approach to impedance control concept, called model reference impedance control, in which the controller is actually a position controller nested within a force feedback loop. Another numerous approaches that provided solutions to improve the contact task can be found in: Anderson & Spong, 1988; Di Maio et al., 2004, Albu & Hirzinger, 2002.

In this paper is developed a method which allows bilateral robots teleoperation in constrained environments using a model-based impedance control strategy.

[FIGURE 1 OMITTED]

A bilateral teleoperation system consists of a human operator interacting with the environment through a teleoperator system as presented in Fig. 1. In current teleoperation architecture the master system (joystick) sends position or velocity commands to a slave system (5-DOF serial robot) and force information induced from interactions with the environment is fed back to the master system in order to have a measure of the robot/environment impedance. Also, this information is used to modify the robot dynamics (control low) in order to avoid dangerous collisions or to control the interaction force. This integrated approach allows the investigation of robot dynamics in constrained environments and the optimization of system in terms of precision, flexibility and adaptability to environment.

2. MANIPULATOR DYNAMICS

The general representation of slave system dynamics (Fig.2) with respect to Cartesian space is

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1)

where: x is the vector of the generalized coordinates (position and orientation of the end-effector); Mx(6) is the Cartesian mass matrix; [V.sub.x]([theta], [theta]'), [G.sub.x]([theta],) [F.sub.x]([theta]) represent velocity, gravity and friction terms in Cartesian space; [F.sub.int] is the interaction force and J, the Jacobian matrix of manipulator. In order to implement manipulator dynamics, it was used a simplified approach based on the export of the manipulator CAD model to Matlab/Simechanics. The exported model includes all previous terms of dynamic equation (1), except the friction, and can be used for both direct and inverse dynamic computations.

[FIGURE 2 OMITTED]

In order to pass from Cartesian space to joint space in terms of position, velocity and acceleration the inverse kinematics is required. A form of these equations can be found in robots literature (Craig, 1989). Due to limited space they will not be detailed here.

3. CONTROL STRATEGY

The operational modes of industrial robots can be divided in two approaches: the first one involves unconstrained motion in space, in which it is sufficient for the manipulator to track a trajectory in space; the second involves motion that is constrained through contact with the environment. Impedance control strategies intend to encompass the traditional positioning tasks performed by robots, including the capability to handle static and dynamic interactions between the manipulator and its environment. In current approach we will assume that the desired end-effector behavior to be imposed on the manipulator is given by

B([[??].sub.0] - [??]) + K([X.sub.0] - X)= [F.sub.int] (2)

where: the term ([X.sub.0] - X) denotes the change in Cartesian position from the commanded trajectory, [X.sub.0] ; B, and K are the damping and stiffness matrices of the target impedance, specified by the user; [F.sub.int] represent the contact force. In Fig. 3 is detailed an equivalent system which could give an explicit image about the manipulator behavior needed to be implemented: the system is driven by [X.sub.o] = [X.sub.r], the reference position given by joystick; in the case of interaction, [X.sub.0] [not equal to] [X.sub.r] and the contact force Fint can be imposed by the difference between X0 and Xr. This behavior will be implemented to controller, through proposed control strategy (Fig. 4).

[FIGURE 3 OMITTED]

In current model-based impedance approach, a new desired trajectory [X.sub.r] is computed by an impedance filter. The new trajectory [X.sub.r] is determined based on a model which can estimate [X.sub.r] when [F.sub.int] is imposed. In free space the interaction force is zero, so the impedance filter will give a reference Cartesian position [X.sub.r] = [X.sub.0] [approximately equal to] X. When a contact force will appear due to interaction with environment, a new position [X.sub.r] will be computed through impedance filter such as the interaction force will be reduced to a desired value, [F.sub.int].

[FIGURE 4 OMITTED]

In this formulation the control strategy does not optimize the transition between unconstrained and constrained motions but once the contact is established the method allows also to control the interaction force. Also kinematic transformations are needed in order to compute some intermediary variables.

4. SIMULATION RESULTS

In order to test the proposed control strategy it was used the model of Mitsubishi RV-2AJ robot (Fig.1). The manipulator will act on a passive environment with a given admittance. The simulations have been done upon one axe of world coordinate system. The controller will compute a new reference value Xr such as relation (2) to be checked (Fig. 5).

[FIGURE 5 OMITTED]

5. CONCLUSION

Tests including trajectory and force tracking in environments with diferent admittances were performed. In these tests, the impedance controller successfully replaced the actual manipulator dynamics with those of the target impedance. This integrated approach allows the investigation of system like a "whole" and also the optimization in terms of precision, flexibility and adaptability to environment. The controller doesn't optimize the contact through environment. In order to control the transition between unconstrained and constrained motions, the control strategy will be improved in the next future, based on environmental estimation methods.

6. REFERENCES

Albu-Schaffer, A. & Hirzinger, G. (2002), Cartesian Impedance Control Techniques for Torque Controlled Light-Weight Robots, Proceedings of 2002 IEEE International Conference on Robotics and Automation, Washington, DC, May, 2002

Anderson, R. J. & Spong, M. W. (1988). Hybrid Impedance Controller of Robotic Manipulators, IEEE Journal of Robotics and Automation, pp. 1185-1190

Craig, John, J. (1989), Introduction to Robotics: Mechanics and Control, Addison-Wesley Publishing Company, Inc. 1989

Di Maio, S. P.; Zaad, K. H. & Salcudean, S. E. (2004). Optimal Selection of Manipulator Impedance for Contact Tasks, Proceedings of the 2004 IEEE International Conference on Robotics and Automation, New Orleans, 2004

Field, G. & Stepanenko, Y. (1993). Mode1 Reference Impedance Control of Robotic Manipulators, Proc. IEEE Pacific Rim Conference, pp. 614-617

Hogan, N. (1985). Impedance Control: An Approach to Manipulation: Parts I, II, III, ASME Journal of Dynamic systems, Measurement, and Control, Vol. 107, pp. 1-24

Kazerooni, H.; Sheridan, T. B. & Houpt, P. K. (1986). Robust Compliant Motion for Manipulators, parts 1 and II--The Fundamental Concepts of Compliant Motion, IEEE Journal of Robotics and Automation, Vol. 2, No. 2, pp. 83-105

Raibert, M. & Craig, J. (1981) Hybrid position/force control of manipulators, Journal of Dynamic Systems, Measurement and Control, vol. 103, no. 2, pp.126-133