The Haptic Impendance Control through Virtual Environment Force Compensation

Transcription

1 The Haptic Impendance Control through Virtual Environment Force Compensation OCTAVIAN MELINTE Robotics and Mechatronics Department Institute of Solid Mechanicsof the Romanian Academy ROMANIA Abtract. This paper presents force-position haptic control methods used to increase trajectory tracking accuracy through the compensation on two axes depending on the forces from a virtual environment. Kinematic structure of the haptic device is analyzed, the end-effector trajectory control loop is modeled using an impedance control function and, in order to eliminate singularities and areas of instability, the real-time control system architecture is designed by direct and inverse kinematic computing using transposed Jacobian matrix instead of inverse matrix computing. A testing and simulation diagram was developed for control system modeling in SIMULINK, using signal generators that are designed to replace the haptic device and virtual interface. To simplify the control scheme the force feedback to the human operator was dropped. The results yielded by the impedance hybrid force position control system have revealed the position compensation when a force is received from the virtual environment while improving the extremely trajectory tracking by the haptic device end-effectorul. Key words: robot control, haptic interface, force-position hibrid control, real time control systems, modeling and simulating mechanical systems 1. Introduction In recent years the introduction of haptic technology has become a way to solve various problems that may arise when using teleoperation in difficult environments so that using haptic response the accuracy of the operation carried out will be increased. Until now several types of haptic devices have been developed among them being: Phantom device developed by MIT, the Delta Haptic Device, Virtuose 6D, some of them using force sensing in order to increase operating accuracy of such devices[1]. Also, to achieve control, various algorithms can be adopted. Such as the open architecture systems for walking robot s control [2] or the fuzzy dynamic modeling for walking modular robot control [3][4]. In the other hand for the haptic control there are two types of control: impedance control and admittance control. The impedance control relies on reading the position and sending the force while the admittance control is concerned on reading the force and sending the position The most used control scheme, and the one which will be discussed in this paper is the impedance control, because of the compliant feature of impedance controllers and the possibility of using force response, while admittance control is used in applications which require large Impedance control provides a relationship between the robot motion error and the interaction force with the environment In order to simulate results the haptic device structure was chosen, comprising two controlled joints and five segments, four of them forming a parallelogram to get better positioning accuracy. For a proper simulation of the haptic device it was consider a control diagram so that the position reference signals coming from the haptic device, are being transformed using an encoder in the required angles (α 1 and α 2 ), which are subsequently used in haptic controller in order to realize the impedance control with force response The difference over other control schemes come from the fact that the force feedback felt by the operator is neglected, being carried out the position compensation depending on the sensed force virtual environment, such a method could be used in virtual simulations which do not require a force feedback to the human operator. ISBN:

2 2. Structure of the Haptic Device Haptic device in Figure 1 consists of four building blocks, for which were considered four degrees of freedom. These four degrees of freedom are all rotation type in the XOY plane, but only two of them have servo motors and encoders to be able to measure the angles between the elements when they are moved by a human operator. Servo-motors also have a role to provide the human operator, a force response for a better simulation of virtual reality, but it is not the case for the example taken in this article As you can see in the figure below, each length is denoted by L 1 -L 4 and the distance from the point of connection between the segments and centers of mass, L C1 -L C4. Also, angles 1 and 2 are the angles of the two sensor equipped joints, and 1 and 2 are the angles of the elements 1 and 4 reported the XOY plane. This haptic device is the human operator interface device for the entire positioning system of the virtual or remote devices. For this, the human operator interacts with the haptic device through a joystick, provided at the edge of segment 4 of the haptic device in figure 1. Fig. 1 Structure of the haptic device At the movement of the device by the human operator, sensors or servo-motors of the two joints, will measure the angles 1 and 2 which will be sent to the control function of the virtual or remote manipulator. 3. Impedance control Haptic technology is closely related to the high precision mechanisms because of its connection with dexterity mechatronic devices with and draws important lines in the theoretical foundations for design, automation and control of manipulators. Haptic interfaces intend to reproduce or to include the touching experience through manipulation or that of perception of real environments using mechatronical devices and computer control. They consist of a haptic device and a computer for control, which incorporates a software that associates input data from the human operator with haptic information rendering. The concept of haptic rendering is relatively simple, there are enough problems in the development of ideal haptic interfaces. In general, haptic interfaces performance specifications are based on human sensory ability and motor control features. A major problem in generating artificial haptic sensitivity is that the human operator movement should be less strict when there is no contact with any virtual or remote object. Haptic devices should allow the human operator to carry out the desired movements, thus requiring backward maneuverability and enough degrees of freedom for movement[5]. In the control diagram which will be presented, the linearized dynamics of the haptic device is represented by j Z h, which is the dynamic impedance and presents the relationship between joint torques and angular differential output. Since positions from the linearized block diagram are represented as deviations from nominal positions, x 0, Cartesian positions of the haptic interface and joint position of the haptic mechanism are related by the Jacobian J. Controller takes the position deviation difference between desired and actual position deviation of the haptic interface, and multiply by the desired impedance of the environment in order to generate a force Fd. Strength in the order form is necessary torque commands using the Jacobian J, which are then applied to the haptic device. An impedance controller with force feedback is shown in figure 3. It may be noted that in this block diagram it is a path for the sensed signal to reach at the haptic device. The force feedback is used to close the loop for the desired force generated by the controller. The influence of impedance error on the force gain can be found in the same diagram. The following relations are obtained [6] : j x J Zh J F (1) 1 T c T c J F d KF Fd F (2) ISBN:

3 d d d F Z x x (3) The difference between closed-loop impedance and desired impedance is the natural impedance of the haptic device Z Z Z (4) h d h CL do experiments on the transfer functions, was necessary to implement the four signal generators, two for generating position (1 and 2) and another two for force generation (decomposed force on the OX and OY axes) which should be received by the virtual environment on which the haptic manipulator acts.[7] Setting and substituting, impedance of the close loop can be determined as CL 1 Z Z I K Z (5) h d F h Fig. 3 Impendance control with force-feedback Fig. 2 Control diagram of haptic interface Although errors due to haptic device dynamics are inversely proportional to gain, Kf, if the gain of force is set to 0, then the controller will use relation (4). The force gain is usually a value as high as possible, in practice, being bounded by the stability determined by the sampling rate and natural frequency of the haptic device. 4. Impedance Control Function Figure 3 presents the general scheme for impedance control with force-feedback. This control was implemented in MATLAB SIMULINK for the modeling and simulation of mechatronic systems (fig. 4). Since the system is modeled on the XOY axes, the control functions will use only the data for the two axes. This is the reason why it can be seen in the figure 4, as its composition blocks are connected by two lines of information transfer for each coordinate axis (X and Y respectively). Since we did not had an actual model of the haptic device we tried to generate the input step signals of position and force in such way that the input angles in de XOY plane to be around 40 0 (degrees) and the force associated with the one that comes from the virtual environment to have a maximum of 5N In a scheme as the one in figure 3, apparently there are basic elements (as the sum operator) but these must also be modeled. Moreover, in order to Thus, taking the data generated for the position reference of the virtual manipulator, it will generate two sets of data, representing angles 1 and 2, corresponding to the haptic manipulator. Using these angles are calculated by transfer block Xd in figure 4, the end-effector position, and then to calculate the positioning error by subtracting from the reference position, the actual end-effector position in XOY space. Applying this impedance, leads to finding the Fd forces from which we subtract the forces which are derived from the generator that simulates the response of the virtual environment. For this difference is applied a KF amplification, which can lead to a open loop system if the gain value is set to zero. After the amplification of the force differentiation, we then add the calculated force from the positioning error. Then we multiply by the haptic manipulator Jacobian. This transfer function will require as input, along with the forces for which the transposed Jacobian matrix is applied, the angles 1 and 2 for the actual calculation of this matrix. In order to avoid singularities given by the transposed Jacobian aplied for this type of manipulator, we introduced a block diagram which was programmed such as the feedback to be calculated. In the next step it s calculated the difference of torque, between the one given to the virtual environment and the one received from it, to be able to compensate the torque. Then, using the reverse transposed Jacobian matrix, the endeffector position is calculated to be returned in the closed loop. ISBN:

4 Fig. 4 Impedance control MATLAB diagram 6. Results and conclusions To test the impedance control of haptic systems and in particular the haptic system presented in this article, we used Matlab simulator in order to model the system. To do this, in the transfer blocks of the model from figure 4, were placed the corresponding data of the haptic manipulator from figure 1. These data have provided the transposed Jacobian matrix, and the reverse transposed Jacobian matrix. But for the simulation to be complete were required generation of the angles 1 and 2, used in calculating the end-effector position, transposed Jacobian matrix, the inverse transpose Jacobian matrix, and the response force. The response force is normally provided, to the haptic manipulator, by the virtual environment connected to it. In figures 5 and 6 is presented a simulation for an end-effector reference, whose position on the XOY axis is provided by the blue(thinnest) lines on the two figures. Also, the values of the components on the two axes of the force which should be received from the virtual environment are given by the red lines. The response given by the control scheme is shown in green, also for the two axes (position on OX and OY axis) and we can see how a force change in the virtual environment can change the position reference for the manipulator s endeffector to compensate for the torque produced by the force of contact with the virtual manipulator controlled by the haptic manipulator. Fig 5 System response for the position and force reference on the OX axis (Xref, X, Fx_ref) Fig 6 System response for the position and force reference on the OY axis (Yref, Y, Fy_ref) ISBN:

5 As can be seen figures 5 and 6 for each change of position of the haptic manipulator, the control will give the position reference to the virtual control of the manipulator, according to the impedance control function. What is most relevant, is when from the virtual environment is received a reaction force on the virtual manipulator. When this happens, you can see in the two figures, how the control law will control the position of the manipulator to compensate for the torque in the joints, and finally the end-effector s force which will act upon the virtual environment, so that it can reach its reference position, as given by the human operator. This control scheme, allows the simulation and regulation of many impedance control laws for which you can see, without the need for a virtual or physical environment, how effective are those control laws proposed by an engineer. References [1] Andrew Zammit Mangion, Simon G. Fabri, Experimental Evaluation of Haptic Control for Human Activated Command Devices, International Conference of Control 2008, Manchester [2] Luige Vladareanu, Radu Munteanu, Adrian Curaj, Ion N. Ion, Open Architecture Systems for MERO Walking Robots Control, Proceedings of the European Computing Conference, 2009, Volume 28, 6, pg [3] Luige Vladareanu Gabriela Tont,Ion Ion, Lucian M. Velea, Alexandru Gal, Octavian Melinte, Fuzzy dynamic modeling for walking modular robot control, AEE'10 Proceedings of the 9th WSEAS international conference on Applications of electrical engineering, ISBN: [4] Doina Marin, Improvement of the machine tools performance, Journal WSEAS Transactions on Systems and Control archive, Volume 5, Issue 3, March 2010 [5] M. Ueberle, M. Buss, Control of Kinesthetic Haptic Interfaces [6] Craig R. Carignan, Kevin R. Cleary, Closed- Loop Force Control For Haptic Simulation Of Virtual Environments, Haptics-e, vol.1, no.2, pp [7] Octavian Melinte, Alexandru Gal, Bond graph modelling for haptic interface robot control,proceedings of the European Computing Conference, Paris, France, April, ISBN: ISBN: