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Table 4: Master and Slave position vectors Symbol Meaning P M P S R M S O M S position of spherical joint centre respect to local frame of master and slave arm rotation matrix from master’s local frame to slave’s one position vector of slave’s local frame respect to master’s one Since the control procedure will provide to use the right arm as motion driver, in the following it will be indicated as master arm and the other one as slave. As mentioned before, the control procedure will provide to store the positions of the path points expressed respect to local frame of two arms (Table 4). By using any free set of three among the stored points (P M 0 P M 1 P M 2 respect to master’s frame and P S 0 P S 1 P S 2 respect to slave’s one), it is possible identify a mobile reference frame which is uniquely identi£ed in both reference systems (Σ0 and Σ1). Such a system can be used to £nd the rotation matrix between master’s and slave’s local frames by the following procedure: 1. using stored point it is possible to determine two intermediate frames with versors i =(P1 − P0)/|P1 − P0| Massimo Bergamasco / Haptic Rendering: Control Strategy j =(P2 − P0) − ((P2 − P0) · i)i k =i ×j 2. the rotation matrixes between the master’s local frame and the intermediate frame and between the slave’s local frame and the intermediate frame simply result R M I =[i M ,j M ,k M ] R S I =[i S ,j S ,k S ] 3. the rotation matrix between the master’s local frame and the slave’s local frame simply results R M S = R M I (R S I )T 4. Once rotation matrix is known, by using one of three stored points P0P1P2 (for example P0) it is possible to £nd the origin position vector of slave’s local frame respect to master’s one: O M S = P M 0 −R M S P S 0 It worths to mention that the procedure is independent from the speci£c trajectory used to £nd the six points set (P M 0 P M 1 P M 2 P S 0 P S 1 P S 2 ). Therefore even in presence of unaccurate position control the calibration procedure can provide exact calibration provided that a synchronized and accurate measure of these points is available. 64 Errors in evaluating stored vectors position can occur when the procedure is carried on. The reasons could be within the following ones: mechanical device could be different from simpli£ed kinematic model: – dimensions of mechanical parts may slightly differs respect to design speci£cations; – the mechanical device is not absolutely rigid therefore elasticity of transmissions and of structures may alter the effective measurement; – backlash of coupled mechanical parts; error in angular offsets evaluation, that will led to imprecise calibration procedure and digital resolution of incremental position sensors can affect computational procedures. In order to reduce calibration errors, a recursive procedure has been implemented by storing a large number of points and by calculating £nal relative position and orientation between two frames using average values. The procedure adopted is the follow: 1. master arm is controlled in order to move the centre of Cardano’s joint along a circumference as shown in Fig. 6; 2. a number of circumference points are stored as indicated during the movement; 3. a group of three points (P0 P1 P2)i are considered for determining the correspondent matrix rotation (R M S )i; 4. from any rotation matrix it is necessary to associate the Roll-Pitch-Yaw angles ( RPY )i; 5. the £nal RPY are calculated as the average values; 6. from the £nal RPY is calculated the £nal rotation matrix. 8. Results Once the calibration has been achieved the control software provides to store it in speci£c OS registry entries and reuse them whenever the system is restarted. In this way the user can operate on the systems as the arms belong to unique OS without caring too much (nor in use, nor in SW development) with the organization of mechanics and system control. If the user will notice that collocation of objects within VE appears to be corrupted he can manage a recalibration of the device at any time. This can be achieved by issuing the relative command from the HI control panel. Some extensive tests have been carried out in order to match the effectiveness of the calibration all over the workspace. The procedure works as follows: different “virtual” axes-aligned square-boxes have been placed on several positions of the arms workspace. HIs have then been moved onto the boxes in order to arrange thimbles is a parallel fashion on the same surface. Relative position has been measured according to the normal to the considered surface. Whenever c○ The Eurographics Association 2005.
the relative position did not matched the relative difference has been logged. The resulted error is almost zero at the centre of the workspace and increases as the thimbles are moved away from the center. The error is almost proportional to the distance from the centre. As a result the calibration procedure, joined with the quality of the device, allows to keep the relative error below 0.5 mm (the difference in evaluation of the same position by right and left arm), at a distance of 100 mm from the workspace center. 9. Acknowledgment The authors would like to acknowledge the EU which contributed to fund the GRAB project as well as all the organizations involved within the project: LABEIN (ES), ONCE (ES), RNIB (UK), NCBI (IE) and HAPTICA (IE). 10. References [AMA03] Avizzano C., Marcheschi S., Angerilli M., Fontana M., Bergamasco M., Gutierrez T., Mannegeis M., A multi-£nger haptic interface for visually impaired people. Robot and Human Interactive Communication, 2003. Proceedings. ROMAN 2003, 165–170. [BLSH95] Brunner B., Landzettel K., Steinmetz B.-M., Hirzinger G. Telesensorprogramming - a task-directed programming approach for sensor-based space robots. Int. Conf. on Advanced Robotics (ICAR), Sant Feliu de Guixols, Spain, Sept 20-22 (1995). [CH88] Colgate J. E., Hogan N. Robust control of dynamically interacting systems. International Journal of Control 48 (1988), 65–88. [Col93] Colgate J. E. Robust impedance shaping telemanipulation. IEEE Transactions on Robotics and Automation 9 (1993), 374–384. [HDD99] Howe R., Debus T., Dupont P. Twice the fun: Two phantoms as a high-performance telemanipulation system. In Proceedings of the Fourth Annual PHANTOM Users Group Workshop, Dedham, MA, October 9-12 (1999). [Jan98] Jansson G. Can a haptic force feedback display provide visually impaired people with useful information about texture roughness and 3d form of virtual objects? In P. Sharkey, D. Rose & J.-I. Lindström (Eds.), The 2nd European Conference on Disability, Virtual Reality and Associated Technologies. Proceedings (pp. 105-111). Reading, UK: University of Reading, Department of Cybernetics. (1998). [Jan01] Jansson G. The potential importance of perceptual £lling-in for haptic perception of virtual object form. In Eurohaptics 2001 Conference Proceedings (Educational Technology Research <strong>Paper</strong>s, ETRP 12, pp. 72-75). Birmingham, c○ The Eurographics Association 2005. Massimo Bergamasco / Haptic Rendering: Control Strategy 65 England: The University of Birmingham (ISSN 1463-9394). (2001). [KL90] Klatzky R., Lederman S. Intelligent exploration by the human hand. Springer-Verlag, 1990, ch. Dextrous robot manipulation. [KL99] Klatzky R., Lederman S. Tactile roughness perception with a rigid link interposed between skin and surface. In Perception & Psychophysics 1999, 61 (4), 591-607 (1999). [PHB99] Pelz J. B., Hayhoe M. M., Ballard D. H., Shrivastava A., Bayliss J. D., von der Heyde M. Development of a virtual laboratory for the study of complex human behavior. In Proceedings of the SPIE - The International Society for Optical Engineering, 3639B (1999). [TGTC98] Turner M., Gomez D., Tremblay M., Cutkosky M. Preliminary tests of an arm-grounded haptic feedback device in telemanipulation. Proc. ASME WAM DSC-64 (1998), 145–149.
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EUROGRAPHICS 2005 Tutorial Multimod
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EUROGRAPHICS 2005 Tutorial Abstract
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