Abstract
This paper handles the problem of collision avoidance in a multi-robot environment. To solve this problem, the motion processes of the mobile robots are modelled in space-time. Since the robots are autonomous and communication is non-deterministic, there is temporal uncertainty in addition to spatial uncertainty. The paper presents a method to model both uncertainty components in a homogeneous way. It is shown, that it is not sufficient to guarantee a spatial security distance between the robots. Distances in space-time and space-time vectors must be considered. The main result of this paper is a straightforward and efficient solution to the problem of collision avoidance between up to three mobile robots by applying a space-time displacement vector. The solution is based on space-time, which is a helpful view onto our world in relativity theory and quantum physics. Space-time methods are also very valuable in Robotics, especially for problems in dynamic environments and for motion coordination of mobile robots. Practical experiments with up to two robots, and simulations of up to three robots have been performed and are reported.
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References
Ayache, N. and Faugeras, O.D. 1989. Maintaining representations of the environment of a mobile robot. IEEE Trans. on Robotics and Automation, 5 (6): 804–819.
Cameron, S. 1990. Collision detection by four-dimensional intersection testing. IEEE Trans. on Robotics and Automation,6(3):291301.
Dickmanns, ED. and Graefe, V. 1988. Dynamic monocular machine vision. In Machine Vi sion and Applications, Springer-Verlag: New York, vol. 1, pp. 223–240.
Dickmanns, E.D. and Thomanek, F. 1992. Obstacle detection, tracking and state estimation for autonomous road vehicle guidance. In Proc. IEEEJRSJ Int. Cont. on Intelligent Robots and Systems, pp. 1399–1405.
Ellis, G.F. and Williams, R.M. 1988. Flat and Curved Space-times,Oxford University Press.
Elnagar, A. and Basu, Anup 1994. Local path planning in dynamic environments with uncertainty. In Proc. of the IEEE Int. Conf. on Multisensor Fusion and Integration for Intelligent Systems (MFT’94), Las Vegas, NV, pp. 183–190.
Feynman, R.P. 1974. The geometry of space-time. The Feynman Lectures on Physics. Vol. I Part I, Mainly Mechanics, Radiation, and Heat, Addison-Wesley Publishing Company.
Fiorini, P. and Shiller, Z. 1993. Motion planning in dynamic environments using the relative velocity paradigm. In Proc. of the IEEE Int. Cord: on Robotics and Automation, pp. 560–565.
Form, P. Airborne Collision Avoidance. 1991. In: Concise Enc. of Traffic and Transportation Systems. Papageorgiou and Markus ( Eds. ). Pergamon Press, pp. 29–36.
Freund, E. and Lammen, B. 1992. Sensor based online collision avoidance for autonomous vehicles. In Proc. International Conference on Automation, Robotics und Computer Vision(ICARCV’92),Singapur.
Fujimura, K. 1991. Motion Planning in Dynamic Environments. From the series: Computer Science Workbench, Springer-Verlag: Tokyo.
Harrison E.R. 1981. Cosmology, Cambridge University Press. Kant, K. and Zucker, S.W. 1986. Toward efficient planning: The path-velocity decomposition. Int. Journal on Robotics Research, 5: 72–89.
Lconard, J.J. and Durrant-Whyte, H.F. 1991. Mobile robot localization by tracking geometric beacons. IEEE Trans. on Robotics and Automation, 7 (3): 376–382.
Loewer, J. 1994. Entwicklung eines rotationsfaehigen StereoUltraschall-Sensorsystems (Development of a rotating stereo ultrasonic sensor system ). Thesis at Forschungszentrum Informatik (FZI) at Karlsruhe University (in German).
Mould, R.A. 1994. Basic Relativity. Springer-Verlag: Berlin, Heidelberg, New York.
Rude, M. 1994. Cooperation of mobile robots by event transforms into local space-time. Proc. of the JEEE/RSJ/GI International Conference on Intelligent Robots and Systems, IROS, Munich, 92, pp. 1501–1507.
Rude, M. 1995. Koordinierte Kollisionsvermeidung Mobiler Roboter mit Hilfe von Kommunikation und Sensorik (Coordinated collision avoidance of mobile robots by the use of communication and sensing). Ph.D.-Thesis at Forschungszentrum Informatik (FZI) at Karlsruhe University. Fortschrittsberichte Reihe 8, Nr. 495, VDI-Verlag Duesseldorf (in German).
Rupp, T. 1996. Kollisionsvermeidung mobiler Roboter durch koordinierte sensorgefuehrte Manoever (Collision avoidance of mobile robots through coordinated, sensor-based manoeuvres). Master-Thesis at Forschungszentrum Informatik (FZI) at Karlsruhe University (in German).
Sandler, M. Autonomous guidance of ships on waterways. In Proc. Intelligent Autonomous Systems (IAS 4), edited by Reinhold., IOS Press, Karlsruhe, Germany, pp. 643–650.
Smith, R., Matthew, S., and Cheeseman, P. 1991. Estimating uncertain spatial relationships in robotics. In Autonomous Robot Vehicles, I.J. Cox and W.T. Wilfong (Eds.), Springer-Verlag: Berlin, Heidelberg, New York.’
Tsubouchi, T. and Arimoto, S. 1994. Behavior of a mobile robot navigated by an “Iterated Forecast and Planning” Scheme in the presence of multiple moving obstacles. In Proc. of the IEEE Int. Conf: on Robotics and Automation, pp. 2470–2475.
Watanabe, Y. and Yuta, S. 1990. Position estimation of mobile robots with internal and external sensors using uncertainty evolution technique. In Proc. IEEE Int. Conf. on Robotics and Automation, pp. 2011–201.
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Rude, M. (1997). Collision Avoidance by Using Space-Time Representations of Motion Processes. In: Arkin, R.C., Bekey, G.A. (eds) Robot Colonies. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-6451-2_6
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DOI: https://doi.org/10.1007/978-1-4757-6451-2_6
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