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A biologically inspired neural net for trajectory formation and obstacle avoidance

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Abstract

In this paper we present a biologically inspired two-layered neural network for trajectory formation and obstacle avoidance. The two topographically ordered neural maps consist of analog neurons having continuous dynamics. The first layer, the sensory map, receives sensory information and builds up an activity pattern which contains the optimal solution (i.e. shortest path without collisions) for any given set of current position, target positions and obstacle positions. Targets and obstacles are allowed to move, in which case the activity pattern in the sensory map will change accordingly. The time evolution of the neural activity in the second layer, the motor map, results in a moving cluster of activity, which can be interpreted as a population vector. Through the feedforward connections between the two layers, input of the sensory map directs the movement of the cluster along the optimal path from the current position of the cluster to the target position. The smooth trajectory is the result of the intrinsic dynamics of the network only. No supervisor is required. The output of the motor map can be used for direct control of an autonomous system in a cluttered environment or for control of the actuators of a biological limb or robot manipulator. The system is able to reach a target even in the presence of an external perturbation. Computer simulations of a point robot and a multi-joint manipulator illustrate the theory.

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References

  1. Amari S (1977) Dynamics of pattern formation in lateral-inhibition type neural fields. Biol Cybern 27:77–87

    Google Scholar 

  2. Barraquand J, Latombe J (1989) Robot motion planning with many degrees of freedom and dynamic constraints. In: Proceedings of the 5th International Symposium on Robotics Research (Tokyo) pp 74–83

  3. Barraquand J, Latombe JC (1990) A Monte-Carlo algorithm for path-planning with many degrees of freedom. In: Proceedings of the IEEE International Conference on Robotics and Automation (Cincinnati, Ohio). IEEE Computer Society Press, Los Alamitos, 1712–1717

    Google Scholar 

  4. Barraquand J, Langlois B, Latombe J (1992) Numerical potential field techniques for robot path planning. IEEE Trans Syst Man Cybern 22:224–241

    Google Scholar 

  5. Bizzi E, Accornero N, Chapelle N, Hogan N (1982) Arm trajectory formation in monkeys. Exp Brain Res 46:139–143

    Google Scholar 

  6. Caminiti R, Johnson PB, Burnod Y, Galli C, Ferraina S (1990) Shifts of preferred directions of premotor cortical cells with arm movements performed across the work-space. Exp Brain Res 83:228

    Google Scholar 

  7. Connolly C, Burns J, Weiss R (1991) Path planning using Laplace's equation. In: Proceedings of the IEEE International Conference on Robotics and Automation. IEEE Computer Society Press, Los Alamitos, pp 2102–2106

    Google Scholar 

  8. Dorst L, Mandhyan I, Trovato K (1991) The geometrical representation of path planning problems. Robotics Autonomous Syst 7:181

    Google Scholar 

  9. Droulez J, Berthoz A (1991) A neural network model of sensoritopic maps with predictive short term memory properties. Proc Nat Acad Sci USA 88:9653–9657

    Google Scholar 

  10. Feldman AG (1986) Once more on the equilibrium-point hypothesis (λ model) for motor control. J Mot Behav 18:17–54

    Google Scholar 

  11. Fritzke B (1991) Unsupervised clustering with growing cell structures. Proceedings of the International Joint Conference on Neural Networks (Seatle, Wash) vol II. Piscataway NJ, IEEE, pp 531–536

    Google Scholar 

  12. Georgopoulos AP, Ashe J, Smyrnis N, Taira M (1992) The motor cortex and the coding of force. Science 256:1692–1695

    Google Scholar 

  13. Glasius R, Komoda A, Gielen CCAM (1994) Population coding in a neural net for trajectory formation. Network: Comput Neural Syst 5:549–563

    Google Scholar 

  14. Glasius R, Komoda A, Gielen CCAM (1995) Neural network dynamics for trajectory formation and obstacle avoidance. Neural Networks 8:125–133

    Google Scholar 

  15. Grossberg S (1984) Nonlinear neural networks: principles mechanisms and architectures. Neural Networks 1:17

    Google Scholar 

  16. Hogan N (1984) An organizing principle for a class of voluntary movements. J Neural Sci 4:2745–2754

    Google Scholar 

  17. Hopfield JJ (1984) Neurons with graded response have collective computational properties like those of two-state neurons. Proc Natl Acad Sci USA 81:3088

    Google Scholar 

  18. Jarris RA (1985) Collision-free trajectory planning using distance transforms. Mech Eng Trans IE Aust ME 10:187

    Google Scholar 

  19. Kalaska JF, Cohen DAD, Prud'homme M, Hyde ML (1992) Comparision of cell discharge in motor, premotor and parietal cortex during reaching: load direction-related activity in primate motor cortex using a two dimensional reaching task. Springer Berlin Heidelberg New York

    Google Scholar 

  20. Kathib O (1986) Real-time obstacle avoindance for manipulators and mobile robots. Int J Robotics Res 5:90–98

    Google Scholar 

  21. Kohonen T (1982) Self-organized formation of topologically correct feature maps. Biol Cybern 43:59–69

    Google Scholar 

  22. Kopecz K, Schöner G (1995) Saccadic motor planning by integrating visual information and pre-information on neural dynamic fields. Biol Cybern 73:49–60

    Google Scholar 

  23. Krogh BH, Thorpe CE (1986) Integrated path planning and dynamic steering control for autonomous vehicles. Proceedings of the IEEE International Conference on Robotics and Automation (Washington, DC). Computer Society Press of the IEEE, Los Angeles, pp 1664–1669

    Google Scholar 

  24. Latombe J (1991) Robot motion planning. Kluwer Academic, Boston

    Google Scholar 

  25. Linsker R (1986a) From basic network principles to neural architecture: emergence of spatial-opponents cells. Proc Natl Acad Sci USA 83:7508–7512

    Google Scholar 

  26. Linsker R (1986b) From basic network principles to neural architecture: emergence of orientation-selective cells. Proc Natl Acad Sci USA 83:8779–8783

    Google Scholar 

  27. Linsker R (1986c) From basic network principles to neural architecture: emergence of orientation columns. Proc Natl Acad Sci USA 83: 7508–7512

    Google Scholar 

  28. Lozano-Perez T (1983) Spatial planning: a configuration space approach. IEEE Trans Comput 32:108–120

    Google Scholar 

  29. Martinetz TM (1993) Competitive Hebbian learning rule forms perfectly topology preserving maps. In: Proceedings of the International Conference on Artificial Neural Networks (Amsterdam, The Netherlands). North-Holland/Springer-Verlag, Amsterdam/Berlin Heidelberg New York, pp 427–434

    Google Scholar 

  30. Newman W, Hogan N (1987) High speed robot control and obstacle avoidance using dynamic potential function. In: Proceedings of the IEEE International Conference on Robotics and Automation (Raleigh, NC). Computer Society Press of the IEEE, Los Angeles, pp 14–24

    Google Scholar 

  31. Prassler E (1989) Electrical networks and a connectionist approach to path-finding. In: Connectionism in perspective. North-Holland, Amsterdam, p 421

    Google Scholar 

  32. Ritter HJ, Martinetz TM, Schulten KJ (1989) Topology-conserving maps for learning visuo-motor-coordination. Neural Networks 2:159–168

    Google Scholar 

  33. Schwartz JT, Sharir M (1983) On the ‘piano’ mover's problem. II. General techniques for computing topological properties of real algeraic manifolds. Adv Appl Math 4:298–351

    Google Scholar 

  34. Warren C (1989) Global path planning using artificial potential fields. In: Proceedings of the IEEE International Conference on Robotics and Automation (Scottsdale, Ariz). Computer Society Press of the IEEE, Los Angeles, pp 316–321

    Google Scholar 

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Authors and Affiliations

  1. Department of Medical Physics and Biophysics, University of Nijmegen, Geert Grooteplein Noord 21, 6525, EZ Nijmegen, The Netherlands

    Roy Glasius, Andrzej Komoda & Stan C. A. M. Gielen

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  1. Roy Glasius
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  2. Andrzej Komoda
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  3. Stan C. A. M. Gielen
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Glasius, R., Komoda, A. & Gielen, S.C.A.M. A biologically inspired neural net for trajectory formation and obstacle avoidance. Biol. Cybern. 74, 511–520 (1996). https://doi.org/10.1007/BF00209422

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  • DOI: https://doi.org/10.1007/BF00209422

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