Bottom-up derivation of the qualitatively different behaviors of a car across varying spatio-temporal scales: A study in abstraction of goal-directed motion

  • Leo Dorst
Inference and Action
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1315)


Driving a car involves considering it at different spatio-temporal scales, and somehow leads to behavior such as the parallel parking maneuver, the three-point turn, free Euclidean driving in a desert, following a road, and translationally passing other vehicles at high speed. In the study of autonomous systems, it is desirable to find a representation in which such different behaviors of a single system can be related to each other, and to find precisely how and under what conditions a change of representation and corresponding choice of motions occurs. In this paper, we formulate an abstraction mechanism based on approximations of flows of commutators of vector fields. We apply it to the goal-directed motion of a car and show how the environmental constraints induce, through this abstraction mechanism, a recognizable hierarchy of descriptions of the car's motion.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    L. Dorst, I. Mandhyan, K.I. Trovato: The Geometrical Representation of Path Planning Problems, Robotics and Ant. Syst., Elsevier, vol.7, 1991, pp.181–195.Google Scholar
  2. 2.
    B. O'Neill: Elementary Differential Geometry, Academic Press, 1966.Google Scholar
  3. 3.
    E. Nelson: Tensor Analysis, Princeton U. & U. of Tokyo Press, 1967.Google Scholar
  4. 4.
    E. Nelson: Topics in Dynamics, I: Flows, Princeton U. & U. of Tokyo Press, 1969.Google Scholar
  5. 5.
    H.F. Trotter: On the product of semi-groups of operators, Proc. AMS 10 (1959), pp.545–551.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Leo Dorst
    • 1
  1. 1.RWCP Novel Functions: SNN Laboratory Amsterdam, Dept. of Mathematics, Computer Science, Physics and AstronomyUniversity of AmsterdamSJ AmsterdamThe Netherlands

Personalised recommendations