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