Analyzing the behaviours of a car: a study in abstraction of goal-directed motions

Driving a car involves simultaneous consideration of events at different spatio-temporal scales. Proper interpretation and planning then leads to behaviour such as the parallel parking manoeuvre, 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 behaviours 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 (the paper also contains an explanation of these concepts). 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. This suggests that this method of analyzing the behaviour to derive a suitable level of description is conceptually correct, and that its implementation would give the right level of computational representation on which to apply one of the standard path planning algorithms.