Plane Motion of a Particle Subject to Curvature Constraints
E. J. Cockayne, Gregory W. Hall · SIAM Journal on Control · 1975
A particle P moves in the plane with constant speed and subject to an upper bound on the curvature of its path. This paper studies the classes of trajectories by which P can reach a given point in a given direction and obtains, for all t, the set $R(t)$ of all possible positions for P at time t, thus extending the results of several recent authors.