Navigation and control of a trolley

This work deals with the guidance and control of the motion of a trolley. The trolley is composed from two rear wheels, each of them controlled separately, and a front castor wheel (see Fig. 1). Given N points P-i, i = 1,...,N in the horizontal plane, a finite time interval [0,t(f)], and a sequence of times tau(1) = 0 < tau(2) < ... < tau(N) = t(f). By using the concept of path controllability a control law for the trolley's rear wheels is derived, to steer the trolley's center (x, y) in such a manne r that (x, y) will pass through P-i at the time tau(i), i = 1,..., N, respectively.