Navigation and control of a trolley by using a dynamical model: the dynamical model revisited

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 from a front castor wheel. Given N points P _i, i=1, ..., N in the horizontal plane, a finite time interval [0, t_f], and a sequence of times τ₁=0<τ₂<...<τ_N=t _f. Based on a dynamical model of the trolley, and by using the concept of path controllability, a control law for the trolley´s rear wheels is derived, to steer the trolley´s center of mass (x,y) in such a manner that (x,y) will pass through P_i, at the time τ_i, i=1, ..., N, respectively