Navigation and control of a system composed of a trolley and a mounted two-link manipulator

This work deals with the guidance and control of the motion of a system which is composed of a trolley and a mounted two-link manipulator. The trolley is composed from two rear wheels, each of them controlled separately, and from two front castor wheels (see Figure 1). Denote by (x, y) the trolleyʹs center of mass, and by α1 and α2 the angles with respect to the horizon of the manipulator arms. Given N points Pi, i = 1, …, N in the horizontal plane, 2N angles αkj, k = 1, 2, j = 1, …, N, a finite time interval [0, tf], and a sequence of times τ1 = 0 < τ2 < … < τN = tf. Based on a dynamical model of the system, and by using the concept of path controllability, a control law for the trolleyʹs rear wheels and for the two-link manipulator torques is derived, to steer the system such that [(x, y), α1, α2] will pass through [Pj, α1j, α2j] at the time τj, j = 1, …, N, respectively.