Control of two manipulation points of a cooperative transportation system with two car-like vehicles following parametric curve paths

The present paper proposes a new feedback control law for a cooperative transportation system comprising two car-like vehicles. The proposed feedback control law controls the two manipulation points, which are revolute joints coupling the two vehicles to a carrier, to follow their parametric curve paths, such as Bezier curves at variable velocities. Thus, the proposed feedback control law makes it possible to specify the motion of the carrier quantitatively using design parameters such as the path shapes and the variable velocity profiles. The convergence of the position of the first manipulation point to its desired position on the first path is guaranteed by linear control theory, and the convergence of the position of the second manipulation point to its desired position on the second path is guaranteed by Lyapunov's second method. In particular, the design of the Lyapunov functions is facilitated by a new form of differential equations that are equivalent to time differential equations in a chained form into which the kinematic equations of the system are converted. The validity of the proposed feedback control law is verified experimentally.