Arbitrary path following control of off-axle tractor-trailer mobile robot

The tractor-trailer mobile robot with off-axle hitching is a classical nonholonomic system. It is difficult to use one controller to achieve path following when the linear velocity of the tractor is time-varying and sign changeable. This paper investigates the arbitrary path following problem of off-axle tractor-trailer robots with time-varying and sign changeable linear velocity. The error state model is first derived from the kinematic equations of the system and the virtual vehicle. The coordinate transformation is used to convert the simplified linearized error model to a normal form, and then a path-following control law is constructed via Lyapunov methods. Assume that the linear velocity of the tractor is bounded, not convergent to zero, and its derivative is bounded, then the designed control law guarantees that the tractor-trailer system is able to follow an arbitrary desired path. The size of the ultimate bound is proportional to the derivative of curvature. Moreover, asymptotic exponential convergence of the tractor-trailer to the desired path is achieved when the derivative of curvature is zero or convergent to zero. Simulation results show the effectiveness of the proposed control scheme.