Lyapunov-based generic controller design for thrust-propelled underactuated systems

Abstract

We present a controller for an underactuated system which is driven by a one dimensional linear acceleration/thrust along a direction vector, by a time-varying gravity, and by the angular acceleration of the direction vector. We propose state and time-dependent control laws for the linear and angular accelerations that guarantee that the position of the system is steered to the origin. The proposed control law depends on (i) a bounded control law for a double integrator system; and (ii) on a Lyapunov function that guarantees asymptotic stability of the origin for the double integrator system when controlled with the previous bounded control law. As such, the control law forms a family of control laws depending on (i) and (ii). The complete state space of the system, under the proposed control laws, has two equilibria, and by proper control design, a trajectory of the system is guaranteed to converge to only one of those. The overall design provides a common framework for controlling different systems, such as quadrotors and slung load transportation systems.