Almost global attitude stabilisation of a 3-D pendulum by means of two control torques

We investigate the problem of stabilising the attitude of a 3-D axially symmetric pendulum. The system is assumed to be actuated by two torques acting on a plane orthogonal to the symmetry axis. We develop a smooth control law to stabilise the pendulum to the upright position with a given orientation starting from almost all initial conditions. Our approach consists in two steps: first, stabilising the kinematic subsystem by using the angular velocity as a virtual input; second, exploiting the actual inputs to force the angular velocity to follow the reference designed in the previous step. Copyright (C) 2020 The Authors.