Finite-time stable tracking control for an underactuated system in SE(3) in discrete time

We consider tracking control of an underactuated system on the tangent bundle of the six-dimensional Lie group of rigid body motions, (Formula presented.). We formulate a finite-time stable (FTS) tracking control scheme for this underactuated system in discrete time. This scheme is based on our recently developed theory for finite-time stability for discrete-time systems using discrete Lyapunov analysis. The proposed scheme here is developed in discrete time as it is more convenient for onboard computer implementation and ensures stability irrespective of the sampling period. This scheme guarantees a stable convergence of translational and rotational tracking errors to the desired trajectory in finite time. Furthermore, the advantages of finite-time stabilisation in discrete-time over finite-time stabilisation of a sampled continuous-time tracking control system is addressed here through a numerical comparison. This comparison is performed using numerical simulations on continuous and discrete FTS tracking control schemes applied to an unmanned aerial vehicle model.