ABSTRACT

We consider tracking control of an underactuated system on the tangent bundle of the six-dimensional Lie group of rigid body motions, $\mathrm{S}\mathrm{E}\left(3\right)$. 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.

摘要

我们考虑在刚体运动的六维李群的切丛上对欠驱动系统进行跟踪控制，$\mathrm{小号}\mathrm{乙}\left(3\right)$. 我们在离散时间内为这个欠驱动系统制定了一个有限时间稳定 (FTS) 跟踪控制方案。该方案基于我们最近开发的使用离散 Lyapunov 分析的离散时间系统的有限时间稳定性理论。这里提出的方案是在离散时间开发的，因为它更便于车载计算机实施，并且无论采样周期如何都能确保稳定性。该方案保证了平移和旋转跟踪误差在有限时间内稳定收敛到所需轨迹。此外，这里通过数值比较解决了离散时间有限时间稳定相对于采样连续时间跟踪控制系统的有限时间稳定的优势。