VNHC-Based Continuous Sliding Mode Control for an Underactuated Tethered UAV System

This article introduces a novel continuous sliding mode control strategy for transporting a tethered payload by a UAV. A key contribution of this work is the development of a feasible sliding manifold based on
virtual nonholonomic constraints
(VNHC), addressing the longstanding challenge of stabilizing both actuated and unactuated states in underactuated systems. Our approach constructs an explicit sliding manifold, a task previously unachieved for tethered UAV systems, and designs a continuous sliding mode controller to guide system states onto this manifold. The proposed continuous sliding mode controller effectively mitigates undesirable chattering effects and facilitates feasible attitude extraction. Rigorous proofs are provided for the finite time reachability of the sliding manifold and the asymptotic stability of the reduced dynamics on the manifold, using the
invariance principle
and homogeneous stability for the
differential inclusion
. Numerical simulations and experiments are conducted to validate the effectiveness of the proposed controller.