Control Barrier Function-Based Quadratic Programming for SafeOperation of Tethered UAVs

TL;DR

The paper addresses safe operation of tethered UAVs by enforcing the tether length constraint $L_{max}$ while achieving precise trajectory tracking. It integrates a nonlinear backstepping nominal controller with a Control Barrier Function Quadratic Program (CBF-QP) to ensure forward invariance of the safety set defined by $h(\chi) = L_{max} - \|\boldsymbol{\xi}\|$ and real-time constraint satisfaction. Key contributions include the development of a backstepping-based TUAV controller, explicit CBF design for tether safety, and a QP that minimally perturbs the nominal input to guarantee safety. Simulations demonstrate that $\|\boldsymbol{\xi}(t)\| \le L_{max}$ with tracking errors converging to zero and bounded control inputs, highlighting the framework's potential for safe, reliable TUAV operation in safety-critical scenarios.

Abstract

Consider an unmanned aerial vehicle (UAV) physically connected to the ground station with a tether operating in a space, tasked with performing precise maneuvers while constrained by the physical limitation of its tether, which prevents it from flying beyond a maximum allowable length. Violating this tether constraint could lead to system failure or operational hazards, making it essential to enforce safety constraints dynamically while ensuring the drone can track desired trajectories accurately. This paper presents a Control Barrier Function Quadratic Programming Framework (CBF-QP) for ensuring the safe and efficient operation of tethered unmanned aerial vehicles (TUAVs). The framework leverages nominal backstepping control to achieve trajectory tracking, augmented with control barrier functions to ensure compliance with the tether constraint. In this proposed method, the tether constraint is directly embedded in the control design and therefore guarantees the TUAV remains within a predefined operational region defined by the maximum tether length while achieving precise trajectory tracking. The effectiveness of the proposed framework is validated through simulations involving set-point tracking, dynamic trajectory following, and disturbances such as incorrect user inputs. The results demonstrate that the TUAV respects the tether constraint ||x(t)||</= Lmax, with tracking errors converging to zero and the control input remaining bounded.

Figures (5)

• Figure 1: Illustration of the flight region of a tethered UAV, constrained within a hemispherical volume defined by the tether length. The inset shows the UAV's orientation dynamics.
• Figure 2: Overall Control Architecture.
• Figure 3: Constraint Validation.
• Figure 4: Performance analysis of the UAV under the CBF-QP controller. The top-left plot shows the radial position $r = \sqrt{x^2 + y^2 + z^2}$ and the maximum tether length $r_{\text{max}}$, demonstrating compliance with the tether constraint. The top-right plot depicts the tracking of desired positions $(x_{\text{des}}, y_{\text{des}}, z_{\text{des}})$ by the UAV’s actual positions $(x, y, z)$, showing precise trajectory tracking. The bottom-left plot presents the error dynamics $\mathbf{e}(t) = [e_x, e_y, e_z]^\top$, which converge to zero over time, indicating asymptotic stability. The bottom-right plot illustrates the bounded control inputs $(u_x, u_y, u_z)$, ensuring the feasibility of the control strategy.
• Figure 5: Maximum tether length surface. The subfigures illustrate the UAV’s trajectory under (a) linear tracking and (b) circular tracking scenarios. In both cases, the UAV respects the tether length constraint defined by $L_{\text{max}}$.