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Collision-free landing of multiple UAVs on moving ground vehicles using time-varying control barrier functions

Viswa Narayanan Sankaranarayanan, Akshit Saradagi, Sumeet Satpute, George Nikolakopoulos

TL;DR

The paper addresses the problem of coordinating multiple UAVs to land on moving UGVs while guaranteeing safety. It introduces a centralized control architecture that uses a time-varying Landing CBF (LCBF) to shape safe landing trajectories and pairwise Spherical CBFs (SCBFs) to prevent inter-UAV collisions, all filtered through a quadratic program-based safety filter that minimally alters a nominal landing controller. Theoretical results establish forward invariance and feasible input sharing for the combined CBF constraints, and simulations with three UAV–UGV pairs validate safe landings under both static and moving targets. This approach enables scalable, collision-free multi-UAV landings on dynamic ground platforms with provable safety guarantees and practical applicability in autonomous inspection and cooperation tasks.

Abstract

In this article, we present a centralized approach for the control of multiple unmanned aerial vehicles (UAVs) for landing on moving unmanned ground vehicles (UGVs) using control barrier functions (CBFs). The proposed control framework employs two kinds of CBFs to impose safety constraints on the UAVs' motion. The first class of CBFs (LCBF) is a three-dimensional exponentially decaying function centered above the landing platform, designed to safely and precisely land UAVs on the UGVs. The second set is a spherical CBF (SCBF), defined between every pair of UAVs, which avoids collisions between them. The LCBF is time-varying and adapts to the motions of the UGVs. In the proposed CBF approach, the control input from the UAV's nominal tracking controller designed to reach the landing platform is filtered to choose a minimally-deviating control input that ensures safety (as defined by the CBFs). As the control inputs of every UAV are shared in establishing multiple CBF constraints, we prove that the control inputs are shared without conflict in rendering the safe sets forward invariant. The performance of the control framework is validated through a simulated scenario involving three UAVs landing on three moving targets.

Collision-free landing of multiple UAVs on moving ground vehicles using time-varying control barrier functions

TL;DR

The paper addresses the problem of coordinating multiple UAVs to land on moving UGVs while guaranteeing safety. It introduces a centralized control architecture that uses a time-varying Landing CBF (LCBF) to shape safe landing trajectories and pairwise Spherical CBFs (SCBFs) to prevent inter-UAV collisions, all filtered through a quadratic program-based safety filter that minimally alters a nominal landing controller. Theoretical results establish forward invariance and feasible input sharing for the combined CBF constraints, and simulations with three UAV–UGV pairs validate safe landings under both static and moving targets. This approach enables scalable, collision-free multi-UAV landings on dynamic ground platforms with provable safety guarantees and practical applicability in autonomous inspection and cooperation tasks.

Abstract

In this article, we present a centralized approach for the control of multiple unmanned aerial vehicles (UAVs) for landing on moving unmanned ground vehicles (UGVs) using control barrier functions (CBFs). The proposed control framework employs two kinds of CBFs to impose safety constraints on the UAVs' motion. The first class of CBFs (LCBF) is a three-dimensional exponentially decaying function centered above the landing platform, designed to safely and precisely land UAVs on the UGVs. The second set is a spherical CBF (SCBF), defined between every pair of UAVs, which avoids collisions between them. The LCBF is time-varying and adapts to the motions of the UGVs. In the proposed CBF approach, the control input from the UAV's nominal tracking controller designed to reach the landing platform is filtered to choose a minimally-deviating control input that ensures safety (as defined by the CBFs). As the control inputs of every UAV are shared in establishing multiple CBF constraints, we prove that the control inputs are shared without conflict in rendering the safe sets forward invariant. The performance of the control framework is validated through a simulated scenario involving three UAVs landing on three moving targets.

Paper Structure

This paper contains 16 sections, 3 theorems, 24 equations, 11 figures.

Table of Contents

  1. Introduction
  2. Notations and Preliminaries
  3. Problem Formulation
  4. Modeling of the UAV
  5. Constraints for Safe Landing
  6. Constraints for Collision Avoidance
  7. Control Architecture
  8. Position Control Loop
  9. Attitude Control Input
  10. Validiy of CBFs and design of a CBF Filter
  11. Landing CBF (LCBF)
  12. Spherical CBF (SCBF)
  13. Quadratic programs for safety guarantees
  14. Input sharing among multiple CBFs
  15. Simulated Results
  16. ...and 1 more sections

Key Result

Proposition 1

The zero super-level set $\mathcal{S}(t)$ of the continuously differentiable function $h(p,t): \mathcal{D}(t) \subset \mathcal{P} \xrightarrow{} \mathbb{R}$ is rendered forward invariant and asymptotically stable in $\mathcal{D}(t)$ by a Lipschitz continuous controller $u(p,t) \in \kappa (p,t)$, whe for the system $\dot{p} = f(p,t) + g(p,t)u$, if $h(p,t)$ is a valid control barrier function on $\m

Figures (11)

  • Figure 1: A schematic of multiple UAVs landing on their respective UGVs.
  • Figure 2: A schematic of a quadrotor UAV with the associated coordinate frames.
  • Figure 3: The constraint for landing a UAV on a UGV combines the properties of ground clearance $c$ and approaching the UGV only from a conical region above the landing position $p_{di}(t=t_1)$. The UAV must perform the landing from its initial position $p_{i}(t=t_1)$ without entering the unsafe region.
  • Figure 4: $\alpha_i$ parameters scale the safe regions horizontally, whereas $\beta_i$ parameters scale them vertically.
  • Figure 5: Block diagram of the proposed control architecture.
  • ...and 6 more figures

Theorems & Definitions (12)

  • Definition 1: Class-$\mathcal{K}$ function
  • Definition 2: Time-varying CBF
  • Proposition 1
  • Remark 1
  • Remark 2
  • Lemma 1
  • proof
  • Remark 3
  • Definition 3: Control Sharing Time-varying CBFs
  • Proposition 2
  • ...and 2 more