Stealthy Coverage Control for UAV 3D Recon

• Stealthy coverage control is a semi-autonomous paradigm that blends human teleoperation with UAV optimization to achieve precise 3D reconstruction.
• It utilizes a nested-loop quadratic programming approach to balance operator commands and information gain while enforcing motion stealth constraints.
• Empirical results demonstrate improved reconstruction completeness, reduced RMSE, and lower operator workload in complex simulated environments.

Stealthy coverage control is a semi-autonomous image sampling paradigm designed to enhance real-time 3D reconstruction by fusing human operator navigation with autonomous coverage optimization, subject to motion “stealthiness” constraints. It specifically addresses the challenge of reconstructing complex structures where the spatially-varying image sampling density required for accurate modeling is not known a priori, leveraging the operator’s situational reasoning while retaining autonomous efficiency (Terunuma et al., 31 Jan 2026).

1. Mathematical Formulation and Problem Setting

The workspace $D \subset \mathbb{R}^3$ contains the objects to be reconstructed. A single UAV (quadrotor) equipped with an RGB–depth camera has state $x(t) \in \mathbb{R}^3$ (position) and $R(t) \in SO(3)$ (orientation). The operator provides commanded velocity $v_h(t) \in \mathbb{R}^3$ and yaw rate $\omega_h(t) \in \mathbb{R}$; the system discretizes $D$ into voxels $\{c_j\}_{j=1}^M$, each with a visibility probability $p_j(t)$.

The information gain for a new observation from $(x,R)$ is defined as: $I(x, R) = \sum_{j=1}^M [1 - p_j(t)] \rho_j(x, R),$ where $x(t) \in \mathbb{R}^3$0 indicates whether voxel $x(t) \in \mathbb{R}^3$1 is visible from $x(t) \in \mathbb{R}^3$2.

The control objective at each time step $x(t) \in \mathbb{R}^3$3 is to compute $x(t) \in \mathbb{R}^3$4 that

• Remains close to operator intent,
• Maximizes information gain,
• Enforces UAV dynamics and the stealth constraint.

The core optimization is: $x(t) \in \mathbb{R}^3$5 with $x(t) \in \mathbb{R}^3$6 weighting human input tracking; $x(t) \in \mathbb{R}^3$7 trades off exploration vs. teleoperation. The "stealth" constraint $x(t) \in \mathbb{R}^3$8 (see Section 4) shapes the allowed set of UAV maneuvers.

2. Human Intention Modeling and Situational Recognition

Human intention is encoded in the commanded $x(t) \in \mathbb{R}^3$9. To ensure stable and intuitive interface dynamics between human and UAV, the system incorporates a passivity-based control interface as in [Atman et al. 2019], stabilizing the coupled arm-eye and drone system.

Situational recognition is formalized by a mapping

$R(t) \in SO(3)$0

where $R(t) \in SO(3)$1 functions as a state machine that reacts to coverage progress (e.g., when $R(t) \in SO(3)$2 drops below a threshold) by suggesting new semantic waypoints or override velocities to the operator. This mechanism allows adaptive macro-navigation through complex environments using high-level human guidance.

3. Algorithm Structure and Control Decoupling

Stealthy coverage control employs a nested-loop architecture:

• The outer loop filters and applies operator commands $R(t) \in SO(3)$3 at low gain for safety.
• The inner loop formulates and solves the QP for $R(t) \in SO(3)$4 as described above, combining operator intent, current map information gain, and the stealth constraint.

Pseudocode outline (per $R(t) \in SO(3)$5 cycle):

$D$6

This structure decouples the human’s macro-level “where to go next” from the UAV’s micro-level “how to sample optimally and stealthily,” allowing simultaneous exploitation of human insight and autonomous local optimization.

4. Fundamental Equations and Stealth Constraint

The information-gain metric (voxelized) is

$R(t) \in SO(3)$6

An alternative view-entropy metric is

$R(t) \in SO(3)$7

where $R(t) \in SO(3)$8 is each pixel’s normalized expected entropy.

The stealth constraint is

$R(t) \in SO(3)$9

with $v_h(t) \in \mathbb{R}^3$0, $v_h(t) \in \mathbb{R}^3$1 tunable parameters, limiting aggressive rotations and rapid movement in directions of high information gain. This constraint "smooths" UAV motion, suppressing conspicuously active maneuvers during coverage.

A linearized closed-form feedback law for the combined control can be written as: $v_h(t) \in \mathbb{R}^3$2 where $v_h(t) \in \mathbb{R}^3$3 is a barrier function term ensuring feasibility under $v_h(t) \in \mathbb{R}^3$4.

5. Simulation Protocol and Performance Metrics

The evaluation environment is a $v_h(t) \in \mathbb{R}^3$5 simulated warehouse with four known-geometry objects. System parameters include $v_h(t) \in \mathbb{R}^3$6\,s, $v_h(t) \in \mathbb{R}^3$7\,m/s, $v_h(t) \in \mathbb{R}^3$8/s, $v_h(t) \in \mathbb{R}^3$9, $\omega_h(t) \in \mathbb{R}$0, and $\omega_h(t) \in \mathbb{R}$1.

Three primary performance metrics are used:

• Reconstruction completeness $\omega_h(t) \in \mathbb{R}$2
• Reconstruction accuracy $\omega_h(t) \in \mathbb{R}$3 (point-to-mesh RMSE in meters)
• Human workload (integral of $\omega_h(t) \in \mathbb{R}$4)

The protocol consists of 10 trials (random seeds), each with 300\,s simulated teleoperation, comparing:

• Stealthy coverage control (“SCC”)
• Standard human + coverage control baseline (no stealth QP constraint)

6. Quantitative Results

Empirical findings are summarized as follows (mean $\omega_h(t) \in \mathbb{R}$5 standard deviation, $\omega_h(t) \in \mathbb{R}$6):

Method	Completeness $\omega_h(t) \in \mathbb{R}$7 [\%]	RMSE $\omega_h(t) \in \mathbb{R}$8 [m]
Baseline	$\omega_h(t) \in \mathbb{R}$9	$D$0
SCC (ours)	$D$1	$D$2

A paired $D$3-test yields $D$4 on both metrics, indicating statistical significance. Additionally, the average deviation between operator and applied controls ($D$5) is decreased by 35%, reflecting a reduction in operator workload (Terunuma et al., 31 Jan 2026).

7. Contributions and Future Outlook

Stealthy coverage control introduces a unified quadratic programming framework that synergistically blends human teleoperation, real-time 3D reconstruction coverage, and a novel stealth constraint. The modular human-in-the-loop approach ensures stability and safety via passivity, while a situational recognition module triggers automatic waypoint generation, facilitating efficient and adaptive coverage. The central mechanism is the decoupling of human-directed macro-navigation from stealthy and information-driven micro-sampling, implemented via null-space/QP projection.

Simulations demonstrate that stealthy coverage control achieves over 15% improvement in reconstruction completeness, halves RMSE, and significantly lowers operator workload, with results robust to random seed variations. The methodology is extensible to multi-UAV systems or advanced human-assistant paradigms, maintaining the foundational stealth property. These findings substantiate stealthy coverage control as an effective integration of human expertise and autonomous active sensing in real-time 3D reconstruction for constrained or complex settings (Terunuma et al., 31 Jan 2026).