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 $\rho_j(x, R) \in [0,1]$ indicates whether voxel $j$ is visible from $(x, R)$.

The control objective at each time step $\Delta t$ is to compute $u(t) = [v(t); \omega(t)]$ that

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

The core optimization is: $$\begin{aligned} u^\star = \arg\min_{u=[v;\omega]} \; & \frac{1}{2} \|v-v_h\|^2_{W_v} + \frac{1}{2}\|\omega - \omega_h\|^2_{W_\omega} \ & -\lambda I\big(x + v\Delta t,\, R e^{\hat\omega\Delta t}\big) \ \text{s.t.} \;\;\;\; & x(t+\Delta t) = x(t) + v\Delta t,\, R(t+\Delta t) = R(t) e^{\hat\omega\Delta t}, \ & \|v\| \leq v_{\max},\, |\omega| \leq \omega_{\max}, \ & h_{\rm stealth}(x,R) \geq 0, \end{aligned}$$ with $W_v, W_\omega \succ 0$ weighting human input tracking; $\lambda>0$ trades off exploration vs. teleoperation. The "stealth" constraint $h_{\rm stealth}$ (see Section 4) shapes the allowed set of UAV maneuvers.

2. Human Intention Modeling and Situational Recognition

Human intention is encoded in the commanded $(v_h, \omega_h)$. 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

$$\Psi: \{\text{current 3D map}\} \rightarrow \{v_h, \omega_h\},$$

where $\Psi$ functions as a state machine that reacts to coverage progress (e.g., when $I(x, R)$ 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 $(v_h, \omega_h)$ at low gain for safety.
• The inner loop formulates and solves the QP for $u^*$ as described above, combining operator intent, current map information gain, and the stealth constraint.

Pseudocode outline (per $\Delta t$ cycle):

1: measure current state (x,R) and map {p_j} 2: read human command (v_h, ω_h) 3: form predicted information-gain function I(x+vΔt, R·e^{ωΔt}) 4: solve QP: minimize ½‖v−v_h‖² + ½‖ω−ω_h‖² − λ I subject to dynamics & stealth 5: apply control u* = [v*; ω*] to UAV 6: update occupancy probabilities p_j using new image 7: if ∑_j (1−p_j) small ⇒ trigger next waypoint via Ψ 8: repeat

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

$I(x, R) = \sum_{j=1}^M [1-p_j] \rho_j(x, R).$

An alternative view-entropy metric is

$$H(x, R) = -\sum_{\text{pixels } i} q_i(x, R) \log q_i(x, R),$$

where $q_i$ is each pixel’s normalized expected entropy.

The stealth constraint is

$$h_{\rm stealth}(x, R) = \alpha - \|\dot R\| - \gamma \|\nabla_x I(x, R)\| \geq 0,$$

with $\alpha$, $\gamma$ 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: $$\begin{bmatrix}v\\omega\end{bmatrix} = \begin{bmatrix} W_v^{-1} & 0 \ 0 & W_\omega^{-1} \end{bmatrix} \left( W u_h + \lambda \nabla_{(x,R)}I(x,R) \right) - \Gamma(x,R)\eta_{\rm stealth}$$ where $\Gamma\eta_{\rm stealth}$ is a barrier function term ensuring feasibility under $h_{\rm stealth} \geq 0$.

5. Simulation Protocol and Performance Metrics

The evaluation environment is a $$10\,\mathrm{m} \times 10\,\mathrm{m} \times 5\,\mathrm{m}$$ simulated warehouse with four known-geometry objects. System parameters include $\Delta t = 0.1$\,s, $v_{\max} = 1.2$\,m/s, $\omega_{\max} = 30^\circ$/s, $\lambda = 2.0$, $\alpha = 0.1$, and $\gamma = 0.5$.

Three primary performance metrics are used:

• Reconstruction completeness $$C = \frac{\# \text{visible voxels}}{\#\text{total surface voxels}}$$
• Reconstruction accuracy $E_{\rm RMSE}$ (point-to-mesh RMSE in meters)
• Human workload (integral of $\|u_h - u\|$)

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 $\pm$ standard deviation, $n=10$):

Method	Completeness $C$ [\%]	RMSE $E_{\rm RMSE}$ [m]
Baseline	$78.3 \pm 4.7$	$0.054 \pm 0.009$
SCC (ours)	$\mathbf{91.1 \pm 2.8}$	$\mathbf{0.032 \pm 0.005}$

A paired $t$-test yields $p < 0.01$ on both metrics, indicating statistical significance. Additionally, the average deviation between operator and applied controls ($\|u_h - u\|$) 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).