Geometric Look-Angle Shaping Strategy for Enclosed Inspection

Amit Shivam; Manuel C. R. M. Fernandes; Sergio Vinha; Fernando A. C. C. Fontes

cs.ROFeb 27, 2026

Geometric Look-Angle Shaping Strategy for Enclosed Inspection

Authors: Amit Shivam, Manuel C. R. M. Fernandes, Sergio Vinha, Fernando A. C. C. Fontes

Organizations: SYSTEC-ISR ARISE, Faculdade de Engenharia, Universidade do Porto, Rua Dr. Roberto Frias, 4200-465 Porto, Portugal

Abstract

This paper introduces inspection through GLASS, a Geometric Look-Angle Shaping Strategy for enclosed regions using unmanned aerial vehicles. In doing so, the vehicles guidance command is constructed through a bounded, geometry-consistent shaping of the look angle relative to a desired standoff path. By embedding a smooth, hyperbolic-tangent-type shaping function within a polar geometric framework, GLASS ensures global existence of the guidance dynamics. It avoids the far-field limitations inherent to conventional formulations. Lyapunov stability analysis establishes asymptotic convergence to a prescribed inspection standoff under explicit curvature feasibility conditions, along with analytical settling-time characteristics. The proposed strategy incorporates maximum turn-rate constraints without inducing singularities throughout the workspace. High-fidelity six-degree-of-freedom quadrotor simulations demonstrate the effectiveness of GLASS in representative enclosed inspection scenarios, highlighting a practically viable guidance framework for autonomous enclosed inspection missions.

Figures & tables

Parameter	Symbol	Value
		Outside	Inside
Initial position	$(x_{0},y_{0})$	(450, -250) m	(45, -25) m
Initial range	$d_{0}$	514.78 m	51.48 m
Initial standoff error	$e_{0}$	314.78 ∘	-148.52 m
Initial LOS angle	$\gamma_{\mathrm{0}}$	-29.05 ∘	-29.05 ∘

TABLE I : Initial conditions for ideal dynamics

Panel of Figure 3 — Fig. 2 : Results for ideal dynamics for outside initial position

Standoff	$k_{G}=0.02$	$k_{G}=0.04$	$k_{G}=0.06$	$k_{G}=0.08$	$k_{G}=0.10$
Inside	22.956	14.328	11.689	10.444	9.729
$(e_{0}<0)$	22.956	14.328	11.689	10.444	9.729
Outside	31.276	22.641	20.002	18.757	18.042
$(e_{0}>0)$	31.276	22.641	20.002	18.757	18.042

TABLE II : Closed-form analytic settling time

T_{\mathrm{s}}

for ideal-manifold dynamics under inside and outside initial conditions for different gain values

k_{G}

Panel of Figure 5 — Fig. 3 : Results for ideal dynamics for inside initial position

Panel of Figure 6 — Fig. 4 : Results for outside initial UAV position

Panel of Figure 7 — Fig. 5 : Results for inside initial UAV position

Case	$(x_{0},y_{0})$ , m	$\chi_{0}$ , deg.	$\lambda_{0}$ , deg.	$T_{\mathrm{ana}}$ , s	$T_{\mathrm{sim}}$ , s
Outside	$(450,-250)$	$150.73$	$179.79$	25.519	25. 978
	$(450,-250)$	$-119.27.7$	$-90.21$	25.519	26.363
	$(450,-250)$	$90.73$	$119.79$	25.519	27.199
Inside	$(50,-25)$	$-20.15$	$6.41$	16.977	16.442
	$(50,-25)$	$69.85$	$96.41$	16.977	17.287
	$(50,-25)$	$-80.15$	$-53.59$	16.977	16.598

TABLE III : Initial conditions and settling times for heading mismatch

Panel of Figure 9 — Fig. 6 : Comparative results for outside initial UAV position

Panel of Figure 11 — Fig. 8 : Results for 6dof dynamic model

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Small free-flying spacecraft can provide vital extravehicular activity (EVA) services like inspection and repair for future orbital outposts like the Lunar Gateway. Operating adjacent to delicate space station and microgravity targets, these spacecraft require formalization to describe the autonomy that a free-flyer inspection mission must provide. This work explores the transformation of general mission requirements for this class of free-flyer into a set of concrete decisions for the planning and control autonomy architectures that will power such missions. Flowing down from operator commands for inspection of important regions and mission time-criticality, a motion planning problem emerges that provides the basis for developing autonomy solutions. Unique constraints are considered such as velocity limitations, pointing, and keep-in/keep-out zones, with mission fallback techniques for providing hierarchical safety guarantees under model uncertainties and failure. Planning considerations such as cost function design and path vs. trajectory control are discussed. The typical inputs and outputs of the planning and control autonomy stack of such a mission are also provided. Notional system requirements such as solve times and propellant use are documented to inform planning and control design. The entire proposed autonomy framework for free-flyer inspection is realized in the SmallSatSim simulation environment, providing a reference example of free-flyer inspection autonomy. The proposed autonomy architecture serves as a blueprint for future implementations of small satellite autonomous inspection in proximity to mission-critical hardware, going beyond the existing literature in terms of both (1) providing realistic system requirements for an autonomous inspection mission and (2) translating these requirements into autonomy design decisions for inspection planning and control.

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