Vertical Planetary Landing on Sloped Terrain Using Optical Flow Divergence Estimates

📅 2025-12-03
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🤖 AI Summary
Small, lightweight spacecraft face challenges in autonomous vertical landing on sloped terrain, where optical flow divergence estimation is corrupted by terrain inclination, and conventional nonlinear controllers suffer from instability. Method: This paper proposes an incremental nonlinear dynamic inversion control strategy based on local optical flow divergence estimation. By computing the mean and difference of divergence values from two localized optical flow regions, the method decouples thrust control (ensuring exponential decay of altitude and velocity errors) from attitude control (enabling precise terrain alignment), thereby avoiding ambiguities inherent in global divergence estimation and enhancing robustness over traditional approaches. The design relies solely on lightweight optical sensors and low-computational-resources hardware. Results: Numerical simulations demonstrate stable, precise landings across diverse slope angles, confirming strong robustness and engineering feasibility for resource-constrained spacecraft.

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📝 Abstract
Autonomous landing on sloped terrain poses significant challenges for small, lightweight spacecraft, such as rotorcraft and landers. These vehicles have limited processing capability and payload capacity, which makes advanced deep learning methods and heavy sensors impractical. Flying insects, such as bees, achieve remarkable landings with minimal neural and sensory resources, relying heavily on optical flow. By regulating flow divergence, a measure of vertical velocity divided by height, they perform smooth landings in which velocity and height decay exponentially together. However, adapting this bio-inspired strategy for spacecraft landings on sloped terrain presents two key challenges: global flow-divergence estimates obscure terrain inclination, and the nonlinear nature of divergence-based control can lead to instability when using conventional controllers. This paper proposes a nonlinear control strategy that leverages two distinct local flow divergence estimates to regulate both thrust and attitude during vertical landings. The control law is formulated based on Incremental Nonlinear Dynamic Inversion to handle the nonlinear flow divergence. The thrust control ensures a smooth vertical descent by keeping a constant average of the local flow divergence estimates, while the attitude control aligns the vehicle with the inclined surface at touchdown by exploiting their difference. The approach is evaluated in numerical simulations using a simplified 2D spacecraft model across varying slopes and divergence setpoints. Results show that regulating the average divergence yields stable landings with exponential decay of velocity and height, and using the divergence difference enables effective alignment with inclined terrain. Overall, the method offers a robust, low-resource landing strategy that enhances the feasibility of autonomous planetary missions with small spacecraft.
Problem

Research questions and friction points this paper is trying to address.

Develops a bio-inspired control strategy for spacecraft landings on slopes
Uses optical flow divergence to regulate thrust and attitude without heavy sensors
Addresses instability from nonlinear control and terrain inclination challenges
Innovation

Methods, ideas, or system contributions that make the work stand out.

Uses local optical flow divergence for thrust control
Employs divergence difference for attitude alignment
Applies Incremental Nonlinear Dynamic Inversion for stability
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Universiti Sains Malaysia