Vision-Guided Optic Flow Navigation for Small Lunar Missions

TL;DR

Private lunar missions require autonomous ego-motion under stringent mass, power, and compute constraints. The paper introduces a motion-field inversion framework that couples sparse monocular optical flow with planar or spherical depth representations, parameterized by a rangefinder and known attitude, to estimate descent velocity on CPU. The approach yields linear least-squares solutions for planar depth and nonlinear residual optimization when slope/attitude variables are included, validated on synthetically rendered lunar sequences with realistic lighting and noise. Results show sub-10% relative velocity error for challenging terrains and ~1% for simpler terrains, with real-time CPU performance, indicating a lightweight alternative to heavier LiDAR/RADAR-based navigation systems for small lunar missions.

Abstract

Private lunar missions are faced with the challenge of robust autonomous navigation while operating under stringent constraints on mass, power, and computational resources. This work proposes a motion-field inversion framework that uses optical flow and rangefinder-based depth estimation as a lightweight CPU-based solution for egomotion estimation during lunar descent. We extend classical optical flow formulations by integrating them with depth modeling strategies tailored to the geometry for lunar/planetary approach, descent, and landing, specifically, planar and spherical terrain approximations parameterized by a laser rangefinder. Motion field inversion is performed through a least-squares framework, using sparse optical flow features extracted via the pyramidal Lucas-Kanade algorithm. We verify our approach using synthetically generated lunar images over the challenging terrain of the lunar south pole, using CPU budgets compatible with small lunar landers. The results demonstrate accurate velocity estimation from approach to landing, with sub-10% error for complex terrain and on the order of 1% for more typical terrain, as well as performances suitable for real-time applications. This framework shows promise for enabling robust, lightweight on-board navigation for small lunar missions.

Figures (11)

• Figure 1: Lunar horizon images captured by ispace's Hakuto‑R lander during Mission 1, April 2023 ispace2023newsplanetary2023hakuto. ispace provided some insights on the typical hardware constraints and trajectory characteristics of a small private lunar mission.
• Figure 2: Illustrations of the two principal depth map geometries evaluated in this work. The planar depth model assumes the local lunar surface can be approximated by a plane and is suitable for low-altitude operations, with optional slope estimation to handle inclined terrain. The spherical depth model represents the lunar surface as part of a sphere and offers improved accuracy at higher altitudes where curvature effects become significant.
• Figure 3: Example of Motion Fields observed when looking ventrally for different regimes of Egomotion. Ventral corresponds to egomotion ventrally toward the surface. Lateral corresponds to egomotion parallel to the surface. Rotational corresponds to rotation about the line-of-sight of the camera.
• Figure 4: Flowchart describing the full motion field inversion from frames and onboard telemetry to egomotion estimation. a) Optical flow arrow components. b) Residual calculation between observed optical flow and estimated motion field from least squares estimated velocity, $\mathbf{v}_{\text{est}}$. Note: For a linear system of equations (i.e. when using flat planar or spherical depth models), the iterative residual least squares calculation segment is not required. However, when a non-linear system of equations is present (i.e. when estimating further parameters such as slope estimation planar model or attitude estimation) iterative non-linear least squares is required - this is shown in the above diagram.
• Figure 5: Example Landing Sequence trajectory showing observed sparse optical flow at various frames throughout the trajectory. a) Shows the non-zero magnitude of the angular velocity throughout the whole trajectory -- explaining the curl of the observed optical flow fields.