# Real Time Shape Reconstruction for Near Earth Asteroid Landing

21 Feb 2018 #Astrodynamics #Geometric Control #Geometric Mechanics #Python #C++ #Publication \[\newcommand{\bracket}[1]{\left[ #1 \right]} \newcommand{\parenth}[1]{\left( #1 \right)} \newcommand{\tr}[1]{\mathrm{tr}\negthickspace\bracket{#1}}\]## Summary

In order to determine the shape of the asteroid, we model a laser ranging sensor (LIDAR) on a maneuvering spacecraft. The LIDAR is able to provide depth measurements of the surface of the asteroid. Given a set of depth measurements it is possible to compute the shape, and hence gravitational potential of the asteroid. Computing the shape of the asteroid on a continual basis avoids the long delay and computational complexity of current asteroid operations. Furthermore, the updated gravitational model enables a spacecraft to autonomously transition from a mapping orbit directly to landing.

We develop a method to incrementally update the shape of an asteroid model using LIDAR measurements. This incremental update occurs in real time and allows for responsive space missions around asteroids.

## Basic procedure

We first begin by simulating LIDAR measurements around an asteroid

Each measurement defines a point that lies on the surface of the asteroid. Taking many measurements defines a point cloud which represents the surface shape.

The end goal is to define a surface mesh which represents the shape of the asteroid.

## Downloads

A compiled version of the PDF is available above using the large PDF link.

All of the code used to generate the images are also available below.

## Videos

Here are some selected videos demonstrating this process.

- Cube into Sphere - Here we show how a cube is incrementally turned into a sphere by incorporating measurements from the surface of the sphere.
- Sphere into Ellipse - Here we incrementally modify a sphere into an ellipse
- Castalia Shape Generation - Here we apply our incremental shape method to a high fidelity simulation around asteroid 4769 Castalia.