Geometric Mechanics and Control for Small Body Missions

The main contributions of the dissertation include:

1. Low thrust propulsion using reachability sets for large scale orbital transfers
2. Geometric control for precise state trajectory tracking
3. Efficient method for the shape reconstruction of an asteroid from range measurements

Shape reconstruction

In order to operate near a small body, we require an accurate gravitational model. The standard approach is to utilize the polyhedron potential model which computes the gravity given the shape of the body. However, prior to arrival only a coarse shape model is possible using ground based measurements.

Ground Model	In-situ Model

As a result, it would be ideal if the spacecraft has the capability to autonomously update the shape given new measurements. CGAL is utilized to perform many of the computational geometry operations, such as raycasting and mesh representation. This allows us to simulate LIDAR measurements of the surface and use these measurements to incrementally update the shape model.

Here are several videos demonstrating this process. Our approach provides an uncertainty metric which allows for a measure of the shape accuracy and is used to color the mesh. This uncertainty also provides an efficient method to compute a guidance trajectory to best update the shape.

Castalia Exploration	Castalia Uncertainty

More videos around several different asteroids are provided here.

Downloads

• Dissertation
• GWU Dissertation
• Defense presentation
• Software
• Shape reconstruction videos