MIT 16.412 - Cognitive Robotics Exploiting Submodularity in Information Gathering: An Application to Spacecraft Berthing

The recent retirement of the Space Shuttle program has prompted NASA to begin outsourcing development of future technologies for transporting supplies and humans to the International Space Station (ISS). Any spacecraft approaching the ISS for docking or berthing is required to estimate its own position relative to the Space Station. We examine a problem of placing sensors on the ISS to aid in position estimation of spacecraft during the berthing process. We assume that NASA has a budget of 5 sensors available to be placed, which leads to an optimization problem of maximizing the sensor coverage of the planar area of the spacecraft operation. With some modest assumptions, this problem can be treated as an information gathering problem and is therefore submodular. By exploiting the submodularity of this problem, greedy algorithms can be used to find approximate solutions with guarantees on lower bounds of performance relative to the optimal solution. We implement a lazy greedy algorithm to solve the coverage maximization problem and discuss the resulting solution quality. We then model the spacecraft position estimation as a Hidden Markov Model, and implement an online greedy algorithm to sequentially probe the sensors based on expected reduction in entropy to update the HMM belief. The results of this algorithm are compared with a random sampling strategy and some implications are discussed. Finally, we describe several lessons that we learned throughout the course of this project.