Merge branch 'main' into Ofer

RunCode.md

@@ -21,8 +21,8 @@ Installation, updating and testing are performed in [Julia's `pkg>` mode](https:
 ### 2. Clone [SDAPOMDPs.jl](https://github.com/CU-ADCL/SDAPOMDPs.jl)
 ```bash
 git clone https://github.com/CU-ADCL/SDAPOMDPs.jl.git
-
 ```
+
 ### 3. Activate experiment environment
 In the SDAPOMDPs.jl directory execute the following command in the command-line to initialize the project:
 ```bash

_includes/research.md

@@ -1,13 +1,38 @@
+
 This research aims to expand the algorithmic capability for tasking sensors to investigate human-specified hypotheses about space objects (SOs).
 The goal is to improve the ability to evaluate internal- and physical- state hypotheses in cases where there are many objects and a collection of sensors with diverse capabilities.
 
 
-**Problem Description**
-Describe the problem of catalog maintenance and hypothesis resolution
+<!-- **Problem Description** -->
+<!-- Describe the problem of catalog maintenance and hypothesis resolution -->
 
 
 **Technical Approach**
-Describe our technical approach:
-1. Generating a base plan using ILP
-2. Plan only over the OOI, where an action is a change in the plan
+The approach can be broken down into two main steps:
+1. Generating a base plan using integer linear programming
+2. Generating a refined MCTS plan accounting for the object of interest
+
+
+### 1) Integer Linear Program
+The base integer linear programming approach aims to judiciously allocate sensors to space objects in a manner where the severity of the worst-case scenario is minimized. 
+
+Formally, the ILP is given by
+<script type="text/javascript" src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script>
+$$
+\begin{aligned}
+\text{maximize} \quad & t \\
+\text{subject to} \quad & X_{ijt} \in \{0,1\}^{I\times J \times T} \\
+& X_{ijt} \preceq O \\
+& t \preceq \sum_{j,t} X_{ijt} \\
+& \sum_{i} X_{ijt} \preceq 1 \, .
+\end{aligned}
+$$
+
+Here $$X_{ijt}$$ is a binary 3-dimensional control variable representing whether or not observer $$j$$ observers object $$i$$ at time step $$t$$, and $$O_{ijt}$$ represents whether or not observer $$j$$ *is able to* observe object $$i$$ at time $$t$$.
+
+For ground based-sensors, the ILP plan can be visualized as follows:
+![ILP-Plan](../assets/images/ilp-plan-600.gif)
+.
 
+### 2) Monte Carlo Tree Search
+Building on the ILP solution as a baseline, we assume the existence of an object of interest in the catalogue, for which we seek to resolve a specific hypothesis. This work focuses on determining the drag configuration for the object in question. To achieve this, we use Monte Carlo Tree Search (MCTS) applied to a belief Markov Decision Process (MDP). The goal of the MCTS solver is to minimize the entropy of the distribution over possible hypotheses while minimally disrupting the baseline catalogue maintenance plan.