Investigating Methods to Improve Underwater Navigation
This project was completed as part of ROB 530: Mobile Robotics for the purpose of improving underwater inertial navigation through the use of probabilistic graphical models and Lie theory.
Utilizing Probabilistic Graphical Models
Probabilistic Graphical models are a class of models that use a graphical representation of conditional probabilities between random variables. This representation then makes it easy to model the joint distribution over a set of random variables.
For our problem, we were particularly concerned with
representing the joint density of a robots’ state over a trajectory as a factor graph. A typical method of solving for the random variables representing the trajectory is to find maximize the posterior distribution P(X|Z), where X represents the state and Z represents the measurements. This is typically known as the Maximum a-posteriori (MAP) problem, and is easily solvable when the measurements are made using linear models.
Unfortunately for most underwater navigation problems, the measurement models are rarely linear; hence, a method that can avoid depending on the linear assumption is desirable. Here comes the factor graph, a structure that uses a bipartite graph with two types of nodes and an edge. The two nodes are factors and variables, and in our context, the factors represent measurements, while the variables represent the states. The edges indicate which factor provides information about which state,
Using Lie Groups for Improving Optimization
Lie Groups are a generalization of matrix groups, and can succinctly be defined as matrices that can be modeled as smooth, differentiable manifolds. Many properties of Lie Groups make them desirable for robotics applications: the fact that they can accurately model robot motion on exponential coordinates, that motion on this manifold can be accurately represented through the study of its tangent space, and that matrix groups that represent rigid body motion and inertial sensor measurements can be categorized under it,. The project initializes a factor graph using a filtering method and then performs optimization upon the initialized trajectory with inertial sensors
Presentation on the method and results
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