Discrete-Continuous Smoothing and Mapping

04/25/2022
by   Kevin J. Doherty, et al.
1

We describe a general approach to smoothing and mapping with a class of discrete-continuous factor graphs commonly encountered in robotics applications. While there are openly available tools providing flexible and easy-to-use interfaces for specifying and solving optimization problems formulated in terms of either discrete or continuous graphical models, at present, no similarly general tools exist enabling the same functionality for hybrid discrete-continuous problems. We aim to address this problem. In particular, we provide a library, DC-SAM, extending existing tools for optimization problems defined in terms of factor graphs to the setting of discrete-continuous models. A key contribution of our work is a novel solver for efficiently recovering approximate solutions to discrete-continuous optimization problems. The key insight to our approach is that while joint inference over continuous and discrete state spaces is often hard, many commonly encountered discrete-continuous problems can naturally be split into a "discrete part" and a "continuous part" that can individually be solved easily. Leveraging this structure, we optimize discrete and continuous variables in an alternating fashion. In consequence, our proposed work enables straightforward representation of and approximate inference in discrete-continuous graphical models. We also provide a method to recover the uncertainty in estimates of both discrete and continuous variables. We demonstrate the versatility of our approach through its application to three distinct robot perception applications: point-cloud registration, robust pose graph optimization, and object-based mapping and localization.

READ FULL TEXT
research
05/22/2012

Learning Mixed Graphical Models

We consider the problem of learning the structure of a pairwise graphica...
research
06/30/2015

Selective Inference and Learning Mixed Graphical Models

This thesis studies two problems in modern statistics. First, we study s...
research
04/25/2023

When to be Discrete: Analyzing Algorithm Performance on Discretized Continuous Problems

The domain of an optimization problem is seen as one of its most importa...
research
07/11/2012

Solving Factored MDPs with Continuous and Discrete Variables

Although many real-world stochastic planning problems are more naturally...
research
02/17/2021

Joint Continuous and Discrete Model Selection via Submodularity

In model selection problems for machine learning, the desire for a well-...
research
06/01/2012

OpenGM: A C++ Library for Discrete Graphical Models

OpenGM is a C++ template library for defining discrete graphical models ...
research
08/12/2022

Handling Constrained Optimization in Factor Graphs for Autonomous Navigation

Factor graphs are graphical models used to represent a wide variety of p...

Please sign up or login with your details

Forgot password? Click here to reset