# CDDT: Fast Approximate 2D Ray Casting for Accelerated Localization

## TL;DR

This paper introduces CDDT, a novel data structure that accelerates 2D ray casting for robot localization, enabling real-time performance on resource-limited mobile robots by significantly reducing memory and computation requirements.

## Contribution

The paper presents the Compressed Directional Distance Transform, a new data structure that provides fast, approximate 2D ray casting with online updates and minimal memory usage.

## Key findings

- Achieves near constant time ray casting performance.
- Maintains 2500 particles at 40Hz on a single CPU thread.
- Requires two orders of magnitude less memory than 3D lookup tables.

## Abstract

Localization is an essential component for autonomous robots. A well-established localization approach combines ray casting with a particle filter, leading to a computationally expensive algorithm that is difficult to run on resource-constrained mobile robots. We present a novel data structure called the Compressed Directional Distance Transform for accelerating ray casting in two dimensional occupancy grid maps. Our approach allows online map updates, and near constant time ray casting performance for a fixed size map, in contrast with other methods which exhibit poor worst case performance. Our experimental results show that the proposed algorithm approximates the performance characteristics of reading from a three dimensional lookup table of ray cast solutions while requiring two orders of magnitude less memory and precomputation. This results in a particle filter algorithm which can maintain 2500 particles with 61 ray casts per particle at 40Hz, using a single CPU thread onboard a mobile robot.