Implementing a Robust 3-Dimensional Egocentric Navigation System

#### Overview

Egospheric Navigation is a method of autonomous navigation in which the robot navigates by building and analyzing egospheres. An egosphere is a memory structure in which sensory data accumulated by the robot is mapped onto a sphere around the robot.

The above image demonstrates how an object in the robot’s environment is mapped onto the egosphere surrounding the robot.

The Center for Intelligent Systems had already developed a method of navigation using 2-Dimensional Egospheres. This work has focused on developing a 3-Dimensional method. Specifically, this work has focused on designing a robotic system which could visually locate landmarks, apply them to an egosphere, and, using 3-Dimensional calculations, determine the robot's correct path and then actuate the motion.

#### Objectives

The objective of this work is to build a robotic system that accomplishes the following tasks:

Recognize Landmarks and store them in an egosphere

Converge on goal regions using 3-Dimensional Egospheric navigation

#### Advantages of 3D Navigation System

This is an extension of the work by Bugra Koku, an alumni of the lab, as well as Dr. Kawamura, Dr. Wilkes, Dr. Peters and Dr. Sekmen. In the paper “Toward Egocentric Navigation”, they outlined what is referred to here as 2-Dimensional Egospheric Navigation. The advantages of the 3-Dimensional system I am designing over the 2-Dimensional are:

Effectively guarantee convergence on goal for two or more landmark scenarios

Improve accuracy and optimality of selected paths

Reduction of required number of landmarks

#### Concept and Research

This research is two-fold: first to design a complete robotic system, which can recognize landmarks, store them in an egosphere, discern direction through 3D Egospheric Navigation and then move. The other half of this research has been to design and simulate the 3-Dimenstional Egospheric Navigation algorithm.

## The Robotic System

The robotic system is broken down into subsystems according to the following flowchart:

This system is implemented in Linux. Briefly the subsystems are:

Visual: Recognize and locate landmarks in scene

Motor Control: Move and turn robot

Memory: Maintain current and stored egospheres

Navigation: Compute 3-Dimensional Egosphere

## 3-Dimensional Egospheric Navigation

The navigational system was designed, built and tested using MATLAB, and a simulation program written for this specific purpose.

#### Results

Simulations demonstrate the 3-Dimensional Egospheric Navigation does achieve its goals in improving robustness and optimality. Below is a simulation result for a robot using 2-Dimensional Egospheric Navigation:

The environment includes two landmarks, which in 2-Dimensional Egospheric navigation is a non-converging case. However, we see that in 3-Dimensional Egospheric Navigation, the robot not only converges to the goal, but does so using the optimal path: a straight line. The performed research demonstrates that this is the case for all realizable scenarios of two landmarks or more.