# Kinematics of Spherical Robots Rolling Over 3D Terrains

## TL;DR

This paper develops and validates kinematic models for spherical robots navigating complex 3D terrains, introducing a new classification and control approach for improved path tracking in 3D environments.

## Contribution

It derives comprehensive kinematic equations for various SR configurations on 3D terrains and proposes a novel classification based on kinematics, enhancing understanding and control.

## Key findings

- Validated models through simulations
- Effective path tracking on 3D terrains
- New classification improves control strategies

## Abstract

Although the kinematics and dynamics of spherical robots (SRs) on flat horizontal and inclined 2D surfaces are thoroughly investigated, their rolling behavior on generic 3D terrains has remained unexplored. This paper derives the kinematics equations of the most common SRs configurations rolling over 3D surfaces. First, the kinematics equations for a geometrical sphere rolling over a 3D surface are derived along with the characterization of the modeling method. Next, a brief review of current SR mechanical configurations is presented as well as a novel classification for spherical robots based on their kinematics. Then, considering the mechanical constraints of each category, the kinematics equations for each group of spherical robots are presented. Afterwards, a path tracking method is utilized for a desired 3D trajectory. Finally, simulations are carried out to validate the developed models and the effectiveness of the proposed control scheme.

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Source: https://tomesphere.com/paper/1906.05228