Is there any package for Mathematica that deals with robotics and their application?
Yes, please check out Controlling Robots with Lego Mindstorms NXT and Mathematica
The book A Mathematical Introduction to Robotic Manipulation talks about kinematic and dynamic modeling for manipulators based on Screw theory. It provides a Mathematica Package for Screw Calculus(click here to download). I find it quite useful.
This book Modern Robotics: Mechanics, Planning, and Control also comes with a Mathematica Package, which can be downloaded here.