Gesture is a way to express our ideas using our head or body.To build a hand gesture robot we will build a system using which our robot can recognize any gesture with the help of its camera,afterwards classify this gesture with the help of some algorithm and respond accordingly. To make it simple, You can understand working of this robot in following steps:
1. Send Signals using Remote Device(Your Hand, Face, Body or remote)
2. Robot receive Signals using Cameras on-board.
3. Use Algorithm to decode signal
4. Match that signal with stored signals
5.If match found then follow instructions as specified.

WiiRobot: In this project,students of Brown University build a simple and reproducible gesture based robot controller.It consists ofWii Remote,Asus eeePC,  Ubuntu Eee(as Operating System), USB Webcam,USB Bluetooth Dongle and other components. To recognize gestures, team of wiiRobot used two algorithms:
1.K-Nearest Neighbor and
2.Sum of square differences

Wireless Gesture Controlled Toy
The objective of this project is to build a toy car that can be controlled by gesture wirelessly. User is able to control motions of the car by wearing the controller glove and performing predefined gestures.
This project provides a basic platform for many potential applications such as wireless controlled toys racing games, gesture human-machine interfacing, and etc.

How it works?

More info at Cornell University Page

How to build one ?
Complete details about Gesture Controlled Tank Toy

Useful Link :
Wireless USB Gesture Input System
Related PDF:
Real Time hand gesture Tele robotic system using Fuzzy Logic (pdf)

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