In this era of automation, it is extremely necessary to find a cheap and accurate navigation system for wheeled robots, so as to bring them to commercial level. Several algorithms have been developed in order to calculate accurate X and Y co-ordinates of wheeled robot, where along with encoders, high cost Inertial Measurement Units have been used for error correction. In order to bring such navigation system at consumer level, where the robots will have to be produced in masses, it is not possible to implement such tedious processes on each manufactured robot. This project is aimed at optimizing the odometry algorithm, required to convert the region of motion into a co-ordinate plane using encoders, or a combination of encoder and low cost gyroscopes. A reliable trajectory generation based solution for desired path of motion of the wheeled robots based on a virtual co-ordinate system is proposed here. This system is further applied to a automate a normal motorized wheel chair so as to enable the wheel chair to move to several locations within the house on its own just by following simple commands. This system can also be applied to several other tasks where automation is essential and accurate feedbacks from surrounding environment are not available. The wheelchair will provide a mean of easy transportation to the physically challenged people in the home area. The wheelchair is designed and tested in various environment to provide all possible real world situations.