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<p>This project focused on building a GPS controlled 6-wheel autonomous robot. It is a self-guided autonomous robot, which can be maneuvered with the help of GPS module and compass together interfaced with the microcontroller Arduino Mega. The 6-wheels of the robot are interfaced with monster motor shield and then connected to the Arduino Mega. The speed of the robot is controlled using PWM signals sent from the Arduino board. When the robot starts, it locates its current position using the GPS module. The destination coordinates are already given in the code. Once the current location is fixed, it calculates the distance and heading between the two points. The compass module tells the current heading of the robot. The final heading is calculated by taking the difference between actual heading and current heading. With the help of final heading angle, the robot moves towards its desired location. As the robot moves close to the destination the distance reduces. The minimum distance is predefined as 5 meters in the algorithm since the precision of GPS module is within the range of 5 to 6 meters. Once the distance is less than 5 meters the robot stops, assuming it has reached to the destination location. </p><p> The purpose of building this robot was to guide the robot to multiple locations autonomously with the destination locations predefined in the algorithm. To maneuver the robot to the multiple locations it is very important to calculate the accurate distance and heading. For this project, the main task was to design an algorithm that can calculate the exact distance between any two locations and guide the robot in the proper direction. The motors used for this project have high torque and the updating speed of the GPS module is slow. It was very important to keep the speed of the motor very low and change the speed of the motor only when there was a need to change the direction of the robot. The algorithm designed was able to fulfill these tasks and guided the robot to multiple locations and reach the final destination. </p>

<p> This dissertation presents the kinematic design of six-bar linkages for function, motion, and path generation by means of polynomial homotopy continuation algorithms. When no link dimensions are specified beforehand, the synthesis formulations for each design objective yield polynomial systems of degrees in the millions and billions, suggesting a large number of solutions. Complete solution sets to these systems have not yet been obtained and is the topic of this dissertation. Function generation for eleven positions is explored in most detail, in particular the Stephenson II and III function generators, for which we calculate multihomogeneous degrees of 264,241,152 and 55,050,240. A numerical reduction using homotopy estimates these systems to have 1,521,037 and 834,441 roots, respectively. For motion generation, the Watt I linkage can be specified for eight positions, producing a system of a multihomogeneous degree over 19 billion. However, for this work we focus on the smaller case of six positions, numerically reducing this system to an estimated 5,735 roots. For path generation we take a different approach. The design of path generators is formulated as RR chains constrained to have a single degree-of-freedom by attaching six-bar function generators to them. This enables us to use our results obtained on Stephenson II and III function generators to create four types of eleven position path generators: the Stephenson I linkage, two types of Stephenson II linkages, and the Stephenson III linkage. </p>