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This book presents a study of two major different types of nonholonomic mobile robot (MR) problems. Different solutions for these problems are proposed. The first problem is the trajectory tracking of nonholonomic MR. In this part, two different types of controller's are designed based on the optimization method (i.e., EA), Which are Fractional Order PID (FOPID) controller and Fuzzy-Backstepping controller. The second problem is the trajectory generation of nonholonomic MR. In this part, an Arnold modified chaotic system, based on the trigonometric functions is proposed.This system is used to design a controller for the MR (chaotic MR). In addition, the effect of vibration on the trajectory tracking performance of the MR is studied experimentally and a fuzzy controller is designed to compensate for the vibration effects. In order to validate the simulation results, an experimental procedure is performed. In this part, an actual MR is developed. The new robot controller circuit (Robot's brain) is equipped with different types of sensors, such as 3-D gyroscope, 3-D accelerometer, and five proximity (Distance) sensors.