Toward the ambitious long-term goal of a fleet of cooperating Flexible Autonomous Machines operating in an uncertain Environment (FAME), this two part paper addresses several critical modeling, design and control objectives for ground vehicles. One central objective was to show how off-the-shelf (low-cost) remote-control (RC) toy vehicles can be converted into intelligent multi-capability robotic-platforms for conducting FAME research. This was done for 13 differential drive RC vehicles called Thunder Tumbler (DDT2). Each DDT2-vehicle was augmented with a suite of sensor-computing-communication devices in order to provide a substantive suite of capabilities. Part I of this two part paper, focusing on a single vehicle, examines the associated non-holonomic dynamical model (including motor dynamics) for the DDT2 vehicle under consideration. We shed light on how vehicle coupling impacts control design a topic not well addressed within the robotics community. Because our vehicle exhibits little coupling, we are able to use classical decentralized control to design a wheel speed inner-loop controller. This controller is used for all of our outer-loop control modes: (speed-direction) cruise control along a curve, planar Cartesian (x, y) stabilization and minimum-time optimal-control around an oval race track. Empirically collected data is shown to agree well with simulation results. Reasons for observed differences are provided. Within Part II, focus is on control laws for the coordination of multiple vehicles. In short, many capabilities that are critical for reaching the longer-term FAME goal are demonstrated within this two part paper.