Dynamic modelling of wheeled mobile robots and automated transit vehicles using dimensionless `roll number´

A comparison is made between two models, one assumed to be two-degree-of-freedom (2-DOF) and the other 3-DOF. To study the dynamic behavior of the two models, transfer functions of the system are used, and root-loci plots are found to be extremely valuable for arriving at some important insights. A dimensionless number, designated as the roll number, is identified, with the property that for a system whose roll number is small, the 3-DOF model is effectively reduced to a 2-DOF model as a result of pole-zero cancellation. This number can be used to great advantage in the structural design of the vehicle. As the forward speed of the vehicle exceeds a certain limit, it is found that the response may become oscillatory, so the speed should be kept within a range to get satisfactory results