The search for a simple and accurate odometry is a main concern when working with mobile robots. This article presents a general analysis of the problem and proposes a particular solution to improve the odometry. The three crucial kinematical aspects of mobile robots (mobility, control, and positioning) are reviewed in detail for vehicles based both in conventional and in omnidirectional wheels. The latter case is more suitable from a maneuvering point of view as it provides the robot frame with the three Degrees Of Freedom (DOF) of plane motion without singular configurations. Moreover, a suitable design of the omnidirectional wheels leads to a strictly invariant Jacobian matrix and thus to a linear control equation with constant coefficients. It is shown that such vehicles may have a holonomic behavior when moving under suitable kinematical restrictions without constraining their trajectory. In that case, the odometry is algebraic (instead of integrative) and thus more accurate. An application case is presented.