The equations that describe the motion of wheeled mobile robots (WMRs) are very different from those that describe manipulators because they are differential rather than algebraic, and often underactuated and constrained. Unlike manipulators, the simplest models of how mobile robots move are nonlinear differential equations. Much of the relative difficulty of mobile robot modelling can be traced to this fact.

This section explores dynamics in two different senses of the term. Dynamics in mechanics refers to the particular models of mechanical systems that are used in that discipline. These tend to be second-order equations involving forces, mass properties, and accelerations. In control theory, dynamics refers to any differential equations that describe the system of interest.

Moving Coordinate Systems

The fact that mobile robot sensors are fixed to the robot and move with them has profound implications. On the one hand, it is the source of nonlinear models in Kalman filters. On the other, it is the source of nonholonomic wheel constraints. This section concentrates on a third effect – the fact that the derivatives of many vector quantities of interest depend on the motion of the robot.