#### Underactuation

Action variables, the components of , are often referred to as actuators, and a system is called underactuated if the number of actuators is strictly less than the dimension of . In other words, there are less independent action variables than the degrees of freedom of the mechanical system. Underactuated nonlinear systems are typically nonholonomic. Therefore, a substantial amount of nonholonomic system theory and planning for nonholonomic systems involves applications to underactuated systems. As an example of an underactuated system, consider a free-floating spacecraft in that has three thrusters. The amount of force applied by each thruster can be declared as an action variable; however, the system is underactuated because there are only three actuators, and the dimension of is six. Other examples appeared Section 13.1.2. If the system is not underactuated, it is called fully actuated, which means that the number of actuators is equal to the dimension of . Kinodynamic planning has mostly addressed fully actuated systems.

Steven M LaValle 2012-04-20