Kinematic reductions for uncertain mechanical contact

This paper describes the methods applicable to the modeling and control of mechanical contact, particularly those systems that experience uncertain stick/slip phenomena. Geometric kinematic reductions are used to reduce a system's description from a second-order dynamic model with frictional disturbances coming from a function space to a first-order model with frictional disturbances coming from a space of finite automata over a finite set. As a result, modeling for purposes of control is made more straight-forward by getting rid of some dependencies on low-level mechanics (in particular, the details of friction modeling). Moreover, the online estimation of the uncertain, discrete-valued variables has reduced sensing requirements. The primary contributions of this paper are the introduction of a simplifying representation of friction and formal tests for kinematic reducibility. Results are illustrated using a slip-steered vehicle model and an actuator array model.