Creep kinematics of nonholonomic systems

Most studies about nonholonomic systems were developed under the absolute relation of constraint equations. Such ideally constrained systems are known somewhat relaxed in real world, which are claimed as complementarily constrained problems. Systems with viscous frictions and/or flexibilities are typical cases at which the constraints are pseudo-violated rather than violated. These nonideal kinematics are treated in terms of nonholonomic creep behaviors, classified by two fundamental types: rotation creep and traverse creep. Creep coefficients are defined and proposed to illustrate the kinematical relations for such complementarily constrained systems. It can be shown that most nonholonomic vehicles can be described by both creep types, while the trailers attached to a car falls into the traverse type only. Therefore, we conclude the existing algorithms for nonholonomic motion planning and control should be modified as intrinsic creeps take place in nature. The creep notion can also be applied to the symmetry systems of conservation of angular momentum