Creep dynamics of nonholonomic systems

Abstract

B a s i c concepts about t h e creep behavior of nonholon o m i c constrained (NC) s y s t e m s w e r e discussed in [5]. Two f u n d a m e n t a l t y p e s o f creep k i n e m a t i c s w e r e proposed a n d t h e hybrid o n e s could be m a d e . In this w o r k , w e e x t e n d to t h e creep d y n a m i c s of typical NC syst e m s such a s t h e disk, sleigh a n d wheel. First, certain reductive m o d e l s o f constrained m o t i o n s u c h a s ideal, relative, pair, a n d general-pair m o d e l s are explored and related. Secondly, by t h e i n v a r i a n t m a n i f o l d m e t h o d of singular perturbation, f u n d a m e n t a l rotational a n d traverse creep d y n a m i c s a n d a hybrid o n e are calculated in a n a p p r o x i m a t e w a y . T h e y c a n be close to t h e c o mplete s y s t e m a s possible. T h e r e f o r e , t h e bridge between reductzve a n d i n v a r i a n t a n a l y s e s c a n be m a d e by t h e m o d e l of general-pair creep a n d c a n help us u n d e r s t a n d physical i m p l i c a t i o n s behind t h e a p p r o x i m a t e solutions. It i s p r o v e n t h a t advanced vehicle techniques, s u c ha s t h e anti-lock braking s y s t e m a n d a special tracking control s y s t e m , c a n be realized b y t h e proposed quasi constrained creeps.