Ultra-chaos of a mobile robot: A higher disorder than normal-chaos

Abstract

The trajectory of a chaotic dynamical system is sensitive to the initial condition, while its statistics normally do not have sensitive dependence on small disturbances. Such a kind of chaos is called normal-chaos. Recently, a new concept named ultra-chaos has been proposed for the first time. Unlike normal-chaos, the small disturbances lead to large deviation even in statistics for ultra-chaos. However, few ultra-chaos have been reported up to now. In this work, we investigate the influences of small disturbances on the chaotic navigation system and the motion of mobile robot, respectively. It is illustrated that the chaotic navigation system of the mobile robot belongs to normal-chaos. However, the motion of chaotic mobile robot belongs to ultra-chaos. Tiny disturbances would cause huge deviation in the motion of chaotic mobile robot, even in the statistical meaning. Thus, the ultra-chaos is indeed a higher-level disorder compared with the normal-chaos and it widely exists in practice. Hopefully, the new concept, i.e., ultra-chaos, could deepen our understandings of chaos and open a new door to explore chaos theory.