Motion analysis of two-link nonholonomic swimmers

Abstract

This paper presents a tool for analyzing the motion of two-link nonholonomic swimmers. We refer to these systems as Land-sharks, which are a generalization of the well known Roller Racers. By exploiting the symmetry of the system, we are able to reduce the equations of motion and construct the scaled momentum evolution equation. This unveils a very useful and intuitive Land-shark motion analysis tool based on the partitioning of the mass and geometry parameter space. In particular, this partitioning reveals that, as opposed to the Roller Racer, the Land-shark’s momentum can be increased and decreased, i.e., the system can be stopped. This is done through the use of steering, which is the system’s only input. Furthermore, we explore the problem of modeling frictional slip by assessing the applicability of a previously proposed friction model to the oscillatory locomotion of the Land-shark. Results show that the proposed friction model is generally applicable to two-link nonholonomic mechanical systems, which is an important step toward establishing the generality of the friction model for nonholonomic mechanical systems.