Variational Analysis of Snakelike Robots

Snakelike robots have been employed in applications ranging from search-and-rescue to minimally invasive surgical procedures, and may yet find new applications in maintaining civil infrastructure and the repair of satellites. This paper reviews how variational methods have been used previously to analyze three classes of snakelike robots: (1) hyper-redundant manipulators guided by backbone curves; (2) flexible steerable needles; and (3) concentric tube continuum robots. Both coordinate-dependent Euler-Lagrange formulations and coordinate-free EulerPoincaré approaches are discussed. Variational methods are used in the context of hyper-redundant manipulators to constrain degrees of freedom and to provide a means of redundancy resolution. In contrast, variational methods are used for nonholonomic steerable needles, which have fewer actuatable degrees of freedom than those in the task space, to generate optimal open-loop plans for the needle to follow, and to model needle-tissue interactions. For concentric tube robots, variational methods provide a means to determine equilibrium conformations dictated by the principles of elastic mechanics. This paper therefore illustrates by example how variational methods are a natural tool for the analysis and planning of various kinds of snakelike robots.