Energy Shaping Control of a Muscular Octopus Arm Moving in Three Dimensions

Interest in soft robots, specifically soft continuum arms (SCA), comes from their potential ability to perform complex tasks in unstructured environments as well as to operate safely around humans, with applications ranging from agriculture [1-3] to surgery [4-6]. An important bio-inspiration for SCAs is provided by octopus arms [7-10]. An octopus arm is hyper-flexible with nearly infinite degrees of freedom, seamlessly coordinated to generate a rich orchestra of motions such as reaching, grasping, fetching, crawling, or swimming [11,12]. How such a marvelous coordination is possible remains a source of mystery and amazement, and of inspiration to soft roboticists. Part of the challenge comes from the intricate organization and biomechanics of the three major muscle groups--transverse, longitudinal, and oblique--which add to the overall complexity of the problem [13-16]. In this paper, we develop a bio-physical model of octopus arm equipped with virtual musculature, using the formalism of the Cosserat rod theory [17,18]. In this type of modeling, a key concept is the stored energy function of nonlinear elasticity theory whereby the internal forces and couples of a hyperelastic rod are obtained as the gradients of the stored energy function. The goal of this work is to extend the energy concept for following inter-related tasks: (i) Bio-physical modeling of the internal muscles, and (ii) Model-based control design. The specific contributions on the two tasks are as follows.