Dynamical Model and Optimal Turning Gait for Mechanical Rectifier Systems

Abstract

Abstract-Animal locomotion can be viewed as mechanical rectification due to the dynamics that convert periodic body movements to a positive average thrust, resulting in a steady locomotion velocity. This paper considers a general multi-body mechanical rectifier under continuous interactions with the environment, with full rotation and translation in three dimensional space. The equations of motion are developed with respect to body coordinates to allow for direct analysis of maneuvering dynamics. The paper then formulates and solves an optimal turning gait problem for a mechanical rectifier traveling along a curved path, with propulsive forces generated by periodic body deformation (gait). In particular, the gait is optimized to minimize a quadratic cost function, subject to constraints on average locomotion velocity and average angular velocity. The problem is proven to reduce to two separate, tractable minimization problems solvable for globally optimal solutions. The first problem solves for the optimal shape offset that results in turning, while the other solves for the optimal gait that results in locomotion along a straight path. A case study of a locomotor in a fluid environment is presented to demonstrate the utility of the method for robotic locomotor design.

Exploiting natural dynamics for gait generation in undulatory locomotion

“…Optimization is useful because it is based on contrived metrics which can be clearly defined for mathematical analysis. Existing strategies include quadratic optimization over all periodic motions (Blair & Iwasaki, 2011;Kohannim & Iwasaki, 2017), parametrization of the geometric configuration over a truncated basis (Cortes, Martinez, Ostrowski, & McIsaac, 2001), calculus of variations (Hicks & Ito, 2005), and mimicking observed kinematics to reduce the number of parameters which are then optimized numerically by gridding the parameter space (McIsaac & Ostrowski, 2003). Some of these methods have been successfully applied to reproduce biological gaits with no presumption on the kinematics (Liu, Fish, Russo, Blemker, & Iwasaki, 2016).…”