No abstract

This article presents a new method to solve the inverse kinematics problem of hyper-redundant and soft manipulators. From an engineering perspective, this kind of robots are underdetermined systems. Therefore, they exhibit an infinite number of solutions for the inverse kinematics problem, and to choose the best one can be a great challenge. A new algorithm based on the cyclic coordinate descent (CCD) and named as natural-CCD is proposed to solve this issue. It takes its name as a result of generating very harmonious robot movements and trajectories that also appear in nature, such as the golden spiral. In addition, it has been applied to perform continuous trajectories, to develop whole-body movements, to analyze motion planning in complex environments, and to study fault tolerance, even for both prismatic and rotational joints. The proposed algorithm is very simple, precise, and computationally efficient. It works for robots either in two or three spatial dimensions and handles a large amount of degrees-of-freedom. Because of this, it is aimed to break down barriers between discrete hyper-redundant and continuum soft robots.

In space- and time-dependent dynamical systems, Lyapunov vectors correspond to spatio-temporal patterns of instability. These patterns can be used to parse and predict the interaction and break-down of coherent structures. The computation of Lyapunov vectors, however, is computationally demanding and has hitherto been restricted to systems with a comparatively low attractor dimension. We aim to study the dynamics of vortices in developed turbulence with an attractor dimension of order O(100). To this end, we compute the linear stability spectrum of an unstable periodic orbit embedded in the turbulent attractor and consider it a proxy for the Lyapunov spectrum. Along the periodic orbit at least 25 Lyapunov vectors can give the largest growth rate locally in time and space. We highlight one instance of a mutually induced instability of a vortex pair localized in the high-strain interstitial region.