FABRIK-based comparison of the inverse kinematic algorithms operation results for multi-section continuum robots

Flexible bend link robots, also called continuum or soft robots, are an urgent research topic. Various algorithms were developed to solve the inverse problem of the multi-section continuum robot kinematics including those based on the FABRIK (Forward And Backward Reaching Inverse Kinematics) algorithm. This algorithm was originally created to solve the inverse kinematics problem of robots consisting of rigid links connected by spherical joints and could also be used in regard to continuum robots, which are arcs smoothly transiting into each other. To work with the FABRIK algorithm, each bend section is approximated to the virtual rigid link. Two known approaches are known to solve the inverse kinematics problem: the first is based on constructing the tangents (bend section transformation into two tangents), and the second is based on constructing the chords (bend section reduction to a chord). Both approaches demonstrate good results in solving the inverse kinematics problem compared to algorithms based on the Jacobian matrix construction. However, scientific literature misses data on comparing methods that use the FABRIK algorithm. In this regard, two approaches were compared to solve the inverse kinematics problem based on implementing the FABRIK algorithm. Results of numerical experiments with three-, five- and ten-sectional robots are presented. Characteristics of the algorithms and boundaries of their application were determined.