A Geometric Design Approach for Continuum Robots by Piecewise Approximation of Freeform Shapes

Abstract

As soft, continuum robots see increasing areas of application, many scenarios have arisen where it is necessary to consider the geometric shape of the robot. The current approaches to robot kinematics, such as the piecewise constant-curvature (PCC) model, are effective in representing simple overall robot geometry and estimating the end-effector state, but they are less intuitive for planning robots that involve complex geometries. In this work, we propose a solution to the geometric design problem by a two-part approach: a freeform spline defines a “shape curve” that describes the overall geometry of the robot, and then a “kinematic curve” composed of shapes that are feasible to replicate with continuum robots is fitted to the shape curve. As an implementation of this approach, we specifically explore the application of piecewise cubic Bezier curves in designing the shape curve of the robot, and pairs of arcs to construct the kinematic curves. Finally, the approach is applied to a tip-extension “vine” robot that is designed and fabricated to “grow” along a designed path and access the top surface of an obstacle.