Inverse Kinematics for a Continuum Robot Through the Workspace Division

Abstract

Continuum robots are flexible robots capable of maneuvering in spaces with complex geometry, such as the insides of complex devices. High maneuverability of continuum robots are ensured due to the elastic bending deformation of the robot’s own body and the linear displacement of the base. Bending deformation can be described by two assumptions: absence of torsion and piecewise constant curvature. The absence of torsion eliminates torsional deformation in the robot. Piecewise constant curvature assumption allows us to describe the shape of the robot’s neutral line. To do this, the bending section is divided into subsections, the neutral line of which can be represented by an arc of a circle. However, this approach complicates the inverse kinematics. The presence of a movable base is also an obstacle to solving the inverse kinematics. This paper presents a solution to the inverse kinematics for a continuous robot with a movable base and variable curvature, which uses the tangent line to the robot’s workspace to determine the amount of base displacement. To determine the tangent, the robot’s work area is divided into several sites. Each site has its own center. A tangent is defined as a perpendicular to a line drawn through the center of the site and to a point in the work area for which the tangent needs to be determined. A comparison of the proposed method with an analogue in numerical experiments shows that the proposed method more accurately determines tangents and is capable of solving a larger portion of inverse kinematics problems than the analogue.