A variable curvature modeling approach for kinematic control of continuum manipulators

Continuum manipulators are continuously bending robots consisting of an infinite number of kinematic degrees of freedom (DOF). To reduce the number of actuators, the manipulators are designed in a way to build several serially connected groups of mechanically coupled DOF. These groups are called sections. For real-time motion control, a kinematic model capable to describe the manipulator´s deflection is necessary. A common way to model the manipulator kinematics is to describe the deformation of a single section by a curve with constant curvature. This assumption constitutes an intense constrain with respect to manipulator design or model accuracy. Thus, a new kinematic modeling approach capable to describe the kinematics of continuum manipulators with variable section curvature is proposed in the present work. It subdivides a single section in a finite number of virtual units with piecewise constant curvature. This provides the possibility to shape the modeled section curvature closely to the deformation of any arbitrarily bending continuum manipulator. To demonstrate that this modeling approach is well suited for real-time control applications, simulation results of a Jacobian based feed-forward pose control are presented that are applied to the common class of three actuator continuum manipulators.