Parallel continuum robots have the potential to provide multi-degree-of-freedom articulation using a structure that is simple, compact, compliant, and highly scalable. These characteristics may be useful in micromanipulation, endoscopic robotic-assisted surgery, and human-robot interaction. Our prior work formulated a kinematic model which treats a parallel continuum robot as a set of multiple Cosserat rods with coupled boundary conditions. In this paper, we detail methods for the efficient numerical solution of this model at rates that enable real-time interactive simulation, motion planning, design optimization, and control. Exploitation of the model structure enables a significant reduction in the number of integrations required to evaluate the boundary value Jacobian matrix used in a shooting method. Our approach is used to teleoperate a prototype robot using real-time inverse kinematics solutions, and simulation tests show that inverse kinematics solutions are consistently computed at rates of several kilohertz using standard desktop computing hardware.

In this paper, we investigate continuum manipulators that are analogous to conventional rigid-link parallel robot designs. These “parallel continuum manipulators” have the potential to inherit some of the compactness and compliance of continuum robots while retaining some of the precision, stability, and strength of rigid-link parallel robots, yet they represent a relatively unexplored area of the broad manipulator design space. We describe the construction of a prototype manipulator structure with six compliant legs connected in a parallel pattern similar to that of a Stewart-Gough platform. We formulate the static forward and inverse kinematics problems for such manipulators as the solution to multiple Cosserat-rod models with coupled boundary conditions, and we test the accuracy of this approach in a set of experiments, including the prediction of leg buckling. An inverse kinematics simulation of slices through the 6 degree-of-freedom (DOF) workspace illustrates the kinematic mapping, range of motion, and force required for actuation, which sheds light on the potential advantages and tradeoffs that parallel continuum manipulators may bring. Potential applications include miniature wrists and arms for endoscopic medical procedures, and lightweight compliant arms for safe interaction with humans.