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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.
Till et al. (Fri,) studied this question.