General Forward Kinematics for Tendon-Driven Continuum Robots

Unlike the inverse kinematics problem of
$n$
-tendon continuum robots, the forward kinematics problem lacks a closed-form analytical solution. In this paper, a novel forward kinematics algorithm for
$n$
-tendon single-segment flexible continuum robots is developed that can determine the resulting beam configuration for any given set of actuator displacements. The algorithm determines key parameters of all possible
$n$
- to 1-tendon combinations and examines them against evaluation criteria to find the final beam configuration as well as the active/slack status of the tendons at this configuration. The algorithm employs a previously developed analytical loading model for
$n$
-tendon continuum robots with general tendon positioning to evaluate the tension loads in tendons for each combination. Potential energy of the beam is also calculated for all combinations and utilized to choose among multiple potential solutions. The model is derived to account for the bending and axial compliance of the manipulator as well as tendon compliance. A multi-tendon continuum robot system is employed to experimentally evaluate the proposed forward kinematics solution. Multiple experiments are carried out for the exhaustive list of all possible combinations of different sets of tendon displacements and the results are reported. The proposed forward kinematics algorithm may be used to understand the implication of control errors and their nonlinear effects for optimal selection of hardware and control algorithm for safety and reliability purposes.