Dimension Reduced Instantaneous Inverse Kinematics for Configuration Variable Limits of Continuum Manipulators Continuum manipulators gain popularity and have been applied in various scenarios due to their advantages such as design compactness, dexterity, intrinsic compliance, etc. Since analytical inverse kinematics for a continuum manipulator with constantlength segments does not exist, numerical approaches, such as resolved motion rates, are usually adopted. A good practice shall ensure numerical stability for the configuration variables near their limits. However, the existing methods mainly focus on preventing the configuration variables from saturation. When an updated configuration variable violates its limit in an inverse kinematics process, the updated variable is simply bounded at the corresponding limit. This handling approach sometimes leads to a position and (or) orientation divergence. This paper hence proposes a dimension reduced instantaneous inverse kinematics for the configuration variable limits of nonredundant continuum manipulators. This dimension reduction method is enabled by the configuration variables that are not at their limits to achieve numerical stability during the entire inverse kinematics process. Numerical Experimental simulations are reported on a 6DoF (Degree of Freedom) continuum manipulator. A clear improvement was identified while compared with the conventional Jacobianbased numerical inverse kinematics.

A Learningbased Inverse Kinematics Solver for a MultiSegment Continuum Robot in RobotIndependent Mapping Inverse kinematics (IK) is one of the most fundamental problems in robotics, as it makes use of the kinematics equations to determine the joint configurations necessary to reach a desired endeffector pose. In the field of continuum robot, solving the IK is relatively challenging, owing to kinematic redundancy with infinite number of solutions.In this paper, we present a simplified model to represent a multisegment continuum robot using virtual rigid links. Based on the model, its IK can be solved using a multilayer perceptron (MLP), a class of feedforward neural network (FNN). The transformation between virtual joint space to task space is described using DenavitHartenberg (DH) convention. Using 20,000 established training data for supervised learning, the MLP reaches a mean squared error of 0.022 for a dualsegment continuum robot. The trained MLP is then used to find the joints for different endeffector positions, and the results show a mean relative error of 2.90% can be on the robot configuration. Hence, this simplified model and its MLP provide a simple method to evaluate the IK solution of a twosegment continuum robot, which can also be further generalized and implemented in multisegment cases.