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 constant-length 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 non-redundant 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 6-DoF (Degree of Freedom) continuum manipulator. A clear improvement was identified while compared with the conventional Jacobian-based numerical inverse kinematics.