Contact-Aware Kinematics for Non-Coaxial Nested Continuum Robots with Arbitrary Play and Cross-Section
Abstract: We propose a physics-based, computationally-efficient method for the forward and inverse kinematics of continuum robots with nested elements, arbitrary cross-sections, inter-element play, and environmental geometries. This represents several applications in minimally-invasive medical interventions, where nested-tube robots are utilized to augment dexterity at the tip and where inverse kinematics computation remains challenging due to the complexity of depicting self-contact and interactions with the anatomy. In our formulation, the slender flexible elements of the robot are described using the Cosserat formulation and their discretized cross-sections as a signed distance field (SDF). The inverse kinematics is computed using the damped Gauss-Newton method, where non-penetration constraints are computed via SDF queries between overlapping cross-sections and are used for residual augmentation of the optimization problem. We perform experimental validation using a 2-tubes concentric tube robot with Nylon elements. Our experiments in 3D show an average error reduction of 20.68% and a maximum reduction of 47.15% error, compared to assuming centerline alignment, as previously proposed. Our method shows an average error of 2.55mm in the absence of environmental constraints and up to 2.76mm when a non-symmetrical tubular environment is added. The overall computation of the proposed inverse kinematics takes less than 0.36s, achieving near real-time computation--fundamental in robot control scenarios.
Advisor: Professor Giovanni Pittiglio
Committee: Professor Loris Fichera, Professor Vincent Aloi