Closed-Loop Position Control for Growing Robots Via Online Jacobian Corrections

Abstract

Growing continuum robots offer improved safety and navigation in confined spaces, due to their inherent compliance and ability to conform to highly curved paths. Navigation of these, and other continuum robots, often involves frequent interactions with the surrounding environment, which are typically unknown and can affect the kinematics of the robot. We propose here an approach for controlling continuum robots based on leveraging real-time position and orientation measurements. This pose information is used to update a local model of the robot's velocity kinematics in an online manner via corrective rotations and magnitude adjustments. We combine the proposed control approach with a method for localizing the tip of a growing robot and evaluate the performance of closed-loop position control on a point-reaching task in unconstrained and constrained environments. The closed-loop system achieves an average total error of 3.22 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\pm$</tex-math></inline-formula> 1.31 mm in the unconstrained case and 4.56 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\pm$</tex-math></inline-formula> 1.56 mm in the constrained case, validating our proposed approach. This work also represents the first method for autonomous position control of growing robots that does not require a map of its environment.