The mechanics of continuum robots: model-based sensing and control

Abstract

This dissertation addresses modeling, control, and sensing with continuum robots. In particular, two continuum robot architectures are studied: (1) concentric-tube designs, and (2) designs actuated by embedded wires, cables, or tendons. The modeling approaches and sensing and control methods developed are also applicable to many other varieties of continuum robot designs.

Concentric-tube continuum robot designs are also termed "active cannulas" because of their potential use as dexterous, needle sized manipulators for minimally invasive medical applications. These robots are composed of multiple pre-shaped tubes arranged concentrically, and their shape and pose are the result of elastic deformations, caused by interaction among the component tubes as well as external loads on the device. We derive two predictive models which describe this behavior using the principle of minimum potential energy and Cosserat-rod theory. The proposed models are each validated experimentally.

Tendon-driven continuum manipulators are also being developed for a variety of applications. The kinematics of these robots are also governed by elastic deformations resulting from tendon interactions with the backbone structure as well as external loading. We show that this behavior may be modeled by coupling the Cosserat-rod model with Cosserat-string models. This approach can be used to analyze designs in which the tendons are routed in general three-dimensional curves, as well as designs with precurved backbone structures, thus providing tools for the analysis and control of a large set of possible designs.

Model-based control of tendon-driven and concentric-tube robots is challenging because solving the kinematic and static models is often computationally burdensome. To address this, a we derive a method for obtaining Jacobians and compliance matrices for flexible robots which is computationally efficient enough to be used for real-time simulation and control. We then describe a Jacobian-based control algorithm and a deflection-based method for estimating applied forces on a flexible robot. The feasibility of these approaches is demonstrated in simulation and on robot hardware.