Mechanics Modeling of Tendon-Driven Continuum Manipulators

Abstract

Continuumrobotic manipulators articulate due to their inherent compliance. Tendon actuation leads to compression of the manipulator, extension of the actuators, and is limited by the practical constraint that tendons cannot support compression. In light of these observations, we present a new linear model for transforming desired beam configuration to tendon displacements and vice versa. We begin from first principles in solid mechanics by analyzing the effects of geometrically nonlinear tendon loads. These loads act both distally at the termination point and proximally along the conduit contact interface. The resulting model simplifies to a linear system including only the bending and axial modes of the manipulator as well as the actuator compliance. The model is then manipulated to form a concise mapping from beam configurationspace parameters to n redundant tendon displacements via the internal loads and strains experienced by the system. We demonstrate the utility of this model by implementing an optimal feasible controller. The controller regulates axial strain to a constant value while guaranteeing positive tendon forces and minimizing their magnitudes over a range of articulations. The mechanics-based model from this study provides insight as well as performance gains for this increasingly ubiquitous class of manipulators.

Algorithms for Automated Pointing of Cardiac Imaging Catheters

“…Several kinematic strategies focused on catheter positioning have already been developed, and we will use these techniques as the basis of our approach to control the ICE catheter [9][10][11][12]. Additionally, researchers have also described the bending characteristics of long deformable objects, sometimes described as remotely actuated continuum robots [13,14].…”

Hysteresis analysis of a notched continuum manipulator driven by tendon

“…Some researchers adopted overall modelling to map driving force and deformation using diverse theorems: energy method such as the principle of virtue power and the transformation of potential energy (Tatlicioglu et al, 2007;Rone and Ben-Tzvi, 2014), Cosserat rod theory (Jones et al 2009;Rucker and Iii, 2011;Giorelli et al, 2012), constant curvature assumption (Camarillo et al, 2008;York et al, 2015;Wu et al, 2017), etc. Moreover, some researchers established a unit model first and then built an integrate deformation model considering unit kinematics and mechanics character (Du et al, 2015b;Kato et al, 2015).…”

Three-Dimensional Passivity-Based Dynamic Control for Tendon-Driven Catheters

“…Kinematic models of continuum robots are presented based on beam theory [14,15], constant curvature [16] or piecewise constant curvature modeling [17], and Cosserat rod theory [18,19]. Constant curvature modeling is an accurate approach provided that external loads are negligible.…”