Modelling of tendon-driven continuum robot based on constraint analysis and pseudo-rigid body model

Quasi-static models of tendon-driven continuum robots (TDCR) require consideration of both the kinematic and static conditions simultaneously. While the Pseudo-Rigid Body (PRB-3R) model has been demonstrated to be efficient, existing works ignore the mechanical effect of the tendons such as elongation. In addition, the static equilibrium equations for the partially constrained tendons have been expressed in different forms within the literature. This leads to inconsistent simulation results which have not been validated by experimental data when external loads are applied. Furthermore, the inverse problem for solving the required inputs for a prescribed end effector pose has not been studied for the PRB-3R model. In this work, we introduce a new modelling approach based on constraint analysis (CA) of a multi-body system and Lagrange multipliers to systematically derive all the relevant governing equations required for a planar TDCR. This method can include tendon mechanics and efficiently solve for the direct and inverse kinetostatic models with either forces or displacements as the actuation inputs. We validate the proposed CA method using numerical simulation of a benchmark model and experimental data.