Shape and contact force estimation of continuum manipulators using pseudo rigid body models

Accurate estimation of deformed shape and reaction forces poses a significant challenge in modeling and control of continuum manipulators interacting with their environment. This paper presents a framework for the analysis of a continuum manipulator subjected to multiple external loads using pseudo rigid body (PRB) modelling method. A PRB model with six degrees of freedom is developed, and the statics equations for a manipulator with multiple loads are presented, followed by the approach for determining the optimal model parameters. Dimensionless constants are used to enable scaling the model to manipulators of different lengths and materials. The approach is first validated by a comparison with Finite Element Analysis, and the results show a low error in estimating the tip deflection (less than 1% of the manipulator length). A magnetically-actuated manipulator driven by an array of electromagnetic coils is used for experimental validation. The optimization for a single segment of the manipulator is performed with experimental data, with an average error of 2.2 mm in calculating the tip position. An experimental setup for a manipulator with multiple loads is created by introducing displacement constraints with fixtures connected to multi-axis force sensors. The model shows good agreement with quasi-static experiments in estimating the reaction forces and predicting the deformed shape of the manipulator. The average error in force estimation is 61 mN, while the average error in estimating tip position is 2.8 mm for a manipulator length of 82 mm. (C) 2019 Elsevier Ltd. All rights reserved.