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Kinematic model to control the end-effector of a continuum robot for multi-axis processing

Published online by Cambridge University Press:  24 November 2015

Salvador Cobos-Guzman ,
David Palmer  and
Dragos Axinte
Salvador Cobos-Guzman*
Affiliation:
University of Nottingham, Machining and Condition Monitoring Research Group, University Park, Nottingham, NG7 2RD, UK.
David Palmer
Affiliation:
University of Nottingham, Machining and Condition Monitoring Research Group, University Park, Nottingham, NG7 2RD, UK.
Dragos Axinte
Affiliation:
University of Nottingham, Machining and Condition Monitoring Research Group, University Park, Nottingham, NG7 2RD, UK.
*
*Corresponding author. E-mail: Salvador.Cobos_Guzman@nottingham.ac.uk, epxdp1@nottingham.ac.uk, dragos.axinte@nottingham.ac.uk
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Summary

This paper presents a novel kinematic approach for controlling the end-effector of a continuum robot for in-situ repair/inspection in restricted and hazardous environments. Forward and inverse kinematic (IK) models have been developed to control the last segment of the continuum robot for performing multi-axis processing tasks using the last six Degrees of Freedom (DoF). The forward kinematics (FK) is proposed using a combination of Euler angle representation and homogeneous matrices. Due to the redundancy of the system, different constraints are proposed to solve the IK for different cases; therefore, the IK model is solved for bending and direction angles between (−π/2 to +π/2) radians. In addition, a novel method to calculate the Jacobian matrix is proposed for this type of hyper-redundant kinematics. The error between the results calculated using the proposed Jacobian algorithm and using the partial derivative equations of the FK map (with respect to linear and angular velocity) is evaluated. The error between the two models is found to be insignificant, thus, the Jacobian is validated as a method of calculating the IK for six DoF.

Keywords

Continuous robotsInverse kinematicKinematics modelJacobian for hyper-redundant systems
Type
Articles
Information
Robotica , Volume 35 , Issue 1 , January 2017 , pp. 224 - 240
Copyright
Copyright © Cambridge University Press 2015 

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