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Research Papers

Kinematics of Continuum Robots With Constant Curvature Bending and Extension Capabilities

[+] Author and Article Information
Arnau Garriga-Casanovas

Mechatronics in Medicine Laboratory,
Department of Mechanical Engineering,
Imperial College London and Rolls-Royce, plc,
London SW7 2AZ, UK
e-mail: a.garriga-casanovas14@imperial.ac.uk

Ferdinando Rodriguez y Baena

Professor
Mechatronics in Medicine Laboratory,
Department of Mechanical Engineering,
Imperial College London,
London SW7 2AZ, UK
e-mail: f.rodriguez@imperial.ac.uk

Contributed by the Mechanisms and Robotics Committee of ASME for publication in the JOURNAL OF MECHANISMS AND ROBOTICS. Manuscript received April 18, 2018; final manuscript received August 11, 2018; published online November 19, 2018. Assoc. Editor: Guimin Chen.

J. Mechanisms Robotics 11(1), 011010 (Nov 19, 2018) (12 pages) Paper No: JMR-18-1110; doi: 10.1115/1.4041739 History: Received April 18, 2018; Revised August 11, 2018

Continuum robots are becoming increasingly popular due to the capabilities they offer, especially when operating in cluttered environments, where their dexterity, maneuverability, and compliance represent a significant advantage. The subset of continuum robots that also belong to the soft robots category has seen rapid development in recent years, showing great promise. However, despite the significant attention received by these devices, various aspects of their kinematics remain unresolved, limiting their adoption and obscuring their potential. In this paper, the kinematics of continuum robots with the ability to bend and extend are studied, and analytical, closed-form solutions to both the direct and inverse kinematics are presented. The results obtained expose the redundancies of these devices, which are subsequently explored. The solution to the inverse kinematics derived here is shown to provide an analytical, closed-form expression describing the curve associated with these redundancies, which is also presented and analyzed. A condition on the reachable end-effector poses for robots with six actuation degrees-of-freedom (DOFs) is then distilled. The kinematics of robot layouts with over six actuation DOFs are subsequently considered. Finally, simulated results of the inverse kinematics are provided, verifying the study.

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Figures

Grahic Jump Location
Fig. 1

Illustration of a robot configuration corresponding to the inverse kinematics solution for a specified end-effector pose, in a robot composed of two sections with a total of six actuation degrees-of-freedom (DOFs)

Grahic Jump Location
Fig. 2

Diagram of one section of the robot (yellow), with the different variables corresponding to the first section description (σi, ζi, ϕi), and the second section description (xiF,yiF,ziF), as well as the reference frame at the base of the section {F}, the rotation vector wi, and rotation angle ρi

Grahic Jump Location
Fig. 3

Conceptual approach to the inverse kinematics solution. The rotations associated with a robot composed of two sections, which are defined by quaternions, are illustrated. The point of junction pmG, and the reference frames {G} and {T} are also included.

Grahic Jump Location
Fig. 4

Reference frames in inverse kinematics solution for a n = 6 robot, with end-effector position at ptG=[2.64,0.92,−0.26] [a.u.] and orientation qt=0.87+0.13iG−0.27jG+0.40kG. The centerline of the first section is plotted in cyan, and the centerline of the second section in magenta, and four lines following the outer surface of both sections of continuum body separated circumferentially at 90 degrees are plotted in red, green, blue and yellow. Reference frame {G} at the robot's proximal end is depicted in turquoise, reference frame {T} at the specified end-effector pose is depicted in purple, and the pose resulting from the robot configuration is shown in dashed green, with an exact overlap.

Grahic Jump Location
Fig. 5

Curve corresponding to the loci of the distal end of the first section, for an n = 6 robot with end-effector position at ptG=[−0.14,5.28,1.02] [a.u.] and orientation qt=0.1+0.36iG−0.17jG+0.91kG. Two of the possible robot configurations to reach this specified end-effector pose are also shown, with the distal end of the first section at two of the possible locations on the curve.

Grahic Jump Location
Fig. 6

Set of inverse kinematics solutions corresponding to a robot with n = 6, for a specified end-effector at ptG=[2.64,0.92,−0.26] [a.u.] and qt=0.87+0.13iG−0.27jG+0.40kG

Grahic Jump Location
Fig. 7

Four inverse kinematics solutions corresponding to the motion of an n = 6 robot with end-effector poses at pt1G=[−2,2,2.97] [a.u.] and qt1=0.73+0.31iG−0.39jG+0.47kG, pt2G=[−2,2,3.30] [a.u.] and qt2=0.73+0.29iG−0.44jG+0.44kG, pt3G=[−2,2,3.64] [a.u.] and qt3=0.73+0.27iG−0.48jG+0.41kG, and pt4G=[−2,2,3.97] [a.u.] and qt4=0.73+0.24iG−0.51jG+0.38kG

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