Mechanics of bending, torsion, and variable precurvature in multi-tube active cannulas
ICRA'09 Proceedings of the 2009 IEEE international conference on Robotics and Automation
Port-based modeling and simulation of mechanical systems with rigid and flexible links
IEEE Transactions on Robotics
Design and control of concentric-tube robots
IEEE Transactions on Robotics
Equilibrium Conformations of Concentric-tube Continuum Robots
International Journal of Robotics Research
Design and Kinematic Modeling of Constant Curvature Continuum Robots: A Review
International Journal of Robotics Research
Humanoid motion planning in the goal reaching movement of anthropomorphic upper limb
ICIRA'11 Proceedings of the 4th international conference on Intelligent Robotics and Applications - Volume Part I
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Numerical integration methods based on the Lie group theoretic geometrical approach are applied to articulated multibody systems with rigid body displacements, belonging to the special Euclidean group SE(3), as a part of generalized coordinates. Three Lie group integrators, the Crouch-Grossman method, commutator-free method, and Munthe-Kaas method, are formulated for the equations of motion of articulated multibody systems. The proposed methods provide singularity-free integration, unlike the Euler-angle method, while approximated solutions always evolve on the underlying manifold structure, unlike the quaternion method. In implementing the methods, the exact closed-form expression of the differential of the exponential map and its inverse on SE(3) are formulated in order to save computations for its approximation up to finite terms. Numerical simulation results validate and compare the methods by checking energy and momentum conservation at every integrated system state.