We present the continuous model of a mobile slender mechanism that is intended to be the structure of an autonomous hyper-redundant slender robotic system. Rigid body degrees-of-freedom (DOF) and deformability are coupled through a Lagrangian weak formulation that includes control inputs to achieve forward locomotion and shape tracking. The forward locomotion and the shape tracking are associated to the coupling with a substrate that models a generic environment with which the mechanism could interact. The assumption of small deformations around rigid body placements allows to adopt the floating reference kinematic description. By posing the distributed parameter control problem in weak form, we naturally introduce an approximate solution technique based on Galerkin projection on the linear mode shapes of the Timoshenko beam model that is adopted to describe the body of the system. Simulation results illustrate coupling among forward motion and shape tracking as described by the equations governing the system.
Path Following and Shape Morphing With a Continuous Slender Mechanism
Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received April 26, 2014; final manuscript received June 10, 2015; published online July 21, 2015. Assoc. Editor: Jwu-Sheng Hu.
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Fattahi, J. S., and Spinello, D. (July 21, 2015). "Path Following and Shape Morphing With a Continuous Slender Mechanism." ASME. J. Dyn. Sys., Meas., Control. October 2015; 137(10): 101007. https://doi.org/10.1115/1.4030816
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