analytical predictions, optimization, and design of a tensegrity-based artificial pectoral fin

for millions of years, aquatic species have utilized the principles of unsteady hydrodynamics to perform efficient, highly maneuverable and silent swimming motions. the manta ray, manta birostris, has been identified as one such high performance species due to their ability to migrate long distances with low energy consumption, maneuver in spaces the size of their tip-to-tip wing span, produce enough thrust to leap out of the water and attain sustained swimming speeds of 2.8 m/s with low flapping frequencies. these characteristics make the manta ray an ideal candidate to emulate in the design of a bio-inspired autonomous underwater vehicle. the enlarged pectoral fins of the manta ray undergo complex motions that couple a curved spanwise deformation with a chordwise traveling wave to produce thrust and to maneuver. to produce an artificial pectoral fin that achieves this compound deformation while supporting large force generation, a tensegrity-based solution is developed. various actuation strategies that are capable of matching these key kinematic features are explored and compared. analytical solutions for active planar tensegrity beam structures are derived. these solutions allow for the direct calculation of optimal parameter values without the need to perform an exhaustive parametric study using a numerical solution. moreover, the analytical solutions provide physical insight into the mechanics of tensegrity beams. building on previous studies of active tensegrity structures, the loading response of different actuation strategies has been investigated analytically and is validated by a nonlinear numerical model and experiments. optimal stiffness-to-mass and strength-to-mass strategies have been identified. utilizing the analytical predictions for the optimal solution, an example design of a tensegrity-based artificial pectoral fin is shown. structural performance metrics were calculated showing that the fin structure can closely match the kinematics of the manta ray, under external loading, using open-loop actuation of four actuators remotely located outside of the active structure. this approach costs minimal power consumption and shows the simple design of a high performance tensegrity-based artificial pectoral fin.