Experimental trajectory optimization of a flapping fin propulsor using an evolutionary strategy.

The experimental optimization of bio-inspired flapping fin trajectories are demonstrated for potential applications as a side or a rear propulsor of an autonomous underwater vehicle. The trajectories are scored based upon their difference from a force set-point and upon their efficiency and are parameterized by 10 variables inspired by fish swimming. The flapping fin is a generic rectangular rigid flat plate with a tapered edge. Optimization occurs as follows. First, a generation of trajectories is created. Second, the trajectories are executed by a spherical parallel manipulator, during which the forces are acquired. Third, the trajectories are scored and a new generation of trajectories is created using the covariance matrix adaptive evolutionary strategy. This loop repeats ad-infinitum until the search converges. Within the first set of searches, two trajectories for optimal side-force generation are found, one is fully three-dimensional while the other is artificially constrained to a line, and one trajectory for optimal thrust generation is found. All searches demonstrate good convergence properties and match the desired force set-point almost immediately. Additional generations primarily improve the efficiency of the maneuver. The two trajectories for generating side-force have a similar efficiency, which shows potential in utilizing a simple trajectory limited to a line. Comparison between the trajectories for generating side-force and thrust suggests that side-force generation is more efficient around Re ~1000, based on the average tip velocity and length of the fin. The second set of searches explores the behavior of the optimal trajectories for generating side-force at a lower force set-point and the third set of searches explores the sensitivity and repeatability of the optimization.