Trajectory Shaping to Reproduce Rod Tip Vibration Suppression in the Rebound Phenomenon of Fly-Casting

Fly-casting is a throwing technique in which a flexible rod is used to cast a lightweight line. In skilled fly-casting, a phenomenon known as the rebound phenomenon is observed, where the residual vibration of the rod tip is suppressed by the re-acceleration of the rod handle during the rod-stop phase. This vibration suppression plays an essential role in the casting performance; however, an engineering method for this phenomenon has not been established. Therefore, the purpose of this study is to propose a trajectory-shaping method by interpreting the rebound phenomenon as a vibration suppression control problem for flexible systems with nonzero initial conditions. The proposed method applies a conventional shaping framework to rod systems by introducing a second-order approximation and repeatedly shaping the input trajectory to suppress the approximation errors. Through simulations using a rod model, it was shown that the shaped trajectory yields the characteristic re-acceleration of the rod-handle angular velocity during the rod-stop phase, consistent with the rebound phenomenon. Through experiments using a robotic prototype, it was confirmed that the rod tip vibration amplitude is suppressed by over 80% in two types of casting. These results are useful for further studies on the engineering realization of fly-casting.