Control of elastic rod tip for fly-casting using single-mode model and integration of output-zeroing control with PD control

This study focuses on fly-casting as a method for throwing lightweight objects, and aims to develop a control method based on its heuristics that accumulates and releases the elastic energy of an elastic rod to accelerate rod-tip linearly. To achieve this, a planar 3-DOF arm with a rod is considered, and the problem of making the rod-tip follow a given straight path is formulated. The arm-rod was modeled as a multibody system, and a temporary single-mode model was proposed to describe its deformation dominated by the first-order buckling mode. Output-zeroing control with input-output linearization was applied to this nonlinear system, while PD control was integrated to suppress torque oscillations and maintain a consistent direction of the arm's motion. The motion was divided into two phases, elastic energy accumulation and release, with distinct control strategies. Simulations demonstrated that the temporary model suppressed higher-order buckling modes, and that the integrated control enabled the rod-tip to be linearly accelerated by its restoring force. A trade-off was observed between straightness of the rod-tip path and directional consistency of the arm's motion. These results verify the effectiveness of combining nonlinear and linear control to reproduce the dynamic principles of fly-casting.