Throw Maneuver: Exact Trajectories for Invariant Target Hitting in Robotic Throwing

Abstract

Robots can throw objects to distant targets using gravity, with applications ranging from material transport to firefighting. Existing approaches typically adopt a singleton throw formulation, where the carrier must reach a specific position–velocity configuration at the moment of throw. This reliance on a single throw point makes target-hitting highly sensitive to release delays. To address this limitation, we introduce the throw maneuver: a carrier trajectory that guarantees target hitting for objects released at any time along the trajectory. By differentiating the governing projectile equations, we derive the throw maneuver in its exact representation as ordinary differential equations, with analytical solutions available in special cases. Simulation results verify its invariant target-hit property and show that throw maneuvers achieve longer available throw time and ranges without target miss compared with a strong baseline throw method. Outdoor quadrotor experiments further demonstrate throw maneuver's improved accuracy and precision under realistic flight conditions compared with several baseline throw methods.