Human-Thrown Non-Rigid Projectile Trajectory Estimation and Interception
Benjamin L. Cohen, Colin P. Duffy, Bryce C. Heitner, Joy Uehara · 2023
Falcon 9, the reusable rocket system from SpaceX, sheds two pieces of its payload fairing upon launch, which fall into the ocean. SpaceX attempted to catch these pieces to reuse them, however, dynamic instability during parachute descent made landing prediction and catching difficult. Taking inspiration from SpaceX, this work designed and employed a retrieval gantry to visually track and intercept non-rigid projectiles (beanbags) thrown with variable initial conditions and significant nonlinear air resistance. The design required simultaneous iteration on a robust mechanical actuator, a representative projectile physics model, vision state estimation, and a performance-oriented control system. Projectiles tested under free-fall flight recordings exhibited a nonlinear drag coefficient of 0.24 ± 0.03 m/pixels normalized by camera frame (1080p), which corresponded up to a 60% variation from predicted particle motion upon reaching the catching plane. The solution featured a 2 ft × 2 ft motor-actuated two-degree-of-freedom gantry inspired by additive manufacturing technology. The projectile was tracked using a tailored image processing algorithm implemented in a two-camera stereo array running at 30fps and a downscaled 540p resolution. The camera array data was fed to a linearized drag model with 0 ± 10% reliability to predict the catching location 250 ms before landing. This position was used as a state estimate for a compensator to actuate the gantry to the predicted position. The fusion of these systems enabled a general catch rate of 40%. Confident landing predictions required up to 8 frames and were heavily hardware-limited by the 30 fps camera polling rate. Bounding the system reaction time to 8 frames resulted in uncertainties of >50% until 250 ms before landing.