Batting an In-Flight Object to the Target

Striking a moving object such as a flying ball to a target location is a highly skillful maneuver that a human being has to learn through a great deal of practice. In robotic manipulation, precision batting remains one of the most challenging tasks in which computer vision, modeling, planning, control, and action must be tightly coordinated in a split second. This paper investigates the problem of a 2-DOF robotic arm intercepting an in-flight object and redirecting it to some target with a single strike, assuming all the movements to take place in one vertical plane. Two-dimensional impact is solved under Coulomb friction and energy-based restitution with a proof of termination. Planning combines impact dynamics and projectile flight mechanics with manipulator kinematics and image-based motion estimation. As the object is on the incoming flight, the post-impact task constraint of reaching the target is propagated backward, while the arm’s kinematic constraints are propagated forward (via joint trajectory interpolation), all to the pre-impact instant when they will meet constraints that allow batting to happen. All the constraints (sixteen in total) are then exerted on the arm’s pre-impact joint angles and velocities, which are repeatedly planned based on updated estimates of the object’s motion as captured by a high speed camera. The arm keeps adjusting its motion in sync with planning to prepare for batting. Experiments with a Barrett Technology WAM Arm batting three objects have demonstrated a performance unmatched by a human being without training. KEY WORDs— Batting, impact, impact planning, manipulator kinematics, trajectory planning, projectile flight mechanics, motion estimation