Striking a flying object such as a ball to some 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 two-degree-of-freedom robotic arm intercepting an object in free flight and redirecting it to some target with a single strike, assuming all the movements 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 in time, 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 (16 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 captured by a high-speed camera. The arm keeps adjusting its motion in sync with planning until batting takes place. Experiments have demonstrated a better batting performance by a Barrett Technology WAM Arm than by a human being without training.

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We study a continuous data assimilation (CDA) algorithm for a velocity-vorticity formulation of the 2D Navier-Stokes equations in two cases: nudging applied to the velocity and vorticity, and nudging applied to the velocity only. We prove that under a typical finite element spatial discretization and backward Euler temporal discretization, application of CDA preserves the unconditional long-time stability property of the velocity-vorticity method and provides optimal long-time accuracy. These properties hold if nudging is applied only to the velocity, and if nudging is also applied to the vorticity then the optimal long-time accuracy is achieved more rapidly in time. Numerical tests illustrate the theory, and show its effectiveness on an application problem of channel flow past a flat plate.

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Particle Swarm Optimization (PSO) has typically been used with small swarms of about 50 particles. However, PSO is more efficiently parallelized with large swarms. We formally describe existing topologies and identify variations which are better suited to large swarms in both sequential and parallel computing environments. We examine the performance of PSO for benchmark functions with respect to swarm size and topology.We develop and demonstrate a new PSO variant which leverages the unique strengths of large swarms. "Hearsay PSO" allows for information to flow quickly through the swarm, even with very loosely connected topologies. These loosely connected topologies are well suited to large scale parallel computing environments because they require very little communication between particles. We consider the case where function evaluations are expensive with respect to communication as well as the case where function evaluations are relatively inexpensive. We also consider a situation where local communication is inexpensive compared to external communication, such as multicore systems in a cluster.