Batting an in-flight object to the target

Abstract

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.

Predicting the Post-Impact Velocity of a Robotic Arm via Rigid Multibody Models: an Experimental Study

“…While admitting instantaneous velocity jumps and impulsive contact forces is a clear idealization of the contact dynamics (for the family of robots we are considering in this work, impact duration is typically in the range of 5 to 10 ms as shown in [21], [22], [23]), advanced impact models can provide impressive prediction capabilities even in the presence of multiple simultaneous impacts [24]. Also, these algebraic impact models have demonstrated extremely effective in planning and control for mechanical systems undergoing impacts, going from the estimation of the distribution of possible poses of a known object dropped on a surface from an arbitrary height [25], model-based dynamic robot locomotion [26], [27], and accurate batting of flying objects [15]. There is therefore good hope that similar models, once validated, can be also of great use in impact-aware robot manipulation.…”

“…Robot-environment collision models have a long history in robotics [9], [10], [11], [12], [13]. Despite this long history, experimental validation of these collision models is currently limited to robot locomotion [14], single free-falling objects (typically, lightweight small spherical objects, cylinders, or dumbbells) impacting a rigid surface or a robot manipulator, but with limited/no effect on the robot dynamics [15]. We are also unaware of publicly available robot-object-environment impact motion databases.…”

Immediate Generation of Jump-and-Hit Motions by a Pneumatic Humanoid Robot Using a Lookup Table of Learned Dynamics

“…In their method, database of ball trajectories were applied using regression with experience data. Jia et al presented a method for hitting a flying object toward a target [11]. The feasible arm state for the batting action was determined from an iterative computation using analytical models of flying objects and those of the impact between the objects and the robot.…”

Impact-Friendly Robust Control Design with Task-Space Quadratic Optimization

“…Correct and complete impact laws for multiple contact and impacts are not known for inelastic impacts [13]. Recently in a flying object batting example, Jia et al [14] validated that we can use the closed-form 2D impact dynamics model to generate the desired impulsive forces. However in 3D cases, Jia and Wang [15] pointed out that unless the initial sliding direction could be controlled along certain directions, a closedform solution to the impact problem does not exist.…”