  We present a novel algorithm for collision-free kinematics of multiple
manipulators in a shared workspace with moving obstacles. Our
optimization-based approach simultaneously handles collision-free constraints
based on reciprocal velocity obstacles and inverse kinematics constraints for
high-DOF manipulators. We present an efficient method based on particle swarm
optimization that can generate collision-free configurations for each redundant
manipulator. Furthermore, our approach can be used to compute safe and
oscillation-free trajectories in a few milli-seconds. We highlight the
real-time performance of our algorithm on multiple Baxter robots with 14-DOF
manipulators operating in a workspace with dynamic obstacles. Videos are
available at https://sites.google.com/view/collision-free-kinematics
