Humanoid throwing: Design of collision-free trajectories with sparse reachable maps

This work shows a method of creating trajectories to achieve end-effector velocity control for high degree of freedom position controlled, high-gain, robots. The focus of this work is throwing an object. It is shown that the full reachable area of the end-effector does not need to be known to achieve the desired velocity when a good collision model of the robot is available. The end-effector velocity (magnitude and direction) is specified as well as a duration of this velocity. A sparse map of reachable end-effector positions in free space and the corresponding poses in joint space is created using random sampling in joint space and forward kinematics. The desired trajectory in free space is placed within the sparse map with the first point of the trajectory being a known pose from the original sparse map. The Jacobian Transpose Controller method of inverse kinematics is then used to find the subsequent points in the trajectory. Each pose in the trajectory is checked against the collision model to guarantee no self-collisions. This method was tested on the 130 cm tall full size humanoid Jaemi Hubo and its virtual representation.