Optimal control goal manifolds for planar nonprehensile throwing

Abstract-This paper presents a throwing motion planner based on a goal manifold for two-point boundary value problem. The article outlines algorithmic and geometric issues for planar throwing of rigid objects with a nonprehensile end-effector. Special attention is paid to the challenge of controlling a desired 6-dimensional state of the object with a planar 3-DoF robot. Modeling of the contacts is discussed using a state vector of the coupled robot and object dynamics. Robustness against uncertainty due to varying model parameters such as object inertia and friction between the end-effector and the object is investigated. An approach for obtaining manifolds of terminal constraints from the goal configuration is described. Classification of these constraints is given. Finally, feasible trajectory generation conditions for successful execution of the generated optimal controls are discussed