Our long-term goal is to develop a unified framework for planning and control of dynamic robotic manipulation. A typical manipulation plan consists of a sequence of manipulation primitives chosen from a library of primitives, with each primitive equipped with its own feedback controller. Problems of interest include planning the motion of the manipulator to achieve the desired motion of the object and feedback control to stabilize the desired trajectory.
As a first step to understand the nature of dynamic nonprehensile manipulation, we study feedback stabilization of a canonical rolling problem: balancing a disk-shaped object on top of a disk-shaped manipulator (referred to as the hand) in a vertical plane. The balancing task is further extended to more difficult problems of stabilization at the upright position while the hand or object (i) rotates to a specific orientation or (ii) spins at a constant velocity. We constrain the motion of the circular hand to rotation about its center. We derive control laws that stabilize the object to the balanced position under the kinematic assumption of rolling at all times. The basin of attraction is reduced when the contact is modeled using Coulomb friction, but it is still large with large friction coefficients. This work is successfully implemented using high-speed vision feedback.
We are currently focusing on motion planning and feedback stabilization of a broad class of rolling trajectories for smooth planar objects rolling on smooth planar hands (other than disks) moving with a full three degrees-of-freedom. The resulting dynamic rolling manipulation primitive will be incorporated into our library of nonprehensile manipulation primitives.
This work is supported by National Science Foundation grant IIS-0964665.