This paper presents feedback stabilization control of a rolling manipulation system called the disk-on-disk. The system consists of two disks in which the upper disk (object) is free to roll on the lower disk (hand) under the influence of gravity. The goal is to stabilize the object at the unstable upright position directly above the hand. We show that it is possible to stabilize the object at the upright position, while the hand or object rotates to a specific orientation or spins at a constant velocity. We use full-state feedback linearization to derive control laws. We present simulation as well as experimental results demonstrating the controllers.

This paper presents stabilization control of a rolling manipulation system called the disk-on-disk. The system consists of two disks in which the upper disk (object) is free to roll on the lower disk (hand) under the influence of gravity. The goal is to stabilize the object at the unstable upright position directly above the hand. We use backstepping to derive a control law yielding global asymptotic stability. We present simulation as well as experimental results demonstrating the controller.

This paper discusses how mobile manipulators with an under-actuated vertical arm can be designed to be differentially flat. The property of differential flatness is achieved by appropriate inertia redistribution of the vertical arm and a wide range of under-actuation becomes possible. As a result of having the flatness property, the under-actuated mobile manipulators are capable of executing point-to-point maneuvers as mobile manipulators with a fully actuated arm would do. In addition, the trajectory planning and feedback controller design for point-to-point motions in state space is considerably simplified despite the under-actuation of the arm and nonholonomic constraints (from no-slip assumption) of the mobile base, which make the system more difficult to plan and control. These ideas are demonstrated through an illustrative example of a mobile manipulator consisting of an under-actuated vertical three-link arm and a two-wheeled differentially driven mobile base using differential flatness.