A Study in Nonprehensile Manipulation Primitives: Control of a Balancing Ball via Rolling

Abstract

Nonprehensile manipulations are ones in which the object being manipulated is not firmly grasped. Instead, the manipulator takes advantage of outside forces, including gravity and contact forces, to control the dynamics of the system. This makes control more complex, as the dynamics of both the manipulator and the object must be taken into account. However, it can also allow the manipulator to control more degrees of freedom of the object than it could while grasping the object. Nonprehensile manipulations can be broken down into several categories of primitives including pushing, rolling, and throwing. This thesis studies the rolling primitive in the ball on ball system. The system is made up of two balls, an upper object ball and a lower hand ball, where the object is balanced about the unstable equilibrium position directly over the hand. I derive the dynamics of the system and then design a controller to stabilize the system. I then present simulations as well as experimental results of the implementation of the designed controller.