Differentially flat mobile manipulators mounted with an under-actuated vertical arm

Abstract

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.