Differentially Flat Designs of Mobile Vehicles With Under-Actuated Manipulator Arms

Differential flatness has been investigated in the context of mobile vehicles for planning and control of their motions. In these models, the wheels are considered to be non-slipping, i.e., the system dynamics is subject to non-holonomic constraints. If a manipulator arm is mounted on such a mobile vehicle, the dynamics becomes highly nonlinear due to the nonlinear coupling between the motions of the mobile vehicle and the manipulator arm. A challenging question is how to perform point-to-point motions of such a system in the state space of the mobile manipulator. If some of the actuators are absent in the mechanical arm, the mobile manipulator becomes under-actuated and consequently even harder to plan and control. This paper presents a methodology for design of mobile vehicles, mounted with under-actuated manipulators operating in a horizontal plane, such that the combined system is differentially flat. In this paper, we show that by appropriate inertia distribution of the links and addition of torsion springs at the joints, a range of under-actuated designs are possible where the underactuated mobile manipulator system is differentially flat. The differential flatness property allows to efficiently solve the problem of trajectory planning and feedback controller design for point to point motions of the system. The proposed method is illustrated by the example of a mobile vehicle with under-actuated three-link manipulator.