Differentially Flat Designs of Underactuated Open-Chain Planar Robots

A fully actuated system can execute any joint trajectory. However, if the system is underactuated, not all joint trajectories are attainable. For such systems, it is difficult to characterize attainable joint trajectories analytically. Numerical methods are generally used to characterize these. This paper investigates the property of differential flatness for underactuated planar open-chain robots and studies dependence on inertia distribution within the system. It is shown that certain choices of inertia distributions make an underactuated open-chain planar robot with revolute joints feedback linearizable, i.e., also differentially flat. Once this property is established, trajectory between any two points in the state space can be planned, and a controller can be developed to correct for errors. To demonstrate the proposed methodology in hardware, experiments with an underactuated 3-DOF planar robot are also presented.