Differentially flat design of under-actuated planar robots: Experimental results

Control of nonlinear under-actuated systems is an area of ongoing research. In certain applications, under- actuated systems are unavoidable. For instance, a biped can not have an actuator between the foot and the ground. In industrial robots, under-actuation can minimize cost and dead weight. Differential flatness, if applicable, provides a systematic approach to plan and control feasible trajectories for such systems. Recently, the authors have formulated a philosophy to design under-actuated planar manipulators that are differentially flat [1]. The design philosophy has two sufficient conditions: (i) an inertia distribution scheme, and (ii) an actuator and torque spring placement scheme. The philosophy covers a broad range of n-DOF manipulator designs with the degree of under- actuation varying from 1 to n - 1 as opposed to under-actuation by one or two in most of the literature on under-actuated manipulators. This paper presents a 3-DOF planar manipulator designed on the basis of this philosophy and an experimental study of controllers based on its differential flatness property. It is demonstrated experimentally that the differential flatness based controllers are able to track the desired trajectories with small tracking errors even in the presence disturbances like friction, parameter uncertainty etc. It is shown via simulation that the errors observed in the trajectories can be attributed to the friction present at the unactuated joint.