Differential flatness theory-based control and filtering for a mobile manipulator

Abstract

The article proposes a differential flatness theory based control and filtering method for the model of a mobile manipulator. This is a difficult control and robotics problem due to the system’s strong nonlinearities and due to its underactuation. Using the Euler-Lagrange approach, the dynamic model of the mobile manipulator is obtained. This is proven to be a differentially flat one, thus confirming that it can be transformed into an input-output linearized form. Through a change of state and control inputs variables the dynamic model of the manipulator is finally written into the linear canonical (Brunovsky) form. For the latter representation of the system’s dynamics the solution of both the control and filtering problems becomes possible. The global asymptotic stability properties of the control loop are proven. Moreover, a differential flatness theory-based state estimator, under the name of Derivative-free nonlinear Kalman Filter, is developed. This comprises (i) the standard Kalman Filter recursion on the linearized equivalent model of the mobile manipulator and (ii) an inverse transformation, relying on the differential flatness properties of the system which allows for estimating the state variables of the initial nonlinear model. Finally, by redesigning the aforementioned Kalman Filter as a disturbance observer one can achieve estimation and compensation of the disturbance inputs that affect the model of the mobile manipulator.

A nonlinear optimal control approach for underactuated power-line inspection robots

“…By incorporating robotic manipulators in these aerial platforms several types of unmanned aerial manipulators are obtained. As far as the third class of robotic systems is concerned that is mobile manipulators and robotic cranes once again one comes against several types of such types of robots (comprising different types of mobile platforms and multi-DOF robotic arms) [53,54].…”

On global trajectory tracking control of robot manipulators with a delayed feedback

“…Proportional-differentiating (PD) controllers are widely used in solving this problem. A fairly complete current state of research on the use of PD controllers in the control of manipulators including mobile ones is available in the papers [Aguinaga-Ruiz et al, 2009], [Kim et al, 2017], [Moreno-Valenzuela et al, 2010], [Nunes et al, 2008], [Oliveira et al, 2015], [Rigatos, 2020]. At the same time, certain difficulties lie in the need to compensate for centrifugal, Coriolis and gravitational forces.…”