CYBERNETICS AND PHYSICS, VOL. 9, NO. 1, 2020, 57–68 DIFFERENTIAL FLATNESS THEORY-BASED CONTROL AND FILTERING FOR A MOBILE MANIPULATOR Gerasimos G. Rigatos Unit of Industrial Automation Industrial Systems Institute 26504, Rion Patras, Greece grigat@ieee.org Article history: Received 15.09.2019, Accepted 10.12.2019 Abstract The article proposes a differential flatness theory- based control and filtering method for the model of a mo- bile 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 manipula- tor 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 canon- ical (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 non- linear Kalman Filter, is developed. This comprises (i) the standard Kalman Filter recursion on the linearized equiv- alent model of the mobile manipulator and (ii) an inverse transformation, relying on the differential flatness prop- erties of the system which allows for estimating the state variables of the initial nonlinear model. Finally, by re- designing the aforementioned Kalman Filter as a distur- bance observer one can achieve estimation and compen- sation of the disturbance inputs that affect the model of the mobile manipulator. Key words Mobile manipulators, differential flatness theory, flat outputs, canonical forms, global linearization, global stability, Kalman Filtering, disturbance observer. 1 Introduction Mobile manipulators are widely used in several indus- trial and human assisting tasks. For instance they can be used in pick and placement tasks and for carrying objects, in assembling, in painting, spraying, harvest- ing, for patrolling and defence purposes, as well as for providing services to the elderly and the disabled [Li et al., 2009], [Dai and Liu, 2017], [Abeygunawardhana and Murakami, 2010], [Andaluz et al., 2015], [Li et al., 2008]. Dexterity and accuracy in the handling of objects as well as in the maneuvers performed by the mobile ma- nipulators depend on the efficiency of the related control algorithms [Rigatos and Busawon, 2018], [Boyle et al., 2003], [Kocemarek et al., 2017], [Koraye and Nekao, 2016]. There are several results on nonlinear control approaches for robotic vehicles and mobile manipula- tors [Rigatos, 2011], [Rigatos, 2015], [Li et al., 2008], [Li et al., 2016], [Najjaran and Goldenberg, 2007]. In particular, the application of sliding-mode and backstep- ping methods can be hindered by the need to transform previously the dynamic model of mobile manipulators into canonical or triangular state-space forms. One can also note results on robust and adaptive control schemes for mobile manipulators which aim at compensating for model uncertainty and disturbances in these robotic sys- tems [Xu et al., 2009], [Souzanchi et al., 2017], [Wu et al., 2014], [Park et al., 2018], [Monzur and Kulawik, 2006]. There are also findings on global linearization- based control schemes for mobile manipulators, as for instance in the case of flatness-based control [Tang et al., 2011], [Morales et al., 2014], [L´ evine, 2011], [Fliess and Mounier, 1999], [Sira-Ramirez and Agrawal, 2004], [Villagra et al., 2007]. Apart from motion control and the end-effector’s positioning problem for mobile ma- nipulators, compliance tasks and joint position and force control problems for the end-effector have been also an- alyzed [Galicki, 2016], [Linn and Goldenberg, 2002], [Mai and Wang, 2014], [Li et al., 2010], [Liu and Liu, 2009]. The development of functional mobile manipula-