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.
Highlights
Mobile manipulators are widely used in several industrial and human assisting tasks
It will be proven that the dynamic model of the mobile manipulator is a differentially flat one, which implies that all its state variables and its control inputs can be expressed as differential functions of a specific subset of its state vector elements which are known as flat outputs of the system
It has been proven that the dynamic model of a mobile manipulator, comprising a four-wheels vehicle and a two-DOF robotic manipulator, is a differentially flat one
Summary
Mobile manipulators are widely used in several industrial and human assisting tasks. For instance they can be used in pick and placement tasks and for carrying objects, in assembling, in painting, spraying, harvesting, 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]. To solve the associated state estimation problem a filtering method under the name of Derivative-free nonlinear Kalman Filter can be used [Rigatos and Tzafestas, 2007], [Basseville and Nikiforov, 1993], [Rigatos and Zhang, 2009] This filtering approach consists of the standard Kalman Filter recursion on the equivalent linearized description of the system and of an inverse transformation that provides estimates for the state variables of the initial nonlinear model of the mobile manipulator.
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