Alberto Luviano-Ju  arez 1 Instituto Polit  ecnico Nacional, UPIITA, Av. IPN 2580, Col. Barrio La Laguna Ticom  an, D.F. C.P. 07340, Mexico e-mail: aluvianoj@ipn.mx John Cort  es-Romero Department of Electrical and Electronics Engineering, Universidad Nacional de Colombia, Carrera 30 No. 45-03, Bogot  a, C.P. 111321, Colombia e-mail: jacortesr@unal.edu.co Hebertt Sira-Ram  ırez Department of Electrical Engineering, Mechatronics Section, CINVESTAV—IPN Av. IPN 2580 Col. San Pedro Zacatenco, D.F. C.P. 07360, Mexico e-mail: hsira@cinvestav.mx Trajectory Tracking Control of a Mobile Robot Through a Flatness-Based Exact Feedforward Linearization Scheme In this article, a multivariable control design scheme is proposed for the reference trajec- tory tracking task in a kinematic model of a mobile robot. The control scheme leads to time-varying linear controllers accomplishing the reference trajectory tracking task. The proposed controller design is crucially based on the flatness property of the system lead- ing to controlling an asymptotically decoupled set of chains of integrators by means of a linear output feedback control scheme. The feedforward linearizing control scheme is invoked and complemented with the, so called, generalized proportional integral (GPI) control scheme. Numerical simulations, as well as laboratory experimental tests, are presented for the assessment of the proposed design methodology. [DOI: 10.1115/1.4028872] 1 Introduction Controlling nonholonomic mobile robots has been an active topic of research during the past three decades due to the wide variety of applications such as: mine excavation, process monitor- ing, material inspection, planetary exploration, military tasks, materials transportation, man–machine interfaces, etc. [1–3]. The main characteristic of a number of mobile robotic systems is that they present nonintegrable (i.e., nonholonomic) kinematic constraints (see Ref. [4]). As a consequence, these constraints can- not be expressed purely in terms of the underlying generalized coordinates. Second, in many of these cases, the lack of compli- ance with Brockett’s necessary conditions for smooth stabilization [5] makes the output trajectory tracking problems particularly challenging. These features restrict the possible control strategies and, additionally, some ad hoc procedures are necessary to decou- ple the system in order to accomplish the control task. Several methods have been proposed, and applied, to solve the regulation and trajectory tracking tasks in mobile robots. These methods range from sliding mode techniques [6–8], backstepping [9], neural networks approaches [10], linearization techniques [11], and classical control approaches (see Ref. [12]) among many other possibilities. Some classical comprehensive contributions to this area are given in Refs. [1] and [13]. A useful approach to control nonholonomic mechanical systems is based on linear time-varying control schemes (see Refs. [14] and [15]). In the pioneering work of Samson [16], smooth feedback controls (depending on an exoge- nous time variable) are proposed to stabilize a wheeled cart. An important property of linear and nonlinear systems, which is strongly related to the structural property controllability, is the differential flatness. Differential flatness allows a complete parametrization of all system variables in terms of a limited set of special, differentially independent, output variables, called the flat outputs, and a finite number of their time derivatives [17–19]. It has been shown that some mobile robotic systems are differentially flat when there is no slippage condition as shown in Ref. [20], or by appropriate inertia distribution of the links for a class of underactuated mobile manipulators [21]. For the case of the differential mobile robot, the center of the axis connecting the wheels can be considered as the flat output. The differential parameterization leads to a flatness based control- ler whose performance is closely related to the exact knowledge of the gain matrix, which is highly nonlinear and whose variations may lead to instabilities or singularities. Besides, the perfect knowledge of this matrix needs the precise measurement of the first time derivative of the set of flat outputs, which is not given in practice, even the positions provided by vision systems are likely to present additive noises for instance. With the help of a nominal feedforward input, deduced from the flatness of the system, it is possible to reduce the control task to that of a linearized multivariable system. This general control- ler design approach was proposed by Hagenmeyer and Delaleau, and it is known as “exact feedforward linearization” [22]. The method is valid for a large class of differentially flat systems and its application requires that initial conditions are found within a vicinity of the desired nominal trajectory. One of the advantages of the method is the fact that an open-loop linearizing feedforward input can, practically, yield a linear system in Brunovsk y form, thus, reducing the problem of controlling a nonlinear system (possibly with nonholonomic constraints), to that of controlling a simple linear system in a canonical form. The feedforward lineari- zation technique provides a good local solution for the regulation and trajectory tracking of a large class of nonlinear systems. The devised controllers perform quite well, even in the case of com- plex trajectories to follow. The feedforward linearization scheme that a feedforward, open- loop, control scheme, computed on the basis of flatness, is capable of locally maintaining the actual states of the system close to a vicinity of a desired trajectory. The open loop controller is com- plemented with a linear control scheme intimately associated with the linearization of the system. In our developments, we consider the feedforward linearization scheme in connection with a flatness based control scheme. Since the obtained linearized system is a set of two second-order integrator chains, they can be controlled by means of regular proportional integral derivative (PID) 1 Corresponding author. Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS,MEASUREMENT, AND CONTROL. Manuscript received March 14, 2012; final manuscript received October 15, 2014; published online December 10, 2014. Editor: Joseph Beaman. 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