An Alternative for Trajectory Tracking in Mobile Robots Applying Differential Flatness

An Alternative for Trajectory Tracking in Mobile Robots Applying Differential Flatness

Elkin Yesid Veslin Díaz (Universidad de Boyacá, Colombia), Jules G. Slama (Universidade Federal do Rio de Janeiro, Brazil), Max Suell Dutra (Universidade Federal do Rio de Janeiro, Brazil), Omar Lengerke Pérez (Universidad Autónoma de Bucaramanga, Colombia) and Hernán Gonzalez Acuña (Universidad Autónoma de Bucaramanga, Colombia)
DOI: 10.4018/978-1-4666-2658-4.ch008


One solution for trajectory tracking in a non-holonomic vehicle, like a mobile robot, is proposed in this chapter. Using the boundary values, a desired route is converted into a polynomial using a point-to-point algorithm. With the properties of Differential Flatness, the system is driven along this route, finding the necessary input values so that the system can perform the desired movement.
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Throughout time, mobile robots have acquired great importance because of a wide variety of applications arising from the potential for autonomy that they present; some examples include autonomous robots and transportation systems (AGV—Automated Guided Vehicles). The function of an autonomous robot is to carry out different tasks without any human intervention in unknown environments, in which transportation systems move objects from place to place without needing a driver. In these operations, the main task is to control the displacement of a robot through a given route. However, the main problem that exists in the control systems is precisely the performance of the system from one space to another, and the mobile robot is not an exception.

Nowadays, researchers in this field have developed several inquiries such as the application of chaotic routes for the exploration of uncertain spaces and the control of AGV systems in order to be applied in industry; the former highlights the application of flexible systems of manufacturing theories or FSF for the generation of routes in vehicles with trailers (Tavera, 2009; Lengerke, 2008).

Due to the existence of friction during displacement, this kind of system presents non-holonomic restrictions in its kinematic structural and, therefore, the mobility is reduced (Siciliano, 2009). It has also been shown that these systems are differentially flat; meaning that the system has a set of outputs called flat outputs, which according to the properties of flat systems, the outputs and their derivatives allow one to describe the whole system (Fliess, 1994). This paper highlights this property in the case of trajectory tracking, with a point-to-point steering algorithm (van Nieuwstadt, 1997; De Doná, 2009). The desired route is reformulated through a function in time and space. The parameterization, which is combined with the differential flatness systems concepts, determines a set of inputs that allows for the control of robot movement by means of such routes.

The methodology designed is conceived from a brief description of differential flatness systems concepts; afterwards the concept of parameterization of routes is introduced, with the tracking method from one point to another in order to be implemented in the system. This analysis provides different graphical simulations that show the outcomes. Finally, a discussion is opened about the advantages of the implementation and future possibilities for studies.

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