TS Fuzzy Null-Space Behavior Control of
Non-Holonomic Robot Formations
Gustavo QUINTANA-CARAPIA1*, Jorge S. BENÍTEZ-READ2,
J. Armando SEGOVIA-DE-LOS-RÍOS3, Mayra P. GARDUÑO-GAFFARE4
1-4 Instituto Tecnológico de Toluca (ITT),
Av. Tecnológico s/n. La Virgen, Metepec, 52149, México
1-3 Instituto Nacional de Investigaciones Nucleares,
Carretera México-Toluca s/n,
La Marquesa, Ocoyoacac, 52750, México
firstname.lastname@example.org; email@example.com; firstname.lastname@example.org
* Corresponding author
Abstract: In this paper, an improved Null Space behavior control of a team of non-holonomic robots that maintains time-varying formations is presented. The task functions: (a) are combined considering the non-holonomic constraints, (b) are designed such that each robot tracks its desired trajectory by synchronizing its motion with the other robots motion, (c) maintain the kinematics relationships required by the formation, (d) include synchronization constraints and synchronization errors, which are a measurement of the formation realization degree that is used to generate suitable actions to reach the goal formation, and (e) are in charge of orientating the robot towards its desired position during shape switching. In order to ensure the operation of the controller, a Takagi-Sugeno (TS) fuzzy system is implemented to keep the task functions solutions below the saturation values determined by the actuators of the differential mobile robots. Finally, simulations and experiments are performed to demonstrate the effectiveness of the proposed Null Space behavior control for non-holonomic robots approach in formation control tasks
Keywords: Formation control; inverse kinematics; null space based behaviour control.
CITE THIS PAPER AS:
Gustavo QUINTANA-CARAPIA, Jorge S. BENÍTEZ-READ, J. Armando SEGOVIA-DE-LOS-RÍOS, Mayra P. GARDUÑO-GAFFARE, TS Fuzzy Null-Space Behavior Control of Non-Holonomic Robot Formations, Studies in Informatics and Control, ISSN 1220-1766, vol. 24 (2), pp. 211-220, 2015.
Nowadays, the field of study of autonomous mobile robotics is very fertile. The topic is attractive due to the fact that certain jobs can be performed faster and better by a group of robots working as a team [1, 2]. A seminal work, where virtual agents controlled their formation by following simple rules , inspired the robot formation control. In a robot formation, the robots in the group are able to maintain predefined positions among them while the group moves as if it were a single individual . Research in robot formation aims to provide control to several robots , joining the different tasks that each robot can assume, depending on its current configuration.
Formation control can be achieved with behavior control. The main idea in behavior control is to simulate the biological and social interactions that occur in animal species with artificial beings . To obtain this, the general problem is decomposed into several sub-problems (denominated behaviours) that are solved simultaneously. The solutions of the sub-problems are then used to assemble the next robot motion commands.
The main difficulty in behaviour control is the asynchronous processing termination of each sub-problem, which can lead to wrong command orders. In order to reduce the uncertainty caused by the asynchronous behaviour termination, special attention must be paid to the composition of the results.
One approach, the competitive method introduced in , considers only one behaviour for the generation of the control command. In this case, the different behaviours compete to be the one and only that determines the command. A different approach was proposed in  to consider the contribution of the entire set of behaviours, by means of a weighted sum, to obtain the control command.
The null space based method was introduced in the seminal work of  and combines both the competitive and cooperative paradigms.
In the null space based method, the behaviours are described using kinematics task functions, which are prioritized in terms of their relevance for the objectives of the application, as in the competitive method . The results of the different task functions are combined, cooperatively, by projecting each behaviour into the null space of the following task function in the order of the ascending hierarchy.
In this paper, an improved null-space based behaviour (NSB) approach is proposed to address the formation control of non-holonomic robots. The new features incorporated in the control scheme are described as follows: First, a successful modification of the NSB control to include the orientation as an additional argument in the definition of the task functions. This feature allows the use of the robot orientations as an important factor in the formation control. Second, the development of a decentralized NSB controller for non-holonomic robots, that considers the relative movement of the other members in the formation. The control algorithm requires local information of two neighbouring robots. Third, simulations are performed in groups of mobile robots to show the effectiveness of the proposed formation control using a generalized super-ellipse, whose parameters are functions of time and gives a variety of reference shapes.
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