This proposed general and low-cost multi-robot formation platform includes the indoor global-positioning system, the multi-robot communication system, and the wheeled mobile robot hardware. Finally, experimental results are shown with different configurations and heterogeneous robots, where the graphics corroborate the expected operation of the proposal.Īimed at the problem that experimental verifications are difficult to execute due to lacking effective experimental platforms in the research field of multi-robot formation, we design a simple multi-robot formation platform. Likewise, the stability of the controller is analyzed to know the required features that have to be met by the control constants, that is, the correct values. The development of the proposal is achieved through the use of controllers based on linear algebra, propounding a low computational cost and high scalability algorithm. This paper presents a proposal for controlling a group of terrestrial robots with heterogeneous characteristics, considering primary and secondary tasks thus that the group complies with the following of a path while modifying its shape and orientation at any time. The obtained results prove the suitability of using a LAMDA Z-number-based controller in the tested systems.Ĭooperative robotics has considered tasks that are executed frequently, maintaining the shape and orientation of robotic systems when they fulfill a common objective, without taking advantage of the redundancy that the robotic group could present. Finally, a complexity analysis is presented to evaluate the feasibility in the implementation of the proposal. The proposed approach provides suitable results at runtime and outperforms the results of the other tested controllers in terms of performance, minimizing the deviation between the current system output and the reference. The fuzzy controller has been tested by simulation in two different tasks: 1) Control of a process that consists of a mixing tank with variable dynamics, and 2) Trajectory tracking of a mobile robot. The LAMDA method is applied to compute a chattering-free control action which is applied to systems with model uncertainties and variable dynamics. The controller uses criteria from the sliding mode control (SMC) and the Lyapunov concepts to guarantee robustness and stability respectively. Due to the potential of Z-numbers, this paper presents the development of a fuzzy controller that combines the fundamentals of LAMDA (Learning Algorithm for Multivariate Data Analysis) with the concepts of the Total Utility of Z-numbers, to establish an inference method to improve the performance in a control system. Z-Numbers is a recent concept related to fuzzy logic where the restriction and reliability criteria are characterized as fuzzy sets. To do that, we solve the problem using the notion of the Cylindrical Algebraic Decomposition, well-known in algebraic geometry. A generalization of the above algorithms is finally proposed to the case where the polynomial P also depends on a set of parameters α = ∈ Rd. We also implement each method in Maple and compare their practical behavior (average complexity). We then compute the worst-case bit complexity of each method and compare their theoretical behavior. In particular, we alternatively study a method based on rational univariate representations, a method based on root separation, and finally a method first based on the sign variation of the leading coefficients of a signed subresultant sequence (Sturm-Habicht) and on the identification of an isolating interval for the maximal y-projection of the real solutions of Σ. Then, we use standard computer algebra methods to solve this problem. This problem is first reduced to the computation of the maximal y-projection of the real solutions (x, y) of a bivariate polynomial equations system Σ =, where P ∈ Z. In this dissertation, we study the computation of the L∞-norm of finite-dimensional linear time-invariant systems.
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