This paper presents a new three-dimensional autonomous chaotic system. The proposed system generates a chaotic attractor with the variation of two parameters. Analytical and numerical studies of the dynamic properties to generate chaos, for continuous version (CV) and discretized version (DV), for the new chaotic system (NCS) were conducted. The CV of the NCS was implemented by using an electronic circuit with operational amplifiers (OAs). In addition, the presence of chaos for DV of the NCS was proved by using the analytical and numerical degradation tests; the time series was calculated to determine the behavior of Lyapunov exponents (LEs). Finally, the DV of NCS was implemented, in real-time, by using a novel embedded system (ES) Mikromedia Plus for PIC32MX7 that includes one microcontroller PIC32 and one thin film transistor touch-screen display (TFTTSD), together with external digital-to-analog converters (DACs).
The problem of leader-follower formation of a platoon of differential-drive wheeled mobile robots without using attitude measurements is addressed in this paper. Contrary to the position-distance approaches existing in the literature, the formation and collision avoidance is achieved by introducing a state-dependent delay in the desired trajectory. The delay is obtained as the output of a dynamical system and its magnitude will decrease/increase depending on the distance between the robots. To guarantee trajectory tracking and to overcome the lack of orientation measurements, an output feedback control and attitude observer are proposed based on the kinematic model of the robots. The attitude observer is designed directly on the special orthogonal group SO(2) and it can be used in open-loop schemes. The proposed control-observer scheme ensures asymptotic convergence of the tracking and observer errors. Finally, experimental results are presented to show the performance of the proposed approach.
This article proposes three control algorithms for the emergence of self-organized behaviours, including aggregation, flocking and rendezvous, in swarm robotics systems. The proposed control algorithms are based on a local polar coordinates' control law available in the literature for posture regulation; this law is adapted to work in a self-organized robotic swarm using distance and bearing as coupling information. Therefore, the robots only need to know the radial distance and orientation to the goal; additionally, the three algorithms are based on self-organization, eliminating the need for a preset coupling topology among the robots. In particular, the flocking algorithm has a first stage for topology creation, while the rendezvous and aggregation algorithms change the topology on every iteration depending on the local interactions of the robots. The effectiveness of the algorithms was evaluated through numerical simulations of swarms of up to 100 differential traction wheeled mobile robots.
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