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.

Heading synchronization is fundamental in flocking behaviors. If a swarm of unmanned aerial vehicles (UAVs) can exhibit this behavior, the group can establish a common navigation route. Inspired by flocks in nature, the k-nearest neighbors algorithm modifies the behavior of a group member based on the k closest teammates. This algorithm produces a time-evolving communication network, due to the continuous displacement of the drones. Nevertheless, this is a computationally expensive algorithm, especially for large groups. This paper contains a statistical analysis to determine an optimal neighborhood size for a swarm of up to 100 UAVs, that seeks heading synchronization using a simple P-like control algorithm, in order to reduce the calculations on every UAV, this is especially important if it is intended to be implemented in drones with limited capabilities, as in swarm robotics. Based on the literature of bird flocks, that establishes that the neighborhood of every bird is fixed around seven teammates, two approaches are treated in this work: (i) the analysis of the optimum percentage of neighbors from a 100-UAV swarm, that is necessary to achieve heading synchronization, and (ii) the analysis to determine if the problem is solved in swarms of different sizes, up to 100 UAVs, while maintaining seven nearest neighbors among the members of the group. Simulation results and a statistical analysis, support the idea that the simple control algorithm behaves like a flock of starlings.

The problem of flocking and formation of a group of nonholonomic wheeled mobile robot is addressed in this paper. Based on the cascade structure of the kinematic model, two kinematic controllers are proposed to achieve formation and flocking behaviors. The proposed control laws present a P and PI-like structure plus a feedforward term and do not require complex calculations. The interaction between the robots is modeled using graph theory. The performance of the proposed control laws is validated by experimental tests on a group of four differential-drive wheeled mobile robots.

This paper presents an adaptive strategy to solve the formation control problem for a set of second-order agents with parametric uncertainty and nonlinearity. The strategy regards a group of agents where the nolinearities and uncertainties are represented by a linearly parametrised term, which allows us to consider non-identical agents. In order to ensure the collision-free motion of agents, we propose the use of a repulsive vector field component that is applied only when a pair of agents become nearer than a predefined minimum bound. Numerical simulations were carried out to show the effectiveness of the proposed scheme, first with a simplified example to verify the key features of the control law and a general case to illustrate the performance of the algorithm in a more complex scenario.

This paper presents an adaptive strategy to solve the formation control problem for a set of second-order agents with parametric uncertainty and nonlinearity. The strategy regards a group of agents where the nonlinearities and uncertainties are represented by a linearly parametrized term, which allows us to consider non-identical agents. In order to ensure the collision-free motion of agents, we propose the use of a repulsive vector field component that is applied only when a pair of agents becomes nearer than a predefined minimum bound. Numerical simulations were carried out to show the effectiveness of the proposed scheme. First, a simplified example was used to verify the key features of the control law, followed by a general case to illustrate the performance of the algorithm in a more complex scenario.