Javier Pliego-Jiménez

This paper studies the attitude trajectory tracking problem of rigid bodies subject to unknown constant disturbances and angular velocity measurements corrupted by constant bias. We employ the exponential coordinates of rotation and the angular velocity to describe the state of the rigid body. Exploiting the structural properties of the attitude kinematics and dynamics of the rigid body, we propose a bias observer that compensates for biased measurements and a nonlinear control law with integral action that achieves attitude tracking for almost all initial conditions and compensates for constant disturbances. We design the control law based on a Barrier Lyapunov function to circumvent the exponential coordinates' singularity. Finally, numerical simulations and experimental tests illustrate the efficacy of our control law and bias observer.

This article addresses the attitude stabilization problem of fully actuated rigid bodies such as quadrotors, spacecraft, or satellites. To describe the attitude of the rigid body, we employ the exponential coordinates of rotation. By exploiting the properties of kinematic and dynamic models, we design a nonlinear attitude controller that guarantees almost global exponential stability (aGES) of the closed-loop dynamics. We also consider the case when the attitude dynamics are subject to constant disturbances. To counteract the external disturbance, we modify the attitude control law to include an integral action that rejects the disturbance and achieves aGES. In addition, we show that the stabilization control law can be extended to address the attitude-tracking problem. Using barrier Lyapunov functions, we demonstrate that the proposed control algorithms avoid the singularity of the exponential coordinates during the transient response. We propose strict Lyapunov functions to prove the aGES of the origin of the closed-loop dynamics. Numerical simulations and experimental results performed on a commercial small aerial robot assessed the effectiveness and feasibility of the proposed control laws.

This paper addresses the synchronization problem in outer topology networks using chaotic nodes with hidden attractors. Specifically, we analyze bidirectionally coupled networks with various inner–outer coupling topologies to identify the optimal configuration that encourages outer synchronization. The inner–outer coupled networks incorporate a chaotic system capable of generating hidden attractors. To assess the stability of the synchronization state, we conduct numerical simulations and examine the maximum Lyapunov exponent of the generic variational equations. Our results reveal the most suitable bidirectional inner–outer coupling network topology for achieving outer synchronization.

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.

In this work, we study the problem of designing control laws that achieve time-varying formation and flocking behaviors in robot networks where each agent or robot presents double integrator dynamics. To design the control laws, we adopt a hierarchical control approach. First, we introduce a virtual velocity, which is used as a virtual control input for the position subsystem (outer loop). The objective of the virtual velocity is to achieve collective behaviors. Then, we design a velocity tracking control law for the velocity subsystem (inner loop). An advantage of the proposed approach is that the robots do not require the velocity of their neighbors. Additionally, we address the case in which the second state of the system is not available for feedback. We include a set of simulation results to show the performance of the proposed control laws.