Distributed Nash Equilibrium Seeking for Multicluster Aggregative Game of Euler-Lagrange Systems With Coupled Constraints.

This article considers the distributed Nash equilibrium seeking problem of a multicluster aggregative game subject to local set constraints, consensus constraints in the same cluster, and coupled linear equality and nonlinear inequality constraints among all clusters. In the considered game, each cluster is composed of a group of players formulated by uncertain Euler-Lagrange (EL) dynamics, and its objective is to minimize its own cost function, which is the sum of the local functions of all players in the cluster. The local cost function of each player depends on its own decision and an aggregate of the decisions of all the players. An adaptive continuous-time distributed strategy is developed for uncertain EL systems to reach the generalized Nash equilibrium (GNE) of multicluster aggregative game. In particular, a new auxiliary system is synthesized using a projection operator, gradient descent, and dynamic average consensus to estimate the GNE. Based on the outputs of the auxiliary system, an adaptive tracking algorithm is developed for an EL system with uncertain parameters. Using the Lyapunov stability theory, it is shown that the developed distributed strategy achieves accurate convergence to the GNE. Finally, a numerical example is presented to demonstrate the theoretical results.

Adaptive Formation Tracking Control of Multiple Vertical Takeoff and Landing UAVs With Bearing-Only Measurements.

This article studies the leader-following formation tracking control problem of multiple vertical takeoff and landing (VTOL) unmanned aerial vehicles (UAVs) subject to uncertain parameters, in which the target formation configuration is defined by using the interneighbors' bearing vectors. An adaptive formation control algorithm with bearing-only measurements is proposed under a hierarchical control framework. More specifically, a saturated adaptive distributed control force is developed in the position loop with bearing-only measurements. Since the bearing vectors with respect to the neighbors can be directly measured by low-cost onboard cameras, the proposed formation algorithm can be implemented without interagent communication. Subsequently, in the attitude loop, an adaptive hybrid control scheme via two modified Rodrigues parameters (MRPs) sets is proposed, which achieves the command attitude tracking globally and also avoids the unwinding problem of MRPs. Based on the Lyapunov stability analysis and hybrid theory, we prove that the overall closed-loop error system is globally asymptotically stable. Finally, we provide a numerical example to demonstrate the effectiveness of the proposed control algorithm.

Global Visual-Inertial Localization for Autonomous Vehicles with Pre-Built Map.

Accurate, robust and drift-free global pose estimation is a fundamental problem for autonomous vehicles. In this work, we propose a global drift-free map-based localization method for estimating the global poses of autonomous vehicles that integrates visual-inertial odometry and global localization with respect to a pre-built map. In contrast to previous work on visual-inertial localization, the global pre-built map provides global information to eliminate drift and assists in obtaining the global pose. Additionally, in order to ensure the local odometry frame and the global map frame can be aligned accurately, we augment the transformation between these two frames into the state vector and use a global pose-graph optimization for online estimation. Extensive evaluations on public datasets and real-world experiments demonstrate the effectiveness of the proposed method. The proposed method can provide accurate global pose-estimation results in different scenarios. The experimental results are compared against the mainstream map-based localization method, revealing that the proposed approach is more accurate and consistent than other methods.

Distributed Optimization for Second-Order Discrete-Time Multiagent Systems With Set Constraints.

The optimization problem of second-order discrete-time multiagent systems with set constraints is studied in this article. In particular, the involved agents cooperatively search an optimal solution of a global objective function summed by multiple local ones within the intersection of multiple constrained sets. We also consider that each pair of local objective function and constrained set is exclusively accessible to the respective agent, and each agent just interacts with its local neighbors. By borrowing from the consensus idea, a projection-based distributed optimization algorithm resorting to an auxiliary dynamics is first proposed without interacting the gradient information of local objective functions. Next, by considering the local objective functions being strongly convex, selection criteria of step size and algorithm parameter are built such that the unique solution to the concerned optimization problem is obtained. Moreover, by fixing a unit step size, it is also shown that the optimization result can be relaxed to the case with just convex local objective functions given a properly chosen algorithm parameter. Finally, practical and numerical examples are taken to verify the proposed optimization results.

Real-time multi-quadrotor trajectory generation via distributed receding architecture and hierarchical planning in complex environments.

Generation of multi-quadrotor trajectories in real-time in complex three-dimensional environments remains a grand challenge. Trajectory planning becomes computationally prohibitive as the number of quadrotors and obstacles increases. This paper proposes the distributed receding architecture-based hierarchical trajectory planning method (drHTP) to tackle this issue. The distributed receding architecture is established to formulate and solve a series of single-quadrotor short-horizon planning problems for reducing the computation complexity. In distributed planning, the time-heuristic priority mechanism is devised to assign a reasonable planning sequence to enhance the convergence performance. The hierarchical planning, including front-end initial trajectory generation and back-end trajectory optimization, is introduced for the single-quadrotor in each short horizon to further reduce the computation time. The sparse A* search algorithm is modified to only consider adjacent obstacles for obtaining the initial trajectory rapidly. The convergence of drHTP is analyzed theoretically. Numerical simulations with moving and dense obstacle scenarios are carried out to verify the effectiveness of drHTP. The comparative simulation results demonstrate that drHTP outperforms the state-of-the-art distributed sequential convex programming and distributed model predictive control methods in terms of computational efficiency. drHTP is also validated by the physical experiment in an indoor testbed.

Targeted Bipartite Consensus of Opinion Dynamics in Social Networks With Credibility Intervals.

This article investigates the targeted bipartite consensus problem of opinion dynamics in cooperative-antagonistic networks. Each agent in the network is assigned with a convergence set to represent a credibility interval, in which its opinion is trustworthy. The network topology is characterized by a signed switching digraph. The objective is to achieve the bipartite consensus targeted within these credibility intervals. A gradient term is introduced in the opinion dynamics besides the consensus term. Under the assumption that the underlying graph is uniformly jointly strongly connected and structurally balanced, it is first shown that the considered opinion dynamics reaches the targeted bipartite consensus within the intersections of the convergence sets associated with two antagonistic groups. Next, by relaxing the connectivity condition to uniform joint quasistrong connectivity, the targeted bipartite consensus result is also proven with an additional convergence set assumption. Numerical examples are provided to validate the proposed theoretical results.

Fully Distributed Event-Triggered Optimal Coordinated Control for Multiple Euler-Lagrangian Systems.

This article studies a fully distributed optimal coordinated control problem with the global cost function for networked Euler-Lagrange (EL) systems subject to unknown model parameters. In particular, the global cost function is the sum of all the local cost functions assigned to each agent and only available to itself. The objective is to minimize the global cost function in a distributed manner while achieving a consensus on its optimal solution. Since the model parameters of the considered EL systems are not available, a new auxiliary system is introduced as a reference model, and its outputs exponentially converge the optimal solution of the global cost function. A fully distributed optimal control algorithm without requiring global information is first proposed. Then, an alternative distributed optimal algorithm via the event-triggered mechanism is proposed to reduce the communication cost. In particular, by combining an edge-based adaptive gain method, the proposed event-triggered optimal algorithm is also fully distributed. Finally, numerical simulation is carried out to validate the theoretical results.

Distributed Nonlinear Placement for Multicluster Systems: A Time-Varying Nash Equilibrium-Seeking Approach.

In this article, a class of distributed nonlinear placement problems is considered for a multicluster system. The task is to determine the positions of the agents in each cluster subject to the constraints on agent positions and the network topology. In particular, the agents in each cluster are placed to form the desired shape and minimize the sum of squares of the Euclidean lengths of the links amongst the center of each cluster and its corresponding cluster members. The problem is converted into a time-varying noncooperative game and then a distributed Nash equilibrium-seeking algorithm is designed based on a distributed observer method. A new iterative approach is employed to prove the convergence with the aid of the Lyapunov stability theorem. The effectiveness of the distributed algorithm is validated by numerical examples.

Development of Co-Based Amorphous Composite Coatings Synthesized by Laser Cladding for Neutron Shielding.

Advanced amorphous coatings consisting of Co-based metallic glasses with ultrahigh strength (6 GPa) and high microhardness (up to 17 GPa) can significantly improve the surface properties of matrix materials. However, the intrinsic brittleness of Co-based metallic glasses can lead to the initiation of microcracks caused by the inevitable generation of thermal stress during the laser cladding process, which severely limits the potential application. In this paper, the methods of increasing substrate temperature and fabricating composite coatings with the addition of toughened Fe powders were adopted to inhibit the generation of microcracks in the Co55Ta10B35 amorphous coatings. Moreover, neutron shielding performances of the cladding coatings with high B content were investigated with a wide range of neutron energy (wavelength: 0.15-0.85 nm). The results indicate that the fully amorphous coating and composite ones can be fabricated successfully. The increase in the substrate temperature and the addition of Fe powders can effectively inhibit the initiation and propagation of microcracks. The fully Co-based amorphous coating with high B content (35 at.%) can exhibit excellent neutron shielding performance. With the addition of Fe powders, the neutron shielding performance is reduced gradually due to the dilution effect of B in the composite cladding coatings, but the microcrack will be completely restrained.

Cooperative Set Aggregation of Second-Order Multiagent Systems: Approximate Projection and Prescribed Performance.

This paper studies the cooperative set aggregation problem for second-order multiagent systems by utilizing the approximate projection algorithm. First, an aggregation law that uses the approximate projection is proposed, where the feasible set of the approximate projection points is established based on an Euclidean distance with respect to the targeted set and a deviated angle with respect to the exact projection point. Under the proposed law, the position vectors of all the agents are shown to reach an agreement in the intersection of their individual targeted sets and the velocity vector of each agent is shown to converge to zero. Then, a time-dependent performance bound is set for the norm of the weighted error of the relative positions among neighboring agents and the absolute velocity of the agent, and a performance-guaranteed aggregation controller is designed to guarantee the prescribed transient performance. During the process of aggregation, the norm of the weighted error is shown to not exceed the performance bound. The convergence conditions of the proposed algorithms with respect to the control strength and the terms induced by the approximate projection are obtained by using the techniques of convex analysis and Lyapunov stability. Simulations are provided to validate the theoretical results.

Velocity-Free Leader-Follower Cooperative Attitude Tracking of Multiple Rigid Bodies on SO(3).

A distributed control algorithm is proposed in this paper to achieve the leader-follower cooperative attitude tracking of multiple rigid bodies without using absolute and relative angular velocity information. The nonlinear manifold SO(3) is applied to represent the attitude of each rigid body. By considering the case of limited information exchange, i.e., not all the rigid bodies have access to the leader's information, a novel continuous nonlinear distributed estimator satisfying the rotation matrix dynamics is first introduced for each rigid body to estimate the leader's information asymptotically. Then, two auxiliary systems driven by proper inputs are designed such that the issues due to the angular velocity unavailability are effectively solved. Next, a feasible distributed protocol is designed by implementing the outputs from the distributed estimator and the auxiliary systems. It is demonstrated in terms of Lyapunov theory that, the developed distributed control algorithm ensures the asymptotically stable cooperative attitude tracking of multiple rigid bodies under the weak tree connectivity assumption. Finally, illustrative examples are provided to validate and highlight the proposed results.

Boundary Constraints for Minimum Cost Control of Directed Networks.

Controlling directed networks with minimum cost has become an emerging branch in the areas of complex networks and control recently. In this paper, we focus on this minimum cost control problem subject to two types of boundary constraints, namely, trace boundary constraint and orthonormal boundary constraint on the input matrices. First, the minimum cost control problem is formulated as an optimization model for each type of boundary constraint. Next, two iterative algorithms, named as trace-constraint-based projected gradient method and orthonormal-constraint-based projected gradient method, are proposed to solve the optimal problem, respectively. Then, convergence properties of both algorithms are established. Finally, extensive simulation results show the effectiveness of our methods based on detailed comparisons between the two boundary conditions. We believe the results reveal some interesting physical insights for the optimal control of directed networks.

Delay-Induced Synchronization of Identical Linear Multiagent Systems.

This paper studies a class of fast consensus algorithms for a group of identical multiagent systems each described by the linear state-space model. By using both the current and delayed state information, the proposed delay-induced consensus algorithm is shown to achieve synchronization with a faster convergence speed than the standard one when the eigenvalues of the open-loop system, control parameters, the Laplacian matrix of the network, and the delay satisfy certain conditions. In addition, some sufficient or necessary and sufficient conditions are established to guarantee the closed-loop stability of the delay-induced consensus algorithm, where an extra control parameter on the coupling strength is introduced to adjust the convergence speed of the closed-loop system flexibly. We then show that the delay-induced algorithm is robust to the small intrinsic communication or input delays, i.e., the proposed delay-induced consensus algorithm may also produce a faster convergence speed than the standard one even if there exist small intrinsic communication or input delays. Furthermore, we extend the results from the case of an undirected communication topology to those of a directed communication topology and a switching communication topology. Several simulation examples are presented to illustrate the theoretical results.

Leaderless and leader-following consensus with communication and input delays under a directed network topology.

In this paper, time-domain (Lyapunov theorems) and frequency-domain (the Nyquist stability criterion) approaches are used to study leaderless and leader-following consensus algorithms with communication and input delays under a directed network topology. We consider both the first-order and second-order cases and present stability or boundedness conditions. Several interesting phenomena are analyzed and explained. Simulation results are presented to support the theoretical results.