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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.

This article studies the constrained optimization problem of integrator chain multiagent systems from the distributed perspective. Particularly, all the agents collaborate to find an optimal solution of a global objective function summed by multiple local ones, each of which is just convex and belongs to an individual agent. However, the potential optimal solutions are simultaneously subject to set constraints and two kinds of equality constraints, i.e., individual equality constraint and aggregate equality constraint, whereas their involved constraint parameters are privately available to individual agents. With a proper coordinate transformation, a distributed optimization protocol is synthesized by introducing proper internal dynamics. Under the Lyapunov framework, it is shown with a convex theory that the synthesized distributed protocol enables the multiagent system to achieve the concerned constrained optimization objective. An example is finally given to confirm the optimization effectiveness.

This article studies the distributed constrained optimization problems for the discrete-time second-order multiagent systems (MASs), in which each agent privately owns local cost function and nonidentical convex set constraints. To solve this problem, a projection-based distributed event-triggered algorithm is developed via the constant step-sizes, which achieves an ergodic convergence rate $O(1/k)$ for the general convex functions. By applying the event-triggered mechanism, the proposed algorithm can avoid unnecessary communication among the agents. Moreover, it is shown that the introduced event-triggered component does not sacrifice the convergence rate. Finally, a simulation example is carried out to demonstrate the theoretical results.

This paper presents an efficient and accurate range-aided visual-inertial odometry (RVIO) system for the global positioning system denied environment. In particular, the ultra-wideband (UWB) measurements are integrated to reduce the long-term drift of the visual-inertial odometry (VIO) system. Our approach starts with a filter-based scheme to localize the unknown UWB anchor in the local world frame. In particular, a novel surface-based particle filter is proposed to localize the UWB anchors efficiently. When the initialization is complete, the UWB location information is utilized to support the subsequent long-term robot positioning. An observability-constrained optimization approach is developed to combine the visual, inertial, and UWB range measurements. Such a framework takes advantage of both VIO and UWB measurements and is feasible even when the number of observed UWB anchors is below four. Experiments on both simulated and real-world scenes demonstrate the validity and superiority of the proposed system.

In this article, the joint estimation of state and noise covariance for linear systems with unknown covariance of multiplicative noise is considered. The measurement likelihood is modeled as a mixture of two Gaussian distributions and a Student's t distribution, respectively. The unknown covariance of multiplicative noise is modeled as an inverse Gamma/Wishart distribution and the initial condition is formulated as the nominal covariance. By using robust design and choosing hierarchical priors, two variational Bayesian-based robust Kalman filters are proposed. The stability and convergence of the proposed filters and the covariance parameters are analyzed. The lower and upper bounds are also provided to guarantee the performance of the proposed filters. A target tracking simulation is provided to validate the effectiveness of the proposed filters.

The autonomous flight of unmanned aerial vehicles (UAVs) relies on a precise and robust geo-localization system. A visual geo-localization system registers the aerial captured image to a geo-referenced satellite map, which enables UAVs to determine their global position without a global navigation satellite system (GNSS). However, it is challenging to achieve precise and robust geo-localization in a large-scale environment due to the notable texture difference between the satellite map and the UAV-captured image. In this article, we design a robust visual geo-localization pipeline that integrates a proposed deep learning-based imagery feature. This pipeline starts with the image retrieval based on the deep feature encoding, to initialize the localization process over large-scale maps without any location prior. With the reuse of the same deep imagery feature, an image registration process enables real-time sequential localization. Besides, the proposed system has the re-localization ability to eliminate the localization drift caused by possible registration failure, especially during long-time flights. Evaluations of datasets and real-world experiments demonstrate that the proposed system is more robust and accurate than other state-of-the-art methods. To encourage further progress on the visual geo-localization problem, our code and materials are publicly available at https://github.com/hmf21/UAVLocalization.

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.

This article proposes three distributed algorithms for solving linear algebraic equations to seek a least-squares (LS) solution via multiagent networks. We consider that each agent has only access to a small and incomplete block of linear equations rather than the complete row or column in the existing results. First, we focus on the case of a homogeneous partition of linear equations. A distributed algorithm is proposed via a single-layered grid network, in which each agent only needs to control three scalar states. Second, we consider the case of heterogeneous partitions of linear equations. Two distributed algorithms with a doubled-layered network are developed, which allow each agent's states to have different dimensions and can be applied to heterogeneous agents with different storage and computation capabilities. Rigorous proofs show that the proposed distributed algorithms collaboratively obtain an LS solution with exponential convergence and also own a solvability verification property, i.e., a criterion to verify whether the obtained solution is an exact solution. Finally, some simulation examples are provided to demonstrate the effectiveness of the proposed algorithms.

This article develops a unified distributed method for solving two classes of constrained networked optimization problems, i.e., optimal consensus problem and resource allocation problem with nonidentical set constraints. We first transform these two constrained networked optimization problems into a unified saddle-point problem framework with set constraints. Subsequently, two projection-based primal–dual algorithms via optimistic gradient descent ascent method and extra-gradient method are developed for solving constrained saddle-point problems. It is shown that the developed algorithms achieve exact convergence to a saddle point with an ergodic convergence rate $O(1/k)$ for general convex–concave functions. Based on the proposed primal-dual algorithms via saddle-point dynamics, we develop unified distributed algorithm design and convergence analysis for these two networked optimization problems. Finally, two numerical examples are presented to demonstrate the theoretical results.

This article studies a class of distributed nonsmooth convex optimization problems subject to local set constraints and coupled nonlinear inequality constraints. In particular, each local objective function consists of one differentiable convex function and multiple nonsmooth convex functions. By applying multiple proximal splittings and derivative feedback techniques, a new distributed continuous-time multiproximal algorithm is developed, whose dynamics satisfies Lipschitz continuity even if the considered problem is nonsmooth. Compared with previous results that rely on either the differentiability or strong convexity of local objective functions, the proposed algorithm can be applied to more general functions, which are only convex and not necessarily smooth. Moreover, in contrast to some results that require some specific initial conditions, the developed algorithm is free of initialization. The convergence analysis of the proposed algorithm is conducted by applying Lyapunov stability theory. It is shown that the states of all the agents achieve consensus at an optimal solution. Finally, a numerical example is presented to demonstrate the effectiveness of the proposed algorithm.

This article investigates the noncooperative game of multiple clusters composed by double-integrator agents subject to set constraints. In particular, by decomposing each cluster cost function into multiple individual ones and allocating them to respective agents, the generalized Nash equilibrium (GNE) associated with the upper cluster layer is sought by the lower agent layer in terms of a hierarchical structure. A particular agent in each cluster is appointed as the messenger that is specialized in interacting with adjacent messengers from other clusters. It is first shown that the concerned seeking objective is achieved provided that the agents from the same cluster reach a consensus on their corresponding component of the GNE. Motivated by this consensus idea, a distributed seeking strategy through the intracluster interaction is first developed, which is applicable to the case where each agent has access to the information of the messengers from other clusters. Based on this result, we next consider a relaxed case where the messenger information is absent for each agent and the inter-cluster information interaction is only allowed via their messengers. Another distributed seeking strategy resorting to a distributed observer is developed via both the inter- and intra-cluster interactions. It is shown that both the developed distributed seeking strategies are capable of seeking out the concerned GNE. As extensions to the double-integrator model, we further consider two evolved models, i.e., Euler–Lagrange model and multi-integrator model. Two modified distributed seeking strategies are developed for achieving the concerned NE seeking objective. Finally, the effectiveness of the developed distributed seeking strategies is validated by an application.

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.

This article studies the bearing-based distributed formation control problem of a group of vertical take-off and landing unmanned aerial vehicles subject to unknown disturbances. Both cases of constant and time-varying velocity leaders are considered and two distributed formation control algorithms are developed based on a hierarchical framework. More precisely, two bearing-based distributed commanded forces are, respectively, proposed to achieve the target formation maneuver. Then, a unified adaptive hybrid attitude control law is designed such that the command attitude, which is extracted from the command force, can be tracked globally. In addition, three auxiliary systems are proposed to guarantee the boundedness of the thrust, to avoid the singular problem of command attitude extraction, to obviate the usage of the acceleration information, and compensate the adverse of the disturbance. Globally, the asymptotic stability of the closed-loop system is proved through Lyapunov stable theory. It is shown that the prescribed formation control objective is achieved. Finally, simulation results are provided to validate the performance of the proposed control algorithms.

This article investigates the leader-following attitude tracking control problem of multiple rigid body systems in the presence of uncertain parameters and disturbances. The communication constraint is considered that only a subset of followers have access to the leader, and a quaternion-based nonlinear hybrid distributed observer is first proposed to estimate the leader's trajectory for each follower. In particular, the proposed distributed attitude observer always evolves on the 3-D unit sphere $\mathbb {S}^{3}$. This property guarantees the feasibility of the observer-based distributed control scheme, since the separation principle is satisfied. By incorporating a hysteresis-based switch of a binary logic variable for each pair of neighboring rigid bodies, the proposed hybrid distributed observer achieves the global asymptotic stability for any initial attitude and avoids the unwinding phenomenon. Next, an observer-based attitude tracking control law is developed by combining adaptive technique and hybrid theory, which does not require precise model information and has good robustness to the disturbances. In addition, it is shown that the attitude tracking errors converge to the origin globally asymptotically. Finally, simulation results are provided to validate the theoretical results.

There are two main trends in the development of unmanned aerial vehicle (UAV) technologies: miniaturization and intellectualization, in which realizing object tracking capabilities for a nano-scale UAV is one of the most challenging problems. In this paper, we present a visual object tracking and servoing control system utilizing a tailor-made 38 g nano-scale quadrotor. A lightweight visual module is integrated to enable object tracking capabilities, and a micro positioning deck is mounted to provide accurate pose estimation. In order to be robust against object appearance variations, a novel object tracking algorithm, denoted by RMCTer, is proposed, which integrates a powerful short-term tracking module and an efficient long-term processing module. In particular, the long-term processing module can provide additional object information and modify the short-term tracking model in a timely manner. Furthermore, a position-based visual servoing control method is proposed for the quadrotor, where an adaptive tracking controller is designed by leveraging backstepping and adaptive techniques. Stable and accurate object tracking is achieved even under disturbances. Experimental results are presented to demonstrate the high accuracy and stability of the whole tracking system.

This article studies a distributed constrained optimization problem of multiple agents characterized by Euler–Lagrange systems with unknown inertial parameters. The optimization objective is to compute a feasible solution within the intersection of a series of constrained sets such that a global payoff function summed by a group of local ones is minimized. Meanwhile, each local payoff function and constrained set are just privately available to their respective agent. To accomplish the concerned constrained optimization objective, a fully distributed continuous-time algorithm resorting to a projection-based auxiliary dynamics is synthesized without using global topology information. The proposed distributed optimization algorithm is privacy-preserving in the sense that no actual state information is exchanged between distinct agents during the seeking progress. Besides, the associated stability analysis is carried out in terms of the Lyapunov theorem. Finally, a source localization example is performed to verify the effectiveness of the proposed distributed optimization algorithm.

This paper presents a robust visual simultaneous localization and mapping (SLAM) system that leverages point and structural line features in dynamic man-made environments. Manhanttan world assumption is considered and the structural line features in such man-made environments provide rich geometric constraint, e.g., parallelism. Such a geometric constraint can be therefore used to rectify 3D maplines after initialization. To cope with dynamic scenarios, the proposed system are divided into four main threads including 2D dynamic object tracking, visual odometry, local mapping and loop closing. The 2D tracker is responsible to track the object and capture the moving object in bounding boxes. In such a case, the dynamic background can be excluded and the outlier point and line features can be effectively removed. To parameterize 3D lines, we use Plückerline coordinates in initialization and projection processes, and utilize the orthonormal representation in unconstrained graph optimization process. The proposed system has been evaluated in both benchmark datasets and real-world scenarios, which reveals a more robust performance in most of the experiments compared with the existing state-of-the-art methods.

A typical formation shape control problem involves point agents sensing relative positions, that is, orientations and distances, of their neighbors and then moving so that these relative positions achieve some prespecified values. Such a procedure, requiring as it does sensing of orientations, implicitly presupposes that all agents have a shared understanding of the common orientations. On the other hand, there may be biases in sensors, variations in the earth's magnetic field interfering with compass-based sensing, or drift in inertial sensors, with the result that orientations are inconsistently measured or measured with error. In this paper, we investigate the formation control problem with mismatched coordinates in the 3-D space, considering the consequences of this error. First, the situation of a two-agent formation is considered. We show that the agents converge to a fixed but distorted formation exponentially fast. In contrast to the matched case, the formation is not asymptotically stationary, but rather instead translates with a certain constant velocity depending on the mismatches. The formation distortion between the actual one and the desired one is obtained, as well as the steady-state velocity of the formation for small mismatch orientations. The case of agents with double integrator dynamics is then considered and similar phenomena are observed. Based on the results, an estimation algorithm is given to obtain the mismatch rotation matrix, which allows a compensation algorithm to be proposed such that the desired formation is achieved with zero steady-state velocity for the formation as a whole. The case of n-agent formations is finally considered, first with a star graph and then with a general graph. Simulations are provided to validate the theoretical results.

Attitude coordinated control of multiple underactuated spacecraft is studied in this paper. We adopt the parametrization proposed by Tsiotras et al. (1995) to describe attitude kinematics, which has been shown to be very convenient for control of underactuated axisymmetric spacecraft with two control torques. We first propose a partial attitude coordinated controller with angular velocity commands. The controller is based on the exchange of each spacecraft's information with local neighbors and a self-damping term. Under a necessary and general connectivity assumption and by use of a novel Lyapunov function, we show that the symmetry axes of all spacecraft are eventually aligned. Full attitude control of multiple underactuated spacecraft is also considered and a discontinuous distributed control algorithm is proposed. It is shown that the proposed algorithm succeeds in achieving stabilization given that control parameters are chosen properly. Discussions on the cases without self damping are also provided for both partial and full attitude controls. Simulations are given to validate the theoretical results and different steady-state behaviors are observed.

This paper studies the containment and group dispersion control for a multi-robot system in the presence of dynamic leaders. Each robot is represented by a doubleintegrator dynamic model and a distributed control algorithm is developed to drive the multi-robot system to follow a group of dynamic leaders with containment and group dispersion behaviors. The effectiveness of the algorithm is then verified on a multi-robot control platform.