Hyo-Sung Ahn

Zhiyong Sun, Myoung-Chul Park, Brian D. O. Anderson et al.

Most rigid formation controllers reported in the literature aim to only stabilize a rigid formation shape, while the formation orientation is not controlled. This paper studies the problem of controlling rigid formations with prescribed orientations in both 2-D and 3-D spaces. The proposed controllers involve the commonly-used gradient descent control for shape stabilization, and an additional term to control the directions of certain relative position vectors associated with certain chosen agents. In this control framework, we show the minimal number of agents which should have knowledge of a global coordinate system (2 agents for a 2-D rigid formation and 3 agents for a 3-D rigid formation), while all other agents do not require any global coordinate knowledge or any coordinate frame alignment to implement the proposed control. The exponential convergence to the desired rigid shape and formation orientation is also proved. Typical simulation examples are shown to support the analysis and performance of the proposed formation controllers.

Mengbin Ye, Minh Hoang Trinh, Young-Hun Lim et al.

In this paper, and inspired by the recent discrete-time model in [1,2], we study two continuous-time opinion dynamics models (Model 1 and Model 2) where the individuals discuss opinions on multiple logically interdependent topics. The logical interdependence between the different topics is captured by a `logic' matrix, which is distinct from the Laplacian matrix capturing interactions between individuals. For each of Model 1 and Model 2, we obtain a necessary and sufficient condition for the network to reach to a consensus on each separate topic. The condition on Model 1 involves a combination of the eigenvalues of the logic matrix and Laplacian matrix, whereas the condition on Model 2 requires only separate conditions on the logic matrix and Laplacian matrix. Further investigations of Model 1 yields two sufficient conditions for consensus, and allow us to conclude that one way to guarantee a consensus is to reduce the rate of interaction between individuals exchanging opinions. By placing further restrictions on the logic matrix, we also establish a set of Laplacian matrices which guarantee consensus for Model 1. The two models are also expanded to include stubborn individuals, who remain attached to their initial opinions. Sufficient conditions are obtained for guaranteeing convergence of the opinion dynamics system, with the final opinions generally being at a persistent disagreement. Simulations are provided to illustrate the results.

Myoung-Chul Park, Zhiyong Sun, Minh Hoang Trinh et al.

In this paper, we propose a distance-based formation control strategy that can enable four mobile agents, which are modelled by a group of single-integrators, to achieve the desired formation shape specified by using six consistent inter-agent distances in a 2-dimensional space. The control law is closely related to a gradient-based control law formed from a potential function reflecting the error between the actual inter-agent distances and the desired inter-agent distances. There are already control strategies achieving the same objective in a distance-based control manner in the literature, but the results do not yet include a global as opposed to local stability analysis. We propose a control strategy modified from the existing gradient-based control law so that we can achieve almost global convergence to the desired formation shape, and the control law uses known properties for an associated formation shape control problem involving a four-agent tetrahedron formation in 3-dimensional space. Simulation results verifying our analysis are also presented.

Hyeonjun Yun, Hyungbo Shim, Hyo-Sung Ahn

This paper considers the economic dispatch problem for a network of power generators and customers. In particular, our aim is to minimize the total generation cost under the power supply-demand balance and the individual generation capacity constraints. This problem is solved in a distributed manner, i.e., a dual gradient-based continuous-time distributed algorithm is proposed in which only a single dual variable is communicated with the neighbors and no private information of the node is disclosed. The proposed algorithm is simple and no specific initialization is necessary, and this in turn allows on-line change of network structure, demand, generation constraints, and even the participating nodes. The algorithm also exhibits a special behavior when the problem becomes infeasible so that each node can detect over-demand or under-demand situation of the power network. Simulation results on IEEE 118 bus system confirm robustness against variations in power grids.

Young-Hun Lim, Hyo-Sung Ahn

This paper consider a standard consensus algorithm under output saturations. In the presence of output saturations, global consensus can not be realized due to the existence of stable, unachievable equilibrium points for the consensus. Therefore, this paper investigates necessary and sufficient initial conditions for the achievement of consensus, that is an exact domain of attraction. Specifically, this paper considers singe-integrator agents with both fixed and time-varying undirected graphs, as well as double-integrator agents with fixed undirected graph. Then, we derive that the consensus will be achieved if and only if the average of the initial states (only velocities for double-integrator agents with homogeneous saturation levels for the outputs) is within the minimum saturation level. An extension to the case of fixed directed graph is also provided in which an weighted average is required to be within the minimum saturation limit.

Seong-Ho Kwon, Hyo-Sung Ahn

This paper discusses generalized weak rigidity theory, and aims to apply the theory to formation control problems with a gradient flow law. The generalized weak rigidity theory is utilized in order that desired formations are characterized by a general set of pure inter-agent distances and angles. As the first result of its applications, the paper provides analysis of locally exponential stability for formation systems with pure distance/angle constraints in the $2$- and $3$-dimensional spaces. Then, as the second result, if there are three agents in the $2$-dimensional space, almost globally exponential stability for formation systems is ensured. Through numerical simulations, the validity of analyses is illustrated.

Seong-Ho Kwon, Minh Hoang Trinh, Koog-Hwan Oh et al.

In this paper, we introduce new concepts of weak rigidity matrix and infinitesimal weak rigidity for planar frameworks. The weak rigidity matrix is used to directly check if a framework is infinitesimally weakly rigid while previous work can check a weak rigidity of a framework indirectly. An infinitesimal weak rigidity framework can be uniquely determined up to a translation and a rotation (and a scaling also when the framework does not include any edge) by its inter-neighbor distances and angles. We apply the new concepts to a three-agent formation control problem with a gradient control law, and prove instability of the control system at any incorrect equilibrium point and convergence to a desired target formation. Also, we propose a modified Henneberg construction, which is a technique to generate minimally rigid (or weakly rigid) graphs. Finally, we extend the concept of the weak rigidity in R^2 to the concept in R^3.

Hyo-Sung Ahn, Kevin L. Moore, Seong-Ho Kwon et al.

This paper presents conditions for establishing topological controllability in undirected networks of diffusively coupled agents. Specifically, controllability is considered based on the signs of the edges (negative, positive or zero). Our approach differs from well-known structural controllability conditions for linear systems or consensus networks, where controllability conditions are based on edge connectivity (i.e., zero or nonzero edges). Our results first provide a process for merging controllable graphs into a larger controllable graph. Then, based on this process, we provide a graph decomposition process for evaluating the topological controllability of a given network.

Yeong-Ung Kim, Hyo-Sung Ahn

In this paper, we develop a distributed algorithm for solving a class of distributed convex optimization problems where the local objective functions can be a general nonsmooth function, and all equalities and inequalities are network-wide coupled. This type of problem arises from many areas, such as economic dispatch, network utility maximization, and demand response. Integrating the decomposition by right hand side allocation and primal-dual methods, the proposed algorithm is able to handle the distributed optimization over networks with time-varying directed graph in fully distributed fashion. This algorithm does not require the communication of sensitive information, such as primal variables, for privacy issues. Further, we show that the proposed algorithm is guaranteed to achieve an $O(1/k)$ rate of convergence in terms of optimality based on duality analysis under the condition that local objective functions are strongly convex but not necessarily differentiable, and the subdifferential of local inequalities is bounded. We simulate the proposed algorithm to demonstrate its remarkable performance.

Tae-Wook Um, Ki-Hyeon Kim, Hyun-Duck Choi et al.

Monocular depth estimation has been increasingly adopted in robotics and autonomous driving for its ability to infer scene geometry from a single camera. In self-supervised monocular depth estimation frameworks, the network jointly generates and exploits depth and pose estimates during training, thereby eliminating the need for depth labels. However, these methods remain challenged by uncertainty in the input data, such as low-texture or dynamic regions, which can cause reduced depth accuracy. To address this, we introduce UM-Depth, a framework that combines motion- and uncertainty-aware refinement to enhance depth accuracy at dynamic object boundaries and in textureless regions. Specifically, we develop a teacherstudent training strategy that embeds uncertainty estimation into both the training pipeline and network architecture, thereby strengthening supervision where photometric signals are weak. Unlike prior motion-aware approaches that incur inference-time overhead and rely on additional labels or auxiliary networks for real-time generation, our method uses optical flow exclusively within the teacher network during training, which eliminating extra labeling demands and any runtime cost. Extensive experiments on the KITTI and Cityscapes datasets demonstrate the effectiveness of our uncertainty-aware refinement. Overall, UM-Depth achieves state-of-the-art results in both self-supervised depth and pose estimation on the KITTI datasets.

Viet Hoang Pham, Hyo-Sung Ahn

Despite the notable success of deep neural networks (DNNs) in solving complex tasks, the training process still remains considerable challenges. A primary obstacle is the substantial time required for training, particularly as high performing DNNs tend to become increasingly deep (characterized by a larger number of hidden layers) and require extensive training datasets. To address these challenges, this paper introduces a distributed training method that integrates two prominent strategies for accelerating deep learning: data parallelism and fully decoupled parallel backpropagation algorithm. By utilizing multiple computational units operating in parallel, the proposed approach enhances the amount of training data processed in each iteration while mitigating locking issues commonly associated with the backpropagation algorithm. These features collectively contribute to significant improvements in training efficiency. The proposed distributed training method is rigorously proven to converge to critical points under certain conditions. Its effectiveness is further demonstrated through empirical evaluations, wherein an DNN is trained to perform classification tasks on the CIFAR-10 dataset.

Shiyu Zhao, Zhiyong Sun, Daniel Zelazo et al.

This paper addresses the problem of constructing bearing rigid networks in arbitrary dimensions. We first show that the bearing rigidity of a network is a generic property that is critically determined by the underlying graph of the network. A new notion termed generic bearing rigidity is defined for graphs. If the underlying graph of a network is generically bearing rigid, then the network is bearing rigid for almost all configurations; otherwise, the network is not bearing rigid for any configuration. As a result, the key to construct bearing rigid networks is to construct generically bearing rigid graphs. The main contribution of this paper is to prove that Laman graphs, which can be generated by the Henneberg construction, are generically bearing rigid in arbitrary dimensions. As a consequence, if the underlying graph of a network is Laman, the network is bearing rigid for almost all configurations in arbitrary dimensions.

Byung-Hun Lee, Hyo-Sung Ahn

In this paper, we propose a novel distributed formation control strategy, which is based on the measurements of relative position of neighbors, with global orientation estimation in 3-dimensional space. Since agents do not share a common reference frame, orientations of the local reference frame are not aligned with each other. Under the orientation estimation law, a rotation matrix that identifies orientation of local frame with respect to a common frame is obtained by auxiliary variables. The proposed strategy includes a combination of global orientation estimation and formation control law. Since orientation of each agent is estimated in the global sense, formation control strategy ensures that the formation globally exponentially converges to the desired formation in 3-dimensional space.