On global convergence of area-constrained formations of hierarchical multi-agent systems

This paper is concerned with a formation shaping problem for point agents in a two-dimensional space, where control avoids the possibility of reflection ambiguities. One solution for this type of problems was given first for three or four agents by considering a potential function which consists of both the distance error and the signed area terms. Then, by exploiting a hierarchical control strategy with such potential functions, the method was extended to any number of agents recently. However, a specific gain on the signed area term must be employed there, and it does not guarantee the global convergence. To overcome this issue, this paper provides a necessary and sufficient condition for the global convergence, subject to the constraint that the desired formation consists of isosceles triangles only. This clarifies the admissible range of the gain on the signed area for this case. In addition, as for formations consisting of arbitrary triangles, it is shown when high gain on the signed area is admissible for global convergence.Comment: Accepted in the 59th IEEE Conference on Decision and Control (CDC 2020). arXiv admin note: text overlap with arXiv:1808.0031

The massive multiple system HD 64315

The O6 Vn star HD 64315 is believed to belong to the star-forming region known as NGC 2467, but previous distance estimates do not support this association. We explore the multiple nature of this star with the aim of determining its distance, and understanding its connection to NGC 2467. A total of 52 high-resolution spectra have been gathered over a decade. We use their analysis, in combination with the photometric data from All Sky Automated Survey and Hipparcos catalogues, to conclude that HD 64315 is composed of at least two spectroscopic binaries, one of which is an eclipsing binary. HD 64315 contains two binary systems, one of which is an eclipsing binary. The two binaries are separated by 0.09 arcsec (or 500 AU) if the most likely distance to the system, around 5 kpc, is considered. The presence of fainter companions is not excluded by current observations. The non-eclipsing binary (HD 64315 AaAb) has a period of 2.70962901+/-0.00000021 d. Its components are hotter than those of the eclipsing binary, and dominate the appearance of the system. The eclipsing binary (HD 64315 BaBb) has a shorter period of 1.0189569+/-0.0000008 d. We derive masses of 14.6+-2.3 M$_\odot$ for both components of the BaBb system. They are almost identical; both stars are overfilling their respective Roche lobes, and share a common envelope in an overcontact configuration. The non-eclipsing binary is a detached system composed of two stars with spectral types around O6 V with minimum masses of 10.8 M$_\odot$ and 10.2 M$_\odot$, and likely masses aprox. 30 M$_\odot$. HD 64315 provides a cautionary tale about high-mass star isolation and multiplicity. Its total mass is likely above 90 M$_\odot$,but it seems to have formed without an accompanying cluster. It contains one the most massive overcontact binaries known, a likely merger progenitor in a very wide multiple system.Comment: 14 pages, 13 figures, 8 Table

Distance-Based Formation Control of Multi-Agent Systems

This Ph.D. dissertation studies the distance-based formation control of multi-agent systems. A new approach to the distance-based formation control problem is proposed in this thesis. We formulated distance-based formation in a nonlinear optimal control framework and used the state-dependent Riccati equation (SDRE) technique as the primary tool for solving the optimal control problem. In general, a distance-based formation can be undirected, where distance constraints between pairs of agents are actively controlled by both adjacent agents, or directed, where just one of the neighboring agents is responsible for maintaining the desired distance. This thesis presents both, undirected and directed formations, and provides extensive simulations to verify the theoretical results. For undirected topologies, we studied the formation control problem where we showed that the proposed control law results in the global asymptotic stability of the closed-loop system under certain conditions. The formation tracking problem was studied, and the uniform ultimate boundedness of the solutions is rigorously proven. The proposed method guarantees collision avoidance among neighboring agents and prevents depletion of the agents' energy. In the directed distance-based formation control case, we developed a distributed, hierarchical control scheme for a particular class of directed graphs, namely directed triangulated and trilateral Laman graphs. The proposed controller ensures the global asymptotic stability of the desired formation. Rigorous stability analyses are carried out in all cases. Moreover, we addressed the flip-ambiguity issue by using the signed area and signed volume constraints. Additionally, we introduced a performance index for a formation mission that can indicate the controller's overall performance. We also studied the distance-based formation control of nonlinear agents. We proposed a method that can guarantee asymptotic stability of the distance-based formation for a broad category of nonlinear systems. Furthermore, we studied a distance-based formation control of uncertain nonlinear agents. Based on the combination of integral sliding mode control (ISMC) theory with the SDRE method, we developed a robust optimal formation control scheme that guarantees asymptotic stability of the desired distance-based formation in the presence of bounded uncertainties. We have shown that the proposed controller can compensate for the effect of uncertainties in individual agents on the overall formation

Swarm Robotics

Collectively working robot teams can solve a problem more efficiently than a single robot, while also providing robustness and flexibility to the group. Swarm robotics model is a key component of a cooperative algorithm that controls the behaviors and interactions of all individuals. The robots in the swarm should have some basic functions, such as sensing, communicating, and monitoring, and satisfy the following properties

Particle Swarm Optimization

Particle swarm optimization (PSO) is a population based stochastic optimization technique influenced by the social behavior of bird flocking or fish schooling.PSO shares many similarities with evolutionary computation techniques such as Genetic Algorithms (GA). The system is initialized with a population of random solutions and searches for optima by updating generations. However, unlike GA, PSO has no evolution operators such as crossover and mutation. In PSO, the potential solutions, called particles, fly through the problem space by following the current optimum particles. This book represents the contributions of the top researchers in this field and will serve as a valuable tool for professionals in this interdisciplinary field

Malignant melanoma of the urethra: a rare histologic subdivision of vulvar cancer with a poor prognosis

Malignant melanoma of the urethra is a rare tumour that is difficult to diagnose and treat, resulting in a poor prognosis. In this paper, we present the case of a 65-year-old woman who was referred to a gynaecologist because of a urethral mass that mimicked a caruncle. The tumour was removed by local excision, and a pathological analysis revealed a malignant melanoma. Distal urethrectomy was performed after three months with no evidence of residual tumour. There was no evidence of disease at a six-year followup. In this paper, we compare the epidemiology, treatment, staging, and prognosis of vulvar cancer in general to malignant melanoma of the vulva in particular