The paper presents a distributed hierarchic control design solving a formations problem in three dimension. The agents are modelled as thrust-underactuated rigid bodies. The class of formations addressed encompasses path following of closed convex paths with shape, size, orientation, relative displacements and relative agents' on-path angular positions all seen as formation parameters. This problem can be seen as a generalization of circular formation problems which acquired particular attention in the field of multi-agents, and the agents model used is one that usually models certain unmanned aerial vehicles and other autonomous vehicles. The solution relies on reduction-based set stabilization where the problem is broken down into simpler nested sub-problems. The results illustrate how addressing complex control problems using hierarchical set stabilization is natural, simplifies the solution, and provides useful properties. The results are illustrated via simulations.

The paper presents the problem of distributing potential games over communication graphs. Suppose a potential game can be designed for a group of agents (players) where each has access to all others' actions (strategies). The paper shows how to design a corresponding potential game for these agents if the full information assumption is replaced with communication over a network depicted by undirected graphs with certain properties. A state-based formulation for potential games is utilized. This provides degrees of freedom to handle the previous information limitation. Notions of Nash's equilibria for the developed game (called here distributed potential game) are presented, and relations between these equilibria and those of the full information game are studied. In part II of the paper learning Nash equilibria for the newly developed game is studied. The development focuses on providing a way to utilize available algorithms of the full information game. The motivation for the results comes from a platoon matching problem for heavy duty vehicles. Utilizing the newly developed distributed game, recent results based on potential games can be extended, providing a basis for an on-the-go strategy where platoon matching on road networks can be solved locally.

In part I of the paper the problem of distributing potential games over undirected graphs was formulated. A restricted information potential game was designed using state-based formulation. Here, learning Nash equilibria for this game is studied. An algorithm is developed with mainly two phases, an estimation phase and a learning phase. The setting allows for available learning methods of the full information game to be directly incorporated in the learning phase. The result matches the outcome (i.e. converges to the same equilibria) of the full information game. In addition, the design takes into account considerations of convergence time, and synchrony of actions update. The developed distributed game and learning algorithm are used to solve a platoon matching problem for heavy duty vehicles. This serves two objectives. First, it provides a motivation for the presented gaming results. Second, the problem addressed can facilitate platoon matching where it provides a basis for an on-the-go strategy. 

The paper addresses circular orbits stabilization for a class of thrust-underactuated satellites, utilizing smooth feedbacks. The problem is first solved in a path-following sense which is pertinent to stabilization of distributed formations. Two orthogonal thrusts are used where, broadly, one is used to stabilize the satellite to the desired orbital plane, and the second is used to stabilize the desired orbit on that plane. Control design follows a five-step hierarchy of stabilizing five nested sets. A main advantage of the approach is its amenability to modification. By redesigning only the last step of the hierarchy, the result is extended to stabilizing time parametrized orbits, i.e. trajectory tracking, and distributed formations of not necessarily co-planar orbits with or without temporal requirements. The results are illustrated through simulations.

The paper presents a hierarchical approach for distributed stabilization of a class of flying formations. The agents are considered as rigid bodies in three-dimensional space. The formation is composed of three aspects: a path following aspect where the agents are required to follow similar smooth Jordan paths that are strictly convex; and two geometric aspects that specify the desired relative displacements of the paths, and the relative positions of the agents on these paths. The solution is based on tools of set stabilization and reduction. The modularity of the approach allows for achieving multiple specifications simultaneously, and for extending, in Part II of this paper, the solution to handle underactuation. The solution is illustrated through simulations, and the relevance of the results in aerial and space vehicles applications is discussed. Copyright

In this paper the flying convex-path-following formations problem (FCxPFF) is solved for two cases of underactuated rigid bodies. In the first case the the rigid bodies have a single degree of underactuation with two thrusts and three torques. In the second, they have two degrees of underactuation with a single thrust. The solution builds on the one developed for fully-actuated agents in Part I of the paper. In addition, the way the solution is tailored for underactuation relies on further utilization of hierarchic set stabilization, and reduction. Additional remarks on the benefits of the approach, and simulation results of the proposed solutions are presented. Copyright