Potential game theoretic attitude coordination on the circle: Synchronization and balanced circular formation

Abstract

In this paper we consider potential game theoretic attitude coordination. We especially focus on two ordered configurations: "synchronization" and "balanced circular formation". We first show that both problems constitute potential games by employing some global and individual objective functions, and a learning algorithm called Restrictive Spatial Adaptive Play (RSAP) leads robots to the ordered configurations with high probability even in the presence of mobility constraints. We moreover show that the problem also constitutes a group-based potential game and convergence of distribution of actions to stationary one can be accelerated. Finally, the effectiveness of the schemes is demonstrated by simulation and experiments on a testbed.

Hierarchic distributed stabilization of a class of three‐dimensional formations for underactuated agents

“…Under the assumptions of Theorem 1, the feedbacks (7), with constant k i f , where the functions u i ( ), w i 2 ( ) and w i 3 ( ) are given in (19), (21), and (22), respectively, with i ( ), i ( ), andû i (b 1 ) as in (23), (25) and (28), and w i 1 ( ) any C 1 uniformly bounded functions. solve C x PFF for fully actuated agents, rendering Γ ′ asymptotically stable, where…”

“…Numerous methods and different instances of the circular formation problem can be found in literature. Common approaches include optimization methods [18], virtual structure control [], model predictive control [20], artificial potential functions [21], leader follower approach [22], and game theory [23]. Cyclic pursuit was studied in [24], Lyapunov guidance vector field was used in [25] for circular orbit stabilization for unmanned aerial vehicles (UAVs), and in [26] circular formations were stabilized using modified Kuramoto model.…”

Fast convergence in semi-anonymous potential games

“…Game theoretic learning algorithms have gained traction as a design tool for distributed control systems [9], [11], [18], [24], [26]. Here, a static game is repeated over time, and agents revise their strategies based on their objective functions and on observations of other agents' behavior.…”

Coarse resistance tree methods for stochastic stability analysis

“…Regular perturbed processes have been used in the social sciences to model natural human tendencies, e.g., mistakes or exploration versus experimentation tradeoff [1], [3], [12]- [14], [21], [27]. In engineering systems, regular perturbed processes have been used to prescribe distributed decision making laws that guarantee desired equilibrium selection [2], [7], [9], [15], [17], [26], [28], [29]. For example, [28] introduces a distributed learning algorithm which is modeled as a regularly perturbed process that guarantees convergence to a pure Nash equilibrium in virtually any game where such an equilibrium exists.…”