A constructive differential game approach to collision avoidance in multi-agent systems

Abstract

The problem of steering a team of agents from their initial positions to a predefined end-configuration while avoiding collisions is formulated as a differential game. A method for approximating the solution of the differential game is then presented, providing -Nash strategies. It is shown that approximate solutions are sufficient to guarantee that the task of reaching the final configuration while avoiding collisions is achieved. The theory is illustrated by simulations.

Approximate optimal monitoring

“…Herein, similarly to what has been done in [12], collision avoidance is included directly in the formulation of the optimal control problem. The problem of collision avoidance can then be dealt with by adding the collision avoidance function (7) to the integrand of (6) and defining the optimal control problem as follows.…”

A differential game approach to urban drainage systems control

“…Differential game (DG) theory [3] gives a natural extension of optimal control to scenarios with multiple controllers that are optimizing its own performance criteria [18], and thus its framework is well suited for optimizationbased distributed control applications. This type of games have been used in the literature to solve problems related to the formation control of mobile robots [13], problems related to demand response in power grids [11], and the control of surge tanks [10].…”

“…The main contribution of this paper is the design of a distributed control methodology based on DGs, in the same spirit as in [13], [18], [17], which seeks to determine the optimal behavior of each active element of the UDS by using a consensus-like algorithm, only using local information of the network. The proposed methodology has the advantages of optimization-based techniques used for the control of UDS, e.g., MPC, as well as the ability to have distributed information on the controllers.…”

Towards a systematic solution for differential games with limited communication

“…For example, game theory and differential games have traditionally played an important role in applications related to military and defense, and economics [4], [5]. Differential games play a role, either as an analysis or design tool, in a variety of other areas, such as biological systems [6]- [9], power systems [10]- [13] and multi-agent systems [14], [15] to mention just a few. Moreover, for the special case in which there is only one player, a differential game boils down to a standard optimal control problem, see for example [16].…”