Recent advances in sensing, communication, and computing technologies have enabled the use of multirobot systems for practical applications such as surveillance, area mapping, and search and rescue. For such systems, a major challenge is to design decision rules that are real-time-implementable, require local information only, and guarantee some desired global performance. Distributed optimization provides a framework for designing such local decision-making rules for multirobot systems. In this article, we present a collection of selected results for distributed optimization for robot networks. We will focus on two special classes of problems: 1) real-time path planning for multirobot systems and 2) self-organization in multirobot systems using game-theoretic approaches. For multirobot path planning, we will present some recent approaches that are based on approximately solving distributed optimization problems over continuous and discrete domains of actions. The main idea underlying these approaches is that a variety of path planning problems can be formulated as convex optimization and submodular minimization problems over continuous and discrete action spaces, respectively. To generate local update rules that are efficiently implementable in real time, these approaches rely on approximate solutions to the global problems that can still guarantee some level of desired global performance. For game-theoretic self-organization, we will present a sampling of results for area coverage and real-time target assignment. In these results, the problems are formulated as games, and online updating rules are designed to enable teams of robots to achieve the collective objective in a distributed manner.

We present a complete design and implementation of a system that consists of multiple quadrotors playing capture the flag game. Our main contributions in this work include a custom built quadrotor platform, an efficient implementation of a distributed trajectory planning algorithm, and a WiFi based communication infrastructure. In our design, we equip the quadrotors with autopilot modules for low level control. Moreover, we install low power computing modules for implementing the distributed trajectory planning algorithm online. Furthermore, we develop a communication infrastructure to enable coordination among the quadrotors, which is required for computing a suboptimal control action in real time. The interactions among all the hardware and software components are managed at a higher level by Robot Operating System (ROS). To test the performance of the system, we select a motivating setup of capture the flag game, which is an adversarial game played between two teams of agents called attack and defense. The system is initially simulated in the Gazebo robot simulator with software in the loop. Finally, the complete system is tested and the flight testing results are presented.

In this paper we investigate how power consumption affects mobility-based coordination algorithms for multi-robot systems by explicitly coupling the control laws to the available power levels. In particular, we will consider a sensor network comprising of mobile sensors which use omni directional RF or radar based antennas for communication, with a disk-shaped communications footprint. As power decrease with time, the footprint shrinks as well, and in this paper we propose a controller that solves the rendezvous problem for such systems, thus providing a novel coupling between mobility algorithms and the available power levels.