Distributed Control of Robot Swarms: A Lyapunov-Like Barrier Functions Approach

Distributed Control of Robot Swarms: A Lyapunov-Like Barrier Functions Approach

Dimitra Panagou (University of Michigan, USA), Dušan M. Stipanović (University of Illinois, USA) and Petros G. Voulgaris (University of Illinois, USA)
DOI: 10.4018/978-1-4666-9572-6.ch005
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This chapter considers the problem of multi-agent coordination and control under multiple objectives, and presents a set-theoretic formulation which is amenable to Lyapunov-based analysis and control design. A novel class of Lyapunov-like barrier functions is introduced and used to encode multiple control objectives, such as collision avoidance, proximity maintenance and convergence to desired destinations. The construction is based on recentered barrier functions and on maximum approximation functions. Thus, a single Lyapunov-like function is used to encode the constrained set of each agent, yielding simple, gradient-based control solutions. The derived control strategies are distributed, i.e., based on information locally available to each agent, which is dictated by sensing and communication limitations. The proposed coordination protocol dictates semi-cooperative conflict resolution among agents, as well as conflict resolution with respect to an agent (the leader) which is not actively participating in collision avoidance, except when necessary. The considered scenario is pertinent to surveillance tasks and involves nonholonomic vehicles. The efficacy of the approach is demonstrated through simulation results.
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Multi-agent systems have seen increased interest during the past decade, in part due to their relevance to many research domains and real world applications, from large-scale systems, such as power and transportation networks, to complex dynamical systems and multi-vehicle networks. Depending on the global and local/individual objectives, various distributed coordination and control problems have been introduced, namely consensus (also seen as agreement/synchronization/rendezvous), formation, distributed optimization and distributed estimation; for a recent survey on the related topics the reader is referred to Ren, W., & Cao, Y. (2011).

The main concerns when coordinating the motions of multi-vehicle or multi-robot (the terms are used interchangeably) teams include inter-agent collision avoidance, convergence to spatial destinations/regions or tracking of reference trajectories, maintenance of information exchange among agents and avoidance of physical obstacles. Such objectives are encountered in flocking (Jadbabaie, A., & Lin, J., & Morse, A. S. (2003), Tanner, H. G. (2004), Olfati-Saber, R. (2006), Tanner, H. G., Jadbabaie, A., & Pappas, G. J. (2007), Sharma, B., Vanualailai, J., & Chand, U. (2009), Su, H., Wang, X., & Lin, Z. (2009)), and in consensus, rendezvous and/or formation control (Ji, M., & Egerstedt, M. (2007), Olfati-Saber, R., Fax, J. A., & Murray, R. M. (2007), Dimarogonas, D. V., & Kyriakopoulos, K. J. (2008a), Dimarogonas, D. V., & Kyriakopoulos, K. J. (2008b), Mastellone, S., Stipanović, D. M., Graunke, C. R., Intlekofer, K. A, & Spong, M. W. (2008), Zavlanos, M. M., Egerstedt, M. B., & Pappas, G. J. (2011)). Collision avoidance is an unnegotiable requirement in such problems, and is often addressed with potential function methods and Lyapunov-based analysis. For a recent survey on potential function methods in formation control and similar problems see Hernandez-Martinez, E. G., & Aranda-Bricaire, E. (2011). It is worth mentioning that these contributions do not consider all the aforementioned control objectives. In fact, the algorithmic planning and control design in such cases is, to the best of our knowledge, a very challenging, often intractable problem, and still remains an open issue in many respects.

When it comes to multi-vehicle systems in particular, a common ground may be that multiple agents need to work together in a collaborative fashion in order to achieve one or multiple common goals. Lately there has been significant interest in the deployment of robotic networks (or teams) for exploration, surveillance and patrolling of inaccessible, dangerous or even hostile (indoor and outdoor) environments, such as oil drilling platforms and nuclear reactors, see for instance (Cortes, J., Martínez, S., Karatas, T. & Bullo, F. (2004), Hussein, I. I., & Stipanović, D. M. (2007), Berman, S., Halász, A., Hsieh, M. A., & Kumar, V. (2009), Schwager, M., Slotine, J. J., & Rus, D. (2011), Renzaglia, A., Doitsidis, L., Martinelli, A., & Kosmatopoulos, E. B. (2012), Pasqualetti, F., Franchi, A., & Bullo, F. (2012), Panagou, D., & Kumar, V. (2014)). Based on the assumptions on the agents’ sensing and communication modeling, as well as on the control objectives, various formulations and solutions have appeared ranging from combinatorial motion planning to optimization-based and Lyapunov-based methods. Coordination and control in such cases is naturally dictated by the available patterns on sensing and information sharing, as well as by physical/ environmental constraints and inherent limitations (e.g., motion constraints, obstacles, unmodeled disturbances, input saturations etc). Therefore, the problem of motion planning, coordination and control has been and still remains an active topic of research within both the robotics and control communities. While it is out of the scope of this chapter to provide an overview of the existing methodologies on these topics, the interested reader is referred to Ren, W., & Cao, Y. (2011), Parker, L. E. (2009), and the references therein.

Key Terms in this Chapter

Robot Swarm: A team of autonomous robots which move in a collaborative fashion towards goal destinations (convergence) while staying sufficiently far apart (collision avoidance) and close enough (proximity/connectivity maintenance) in order to exchange information on their states through wireless communication links.

Limited Sensing/Communication: The considered information sharing is based on the following pattern: The leader has access only to its own state, i.e., does not sense or receive any information on the states of the remaining agents, and communicates information to them regarding to their goal destinations. Each follower has access to its own state, measures the position of agents lying in its sensing area, exchanges information on pose and velocity with agents lying in its safety area, and receives information from the leader regarding to its goal destination, as long as the leader lies within an upper bounded distance with respect to the follower.

Leader Agent: The agent which is responsible for guiding the group throughout an obstacle environment, without actively participating in collision avoidance with other agents.

Follower Agent: Any other agent of the team, except for the leader, which needs to move and remain close to its goal destination while avoiding collisions with the other members of the team.

Lyapunov-Like Barrier Function: A positive definite function encoding the safe (constrained) set of each agent in terms of the imposed collision avoidance, proximity and convergence objectives.

Semi-Cooperative Collision Avoidance by Agent j (resp. k): For a pair of agents j , k we say that collision avoidance is semi-cooperative by agent j (resp. k ) if the motion of agent k (resp. agent j ) alone results in a decrease of the inter-agent distance and therefore potential collision, but the motion of agent j (resp. agent k ) contributes towards increasing the distance between agents, achieving hence collision avoidance.

Fully-Cooperative Collision Avoidance: For a pair of agents j , k we say that collision avoidance is fully cooperative if the motion of both agents j , k is such that they both contribute towards increasing their inter-agent distance and hence avoiding each other.

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