A collisionless singular cucker-smale model with decentralized formation control

Peters, Andr�s A; Choi, Young-Pil; Kalise, Dante; Peszek, Jan

Abstract

We address the design of decentralized feedback control laws inducing consensus and prescribed spatial patterns over a singular interacting particle system of Cucker-Smale type. The control design consists of a feedback term regulating the distance between each agent and pre-assigned subset of neighbours. Such a design represents a multidimensional extension of existing control laws for 1d platoon formation control. For the proposed controller we study consensus emergence, collision-avoidance and formation control features in terms of energy estimates for the closed-loop system. Numerical experiments in 1, 2 and 3 dimensions assess the different features of the proposed design. 1. Introduction. Multi-agent systems (MAS) provide a versatile framework for modelling different challenges arising in Science and Engineering, such as collective animal and human behaviour [46, 47], dynamic networks [39], and autonomous vehicles [5], among many others. From a mathematical viewpoint, MAS are often modelled as large-scale dynamical systems where each agent is represented by a subset of states which are updated via "physical" interaction rules [27, 25] (attraction, repulsion, alignment, synchronization etc.), or by means of a control/game framework [34, 29]. In this work, we are concerned with the design of dynamic interactions and external control laws for nonlinear MAS representing the physical motion of a swarm of agents. Our mathematical modelling is inspired by animal collective dynamics, where large populations of birds and fish normally exhibit self-organization behaviour such as flocking, swarming, milling, and alignment. Other remarkable examples are linked to pedestrian behaviour and to platoons of unmanned aerial vehicles (UAVs). In particular, we are interested in prescribing nonlinear dynamics for the MAS leading to self-organized flocking and trajectories with collision-avoidance features, the latter being a fundamental aspect for a realistic model. The emergence of collision-less flocking behaviour, understood as a configuration in which agents travel with the same constant velocity, is already a complex dynamic equilibrium of interest on its own right. However, a flocking regime does not provide a complete account of the spatial configuration of the swarm, thus limiting its practical interest for applications, such as pedestrian modelling and UAV control. Hence, it is desirable to endow the MAS dynamics with additional forcing terms which can also induce the formation of a given spatial configuration. In this paper, we propose a dynamical MAS model including collisionless flocking, together with a control law inducing a given spatial

Citation

Peters, A. A., Choi, Y., Kalise, D., & Peszek, J. (2019). A collisionless singular cucker-smale model with decentralized formation control. SIAM Journal on Applied Dynamical Systems, 18(4), 1954-1981. https://doi.org/10.1137/19M1241799

• Journal Article Type: Article
• Acceptance Date: Aug 29, 2019
• Online Publication Date: Nov 7, 2019
• Publication Date: Nov 7, 2019
• Deposit Date: Sep 5, 2019
• Publicly Available Date: Sep 12, 2019
• Journal: SIAM Journal of Applied Dynamical Systems
• Print ISSN: 1536-0040
• Electronic ISSN: 1536-0040
• Publisher: Society for Industrial and Applied Mathematics
• Peer Reviewed: Peer Reviewed
• Volume: 18
• Issue: 4
• Pages: 1954-1981
• DOI: https://doi.org/10.1137/19M1241799
• Keywords: Multi-agent systems; decentralized control; flocking; pattern formation AMS subject classifications 34H05; 93A15; 93C10
• Public URL: https://nottingham-repository.worktribe.com/output/2574253
• Publisher URL: https://epubs.siam.org/doi/abs/10.1137/19M1241799