A Mean-Field Game Control for Large-Scale Swarm Formation Flight in Dense Environments

As an important part of cyberphysical systems (CPSs), multiple aerial drone systems are widely used in various scenarios, and research scenarios are becoming increasingly complex. However, planning strategies for the formation flying of aerial swarms in dense environments typically lack the capability of large-scale breakthrough because the amount of communication and computation required for swarm control grows exponentially with scale. To address this deficiency, we present a mean-field game (MFG) control-based method that ensures collision-free trajectory generation for the formation flight of a large-scale swarm. In this paper, two types of differentiable mean-field terms are proposed to quantify the overall similarity distance between large-scale 3-D formations and the potential energy value of dense 3-D obstacles, respectively. We then formulate these two terms into a mean-field game control framework, which minimizes energy cost, formation similarity error, and collision penalty under the dynamical constraints, so as to achieve spatiotemporal planning for the desired trajectory. The classical task of a distributed large-scale aerial swarm system is simulated by numerical examples, and the feasibility and effectiveness of our method are verified and analyzed. The comparison with baseline methods shows the advanced nature of our method.

L2-CalSat: A Calibration Satellite for Ultra-Sensitive CMB Polarization Space Missions

In this work, the use of a calibration satellite (L2-CalSat) flying in formation with a Cosmic Microwave Background (CMB) polarization mission in an orbit located at the second Lagrange point, is proposed. The new generation of CMB telescopes are expected to reach unprecedented levels of sensitivity to allow a very precise measurement of the B-mode of polarization, the curl-like polarization component expected from gravitational waves coming from Starobinski inflationary models. Due to the CMB polarized signal weakness, the instruments must be subjected to very precise calibration processes before and after launching. Celestial sources are often used as external references for calibration after launch, but these sources are not perfectly characterized. As a baseline option, L2-CalSat is based on the CubeSat standard and serves as a perfectly known source of a reference signal to reduce polarization measurements uncertainty. A preliminary design of L2-CalSat is described and, according to the scanning strategy followed by the telescope, the influence of the relative position between the spacecrafts in the calibration process is studied. This new calibration element will have a huge impact on the performance of CMB space missions, providing a significant improvement in the measurements accuracy without requiring new and costly technological developments.

Decentralized Mesh-Based Model Predictive Control for Swarms of UAVs

This paper deals with the design of a decentralized guidance and control strategy for a swarm of unmanned aerial vehicles (UAVs), with the objective of maintaining a given connection topology with assigned mutual distances while flying to a target area. In the absence of obstacles, the assigned topology, based on an extended Delaunay triangulation concept, implements regular and connected formation shapes. In the presence of obstacles, this technique is combined with a model predictive control (MPC) that allows forming independent sub-swarms optimizing the formation spreading to avoid obstacles and collisions between neighboring vehicles. A custom numerical simulator was developed in a Matlab/Simulink environment to prove the effectiveness of the proposed guidance and control scheme in several 2D operational scenarios with obstacles of different sizes and increasing number of aircraft.

Relation between travel strategy and social organization of migrating birds with special consideration of formation flight in the northern bald ibis

A considerable proportion of the world's bird species undertake seasonal long-distance migrations. These journeys are energetically demanding. Two major behavioural means to reduce energy expenditure have been suggested: the use of thermal uplifts for a soaring-gliding migration style and travelling in echelon or V-shaped formation. Both strategies have immediate consequences for the social organization of the birds as they either cause large aggregations or require travelling in small and stable groups. Here, we first discuss those consequences, and second present an analysis of formation flight in a flock of northern bald ibis on their first southbound migration. We observe clear correlations between leading and trailing on the dyadic level but only a weak correlation on the individual level during independent flight and no convincing correlation during the human guided part of the migration. This pattern is suggestive of direct reciprocation as a means for establishing cooperation during formation flight. In general, we conclude that behavioural adaptations for dealing with physiological constraints on long-distance migrations either necessitate or ultimately foster formation of social groups with different characteristics. Patterns and social organization of birds travelling in groups have been elusive to study; however, new tracking technology-foremost lightweight GPS units-will provide more insights in the near future.This article is part of the themed issue 'Physiological determinants of social behaviour in animals'.

Matching times of leading and following suggest cooperation through direct reciprocity during V-formation flight in ibis

One conspicuous feature of several larger bird species is their annual migration in V-shaped or echelon formation. When birds are flying in these formations, energy savings can be achieved by using the aerodynamic up-wash produced by the preceding bird. As the leading bird in a formation cannot profit from this up-wash, a social dilemma arises around the question of who is going to fly in front? To investigate how this dilemma is solved, we studied the flight behavior of a flock of juvenile Northern bald ibis (Geronticus eremita) during a human-guided autumn migration. We could show that the amount of time a bird is leading a formation is strongly correlated with the time it can itself profit from flying in the wake of another bird. On the dyadic level, birds match the time they spend in the wake of each other by frequent pairwise switches of the leading position. Taken together, these results suggest that bald ibis cooperate by directly taking turns in leading a formation. On the proximate level, we propose that it is mainly the high number of iterations and the immediacy of reciprocation opportunities that favor direct reciprocation. Finally, we found evidence that the animals' propensity to reciprocate in leading has a substantial influence on the size and cohesion of the flight formations.