Circular formation control of fixed-wing UAVs with constant speeds

Marina, Héctor García de; Sun, Zhiyong; Bronz, Murat; Hattenberger, Gautier

doi:10.1109/iros.2017.8206422

Cited by 28 publications

(29 citation statements)

References 37 publications

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“…Lemma 3: The zero vector 0 ∈ R n−1 is a regular value of the C 2 function e in (6), and hence the desired path P is a C 2 embedded submanifold 4 in R n .…”

Section: B General Guiding Vector Fieldmentioning

confidence: 99%

Singularity-Free Guiding Vector Field for Robot Navigation

et al. 2021

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In robot navigation tasks, such as unmanned aerial vehicle (UAV) highway traffic monitoring, it is important for a mobile robot to follow a specified desired path. However, most of the existing path-following navigation algorithms cannot guarantee global convergence to desired paths or enable following self-intersected desired paths due to the existence of singular points where navigation algorithms return unreliable or even no solutions. One typical example arises in vector-field guided path-following (VF-PF) navigation algorithms. These algorithms are based on a vector field, and the singular points are exactly where the vector field diminishes. Conventional VF-PF algorithms generate a vector field of the same dimensions as those of the space where the desired path lives. In this article, we show that it is mathematically impossible for conventional VF-PF algorithms to achieve global convergence to desired paths that are self-intersected or even just simple closed (precisely, homeomorphic to the unit circle). Motivated by this new impossibility result, we propose a novel method to transform selfintersected or simple closed desired paths to nonself-intersected and unbounded (precisely, homeomorphic to the real line) counterparts in a higher dimensional space. Corresponding to this new desired path, we construct a singularity-free guiding vector field on a higher dimensional space. The integral curves of this new guiding vector field is thus exploited to enable global convergence to the higher dimensional desired path, and therefore the projection of the integral curves on a lower dimensional subspace converge to the physical (lower dimensional) desired path. Rigorous theoretical analysis is carried out for the theoretical results using dynamical systems theory. In addition, we show both by theoretical analysis and numerical simulations that our proposed method is an extension combining conventional VF-PF algorithms and trajectory tracking Manuscript

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“…Lemma 3: The zero vector 0 ∈ R n−1 is a regular value of the C 2 function e in (6), and hence the desired path P is a C 2 embedded submanifold 4 in R n .…”

Section: B General Guiding Vector Fieldmentioning

confidence: 99%

Singularity-Free Guiding Vector Field for Robot Navigation

et al. 2021

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“…To hold a formation, the MAVs must hold a relative position or distance between given neighbors, such that they can move as one unit through space. See, for instance, the works of Quintero et al ( 2013 ), Schiano et al ( 2016 ), de Marina et al ( 2017 ), Yuan et al ( 2017 ), and de Marina and Smeur ( 2019 ). One advantage of flying in formation for MAV swarms is their predictability during operations.…”

Section: Swarm-level Controlmentioning

confidence: 99%

A Survey on Swarming With Micro Air Vehicles: Fundamental Challenges and Constraints

et al. 2020

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This work presents a review and discussion of the challenges that must be solved in order to successfully develop swarms of Micro Air Vehicles (MAVs) for real world operations. From the discussion, we extract constraints and links that relate the local level MAV capabilities to the global operations of the swarm. These should be taken into account when designing swarm behaviors in order to maximize the utility of the group. At the lowest level, each MAV should operate safely. Robustness is often hailed as a pillar of swarm robotics, and a minimum level of local reliability is needed for it to propagate to the global level. An MAV must be capable of autonomous navigation within an environment with sufficient trustworthiness before the system can be scaled up. Once the operations of the single MAV are sufficiently secured for a task, the subsequent challenge is to allow the MAVs to sense one another within a neighborhood of interest. Relative localization of neighbors is a fundamental part of self-organizing robotic systems, enabling behaviors ranging from basic relative collision avoidance to higher level coordination. This ability, at times taken for granted, also must be sufficiently reliable. Moreover, herein lies a constraint: the design choice of the relative localization sensor has a direct link to the behaviors that the swarm can (and should) perform. Vision-based systems, for instance, force MAVs to fly within the field of view of their camera. Range or communication-based solutions, alternatively, provide omni-directional relative localization, yet can be victim to unobservable conditions under certain flight behaviors, such as parallel flight, and require constant relative excitation. At the swarm level, the final outcome is thus intrinsically influenced by the on-board abilities and sensors of the individual. The real-world behavior and operations of an MAV swarm intrinsically follow in a bottom-up fashion as a result of the local level limitations in cognition, relative knowledge, communication, power, and safety. Taking these local limitations into account when designing a global swarm behavior is key in order to take full advantage of the system, enabling local limitations to become true strengths of the swarm.

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“…For example, we can modify the nominal guiding vector field (5) in a minimally invasive way using safety barrier certificates [49], [50]. Specifically, we add an extra term u col i ∈ R n+1 to the vector field in (5), and this term is calculated by a quadratic program min u col i (t) 2 subject to the constraintsḂ ij (ξ i , ξ j ) ≤ 1/B ij (ξ i , ξ j ) for j = i and i, j ∈ Z N 1 , where B ij (ξ i , ξ j ) is a control barrier function [51] (e.g., B ij (ξ i , ξ j ) = 1/( p i − p j 2 − R 2 ), where p i is the physical position and R is the safe distance between robots). The collision avoidance behavior is shown in the supplementary video, but the theoretical analysis is left for future work.…”

Section: Convergence Analysismentioning

confidence: 99%

“…In this experiment, two autonomous fixed-wing aircraft (i.e., Autonomous Opterra 1.2m) similar to [5], [57] are employed to validate Theorem 2. The aircraft are equipped with the opensource software/hardware project Paparazzi [58].…”

Section: B Flights With Fixed-wing Aircraftmentioning

confidence: 99%

Robotic Path Following in 3D Using a Guiding Vector Field

Yao

Kapitanyuk

Cao

2018

2018 IEEE Conference on Decision and Control (CDC)

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It is essential in many applications to impose a scalable coordinated motion control on a large group of mobile robots, which is efficient in tasks requiring repetitive execution, such as environmental monitoring. In this paper, we design a guiding vector field to guide multiple robots to follow possibly different desired paths while coordinating their motions. The vector field uses a path parameter as a virtual coordinate that is communicated among neighboring robots. Then, the virtual coordinate is utilized to control the relative parametric displacement between robots along the paths. This enables us to design a saturated control algorithm for a Dubins-car-like model. The algorithm is distributed, scalable, and applicable for any smooth paths in an n-dimensional configuration space, and global convergence is guaranteed. Simulations with up to fifty robots and outdoor experiments with fixed-wing aircraft validate the theoretical results.

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Circular formation control of fixed-wing UAVs with constant speeds

Cited by 28 publications

References 37 publications

Singularity-Free Guiding Vector Field for Robot Navigation

Singularity-Free Guiding Vector Field for Robot Navigation

A Survey on Swarming With Micro Air Vehicles: Fundamental Challenges and Constraints

Robotic Path Following in 3D Using a Guiding Vector Field

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