The VFO path-following kinematic controller for robotic vehicles moving in a 3D space

Łakomy, Krzysztof; Michałek, Maciej Marcin

doi:10.1109/romoco.2017.8003923

Cited by 13 publications

(30 citation statements)

References 14 publications

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“…Another type of variants adds time-varying gains or an additional time-varying component [3], [17]. Thus, the vector fields in [5], [7], [16], and [44] can be regarded as 2-D variants of (4), and those in [7], [9], [13], [22], and [45], as 3-D variants of (4). Therefore, the study of the basic vector field in (4) is of great significance.…”

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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Section: B General Guiding Vector Fieldmentioning

confidence: 99%

Singularity-Free Guiding Vector Field for Robot Navigation

et al. 2021

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“…For example, we only assign the vehicle to visit a collection of connected points in the space (a geometric object); thus, we do not concern ourselves when the vehicle visits a specific point of such a geometric object. Guiding vector fields have been widely studied and employed in many different kinds of vehicles [2,3,4,5,6,7].…”

Section: Introductionmentioning

confidence: 99%

Guiding vector fields in Paparazzi autopilot

de Marina,

Bronz,

Hattenberger

2021

Preprint

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This article is a technical report on the two different guidance systems based on vector fields that can be found in Paparazzi, a free sw/hw autopilot. Guiding vector fields allow autonomous vehicles to track paths described by the user mathematically. In particular, we allow two descriptions of the path with an implicit or a parametric function. Each description is associated with its corresponding guiding vector field algorithm. The implementations of the two algorithms are light enough to be run in a modern microcontroller. We will cover the basic theory on how they work, how a user can implement its own paths in Paparazzi, how to exploit them to coordinate multiple vehicles, and we finish with some experimental results. Although the presented implementation is focused on fixed-wing aircraft, the guidance is also applicable to other kinds of aerial vehicles such as rotorcraft.

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“…One can find in the literature a variety of robot-specific VF-PF algorithms [3], [6], [7], [8], [9], [5], [10]. However, the encountering of singular points where a vector field becomes zero may compromise the global convergence to the desired path.…”

Section: Introductionmentioning

confidence: 99%

Vector Field Guided Path Following Control: Singularity Elimination and Global Convergence

Yao

Marina

Cao

2020

2020 59th IEEE Conference on Decision and Control (CDC)

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In vector-field-based path following (VF-PF), a vector field is designed and utilized to guide a robot to follow a desired path. VF-PF algorithms have been shown to achieve high path-following precision under small control effort compared with many other path following algorithms. However, due to the existence of singular points where the vector field vanishes, the global convergence of VF-PF algorithms to the desired path cannot be guaranteed. Moreover, as it holds for most of the existing path following algorithms, VF-PF algorithms may fail to enable following a self-intersected desired path. In this paper, we propose a method to assist generic VF-PF algorithms in their global convergence. In particular, our method creates vector fields free of singular points in a higher-dimensional space containing the lower-dimensional desired path. Subsequently, the projection of our vector fields on the lower-dimensional space of the desired path can be exploited to guarantee the global convergence of the robot to the desired path, including those self-intersected. Finally, we show that our algorithm combines and fairly extends features from existing path following algorithms and a nonlinear trajectory tracking algorithm. The theoretical results have been validated by experiments and simulations.

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The VFO path-following kinematic controller for robotic vehicles moving in a 3D space

Cited by 13 publications

References 14 publications

Singularity-Free Guiding Vector Field for Robot Navigation

Singularity-Free Guiding Vector Field for Robot Navigation

Guiding vector fields in Paparazzi autopilot

Vector Field Guided Path Following Control: Singularity Elimination and Global Convergence

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