Further results on the distance and area control of planar formations

Liu, Tairan; Queiroz, M.S. de; Zhang, Pengpeng; Khaledyan, Milad

doi:10.1080/00207179.2019.1616824

Cited by 18 publications

(5 citation statements)

References 27 publications

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“…The expression 9 z 23 " 0 2 can be transformed to the following set of angle constraints, namely 10), we obtain pg 12 , g 13 q " pg ‹ 12 , g ‹ 13 q corresponding to the equilibrium configurations in S p while the solution in (11) (8). By an immediate substitution, we obtain for the dynamics of the bearing robot R2, 9 p 2 " K b b ‹ sum ": w. Remark 1: The signed area for a triangle can be obtained using the expression [15], [16]. The signed area of the desired formation shape evaluates to…”

Section: B Moving Configurationsmentioning

confidence: 99%

Stability Analysis of Gradient-Based Distributed Formation Control With Heterogeneous Sensing Mechanism: The Three Robot Case

Chan

Jayawardhana

Marina

2022

IEEE Trans. Automat. Contr.

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This paper focuses on the stability analysis of a formation shape displayed by a team of mobile robots that uses heterogeneous sensing mechanism. For the setups consisting of three robots, we show that the use of heterogeneous gradientbased control laws can give rise to undesired invariant sets where a distorted formation shape is possibly moving at a constant velocity. We guarantee local asymptotic stability for the correct and desired formation shape. For the setup with one distance and two bearing robots, we identify the conditions such that an incorrect moving formation is locally attractive.

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Section: B Moving Configurationsmentioning

confidence: 99%

Stability Analysis of Gradient-Based Distributed Formation Control With Heterogeneous Sensing Mechanism: The Three Robot Case

Chan

Jayawardhana

Marina

2022

IEEE Trans. Automat. Contr.

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“…, it is easy to see η ij = 0 if and only if e ij = 0. Therefore, instead of using e ij directly, we will use the squared distance error (24) to impose specific prescribed performance bounds for all times. Similar to the results developed in [36][37][38]53], for each edge of the rigid framework, first a smooth decreasing performance function…”

Section: Prescribed Performance Boundsmentioning

confidence: 99%

“…A method for dealing with the problem of convergence to incorrect equilibrium points (undesired shapes) of distance-based formation acquisition controllers was recently proposed in [23], introducing an additional control variable (the signed area of a triangle) for triangular shapes. Later, Liu et al [24] tried to generalize this method for planar formations with n > 3 agents. Furthermore, the authors in [25] have analyzed the effects of distance mismatches between neighboring agents in distance-based formation stabilization.…”

Section: Introductionmentioning

confidence: 99%

Prescribed Performance Distance-Based Formation Control of Multi-Agent Systems (Extended Version)

Mehdifar,

Bechlioulis,

Hashemzadeh

et al. 2019

Preprint

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This paper presents a novel control protocol for robust distance-based formation control with prescribed performance in which agents are subjected to unknown external disturbances. Connectivity maintenance and collision avoidance among neighboring agents are also handled by the appropriate design of certain performance bounds that constrain the inter-agent distance errors. As an extension to the proposed scheme, distance-based formation centroid maneuvering is also studied for disturbance-free agents, in which the formation centroid tracks a desired time-varying velocity. The proposed control laws are decentralized, in the sense that each agent employs local relative information regarding its neighbors to calculate its control signal. Therefore, the control scheme is implementable on the agents' local coordinate frames. Using rigid graph theory, input-to-state stability, and Lyapunov based analysis, the results are established for minimally and infinitesimally rigid formations in 2-D or 3-D space. Furthermore, it is argued that the proposed approach increases formation robustness against shape distortions and can prevent formation convergence to incorrect shapes, which is likely to happen in conventional distance-based formation control methods. Finally, extensive simulation studies clarify and verify the proposed approach.

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“…To effectively track the leader, follower agents require sufficiently accurate estimates of the leader's pose in the inertial frame, which can be affected by noisy sensor measurements, exogenous disturbances from the environment, such as wind or downwash from nearby agents -in the case where the agents are aerial vehicles -or even uncertainty in the communication network from delays and packet drops. Thus, it is often the case that the multiagent system (MAS) will fail to track the reference trajectory while keeping formation, or deviate from the desired formation altogether, causing unintended and even unsafe effects [6]. Furthermore, the disturbances themselves may be difficult, computationally expensive, or impossible to estimate, making formation tracking under uncertainty both a safety-critical requirement and a nontrivial problem.…”

Section: Introductionmentioning

confidence: 99%

Distributed Optimal Formation Control for an Uncertain Multiagent System in the Plane

Enwerem¹,

Baras²,

Romero³

2023

Preprint

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In this paper, we present a distributed optimal multiagent control scheme for quadrotor formation tracking under localization errors. Our control architecture is based on a leader-follower approach, where a single leader quadrotor tracks a desired trajectory while the followers maintain their relative positions in a triangular formation. We begin by modeling the quadrotors as particles in the YZ-plane evolving under dynamics with uncertain state information. Next, by formulating the formation tracking task as an optimization problem -with a constraint-augmented Lagrangian subject to dynamic constraints -we solve for the control law that leads to an optimal solution in the control and trajectory error costminimizing sense. Results from numerical simulations show that for the planar quadrotor model considered -with uncertainty in sensor measurements modeled as Gaussian noise -the resulting optimal control is able to drive each agent to achieve the desired global objective: leader trajectory tracking with formation maintenance. Finally, we evaluate the performance of the control law using the tracking and formation errors of the multiagent system.

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Further results on the distance and area control of planar formations

Cited by 18 publications

References 27 publications

Stability Analysis of Gradient-Based Distributed Formation Control With Heterogeneous Sensing Mechanism: The Three Robot Case

Stability Analysis of Gradient-Based Distributed Formation Control With Heterogeneous Sensing Mechanism: The Three Robot Case

Prescribed Performance Distance-Based Formation Control of Multi-Agent Systems (Extended Version)

Distributed Optimal Formation Control for an Uncertain Multiagent System in the Plane

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