Distance-based Formation Control Using Angular Information Between Robots

Ferreira, Enrique; Hernández‐Martínez, Eduardo Gamaliel; Flores-Godoy, J.J.; Fernández‐Anaya, Guillermo; Paniagua-Contro, P.

doi:10.1007/s10846-015-0312-1

Cited by 37 publications

(19 citation statements)

References 32 publications

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“…Theorem 1 For the formation control defined as a noncooperative LQ differential game by (1) and 6, let there exist a solution set P i (i = 1, . .…”

Section: Problem Definitionmentioning

confidence: 99%

“…Formation control of multi-agent systems is a frontier research topic of control science and has found applications in diverse areas, such as mobile robots [1,2], satellite control [3], unmanned surface vessels (USVs) [4,5], and unmanned aerial vehicles (UAVs) [6,7]. The formation control objective is to design a controller that drives all agents to the desired formation in the state space.…”

Section: Introductionmentioning

confidence: 99%

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On the finite horizon Nash equilibrium solution in the differential game approach to formation control

Jond¹,

Nabiyev²

2019

Jsee

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The solvability of the coupled Riccati differential equations appearing in the differential game approach to the formation control problem is vital to the finite horizon Nash equilibrium solution. These equations (if solvable) can be solved numerically by using the terminal value and the backward iteration. To investigate the solvability and solution of these equations the formation control problem as the differential game is replaced by a discrete-time dynamic game. The main contributions of this paper are as follows. First, the existence of Nash equilibrium controls for the discretetime formation control problem is shown. Second, a backward iteration approximate solution to the coupled Riccati differential equations in the continuous-time differential game is developed. An illustrative example is given to justify the models and solution.

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“…Theorem 1 For the formation control defined as a noncooperative LQ differential game by (1) and 6, let there exist a solution set P i (i = 1, . .…”

Section: Problem Definitionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

On the finite horizon Nash equilibrium solution in the differential game approach to formation control

Jond¹,

Nabiyev²

2019

Jsee

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“…A few approaches have been recently proposed to address the aforementioned issues with distance-based controllers. In [8], a combination of inter-agent distance and angular constraints was used to reduce the likelihood of convergence to noncongruent formations in two dimensions (2D). Although the region of attraction of the desired equilibrium can be somewhat enlarged by a proper choice of control gains, the stability of the control proposed in [8] is still local in nature.…”

Section: Introductionmentioning

confidence: 99%

“…In [8], a combination of inter-agent distance and angular constraints was used to reduce the likelihood of convergence to noncongruent formations in two dimensions (2D). Although the region of attraction of the desired equilibrium can be somewhat enlarged by a proper choice of control gains, the stability of the control proposed in [8] is still local in nature. An extension of this work to 3D appeared in [9] by using area and volume constraints.…”

Section: Introductionmentioning

confidence: 99%

Directed Formation Control of n Planar Agents with Distance and Area Constraints

Liu

Queiroz

Zhang

et al. 2019

2019 American Control Conference (ACC)

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In this paper, we take a first step towards generalizing a recently proposed method for dealing with the problem of convergence to incorrect equilibrium points of distance-based formation controllers. Specifically, we introduce a distance and area-based scheme for the formation control of n-agent systems in two dimensions using directed graphs and the singleintegrator model. We show that under certain conditions on the edge lengths of the triangulated desired formation, the control ensures almost-global convergence to the correct formation.

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“…Experimental work is found in Fidan et al [11] using local video cameras and Antonelli et al [12] with laser range finder devices. Our previous contributions in DFC are in Lopez-Gonzalez et al [13] for a distance-orientation scheme, Ferreira-Vazquez et al [14] adding desired internal angles in the formation pattern to compensate for the flip ambiguity problem, and Ferreira-Vazquez et al [15] using planar as well as volume constraints for DFC in 3D. A recent paper by Anderson et al [16] makes a detailed convergence analysis of DFC with signed area constraints using standard 2 Complexity potential functions.…”

Section: Introductionmentioning

confidence: 99%

Formation Tracking of Heterogeneous Mobile Agents Using Distance and Area Constraints

et al. 2017

Self Cite

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This paper presents two formation tracking control strategies for a combined set of single and double integrator agents with an arbitrary undirected communication topology. The first approach is based on the design of distance-based potential functions with interagent collision avoidance using local information about the distance and orientation between agents and the desired trajectory. The second approach adds signed area constraints to the desired formation specification and a control strategy that uses distance as well as area terms is designed to achieve tracking convergence. Numerical simulations show the performance from both control laws.

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Distance-based Formation Control Using Angular Information Between Robots

Cited by 37 publications

References 32 publications

On the finite horizon Nash equilibrium solution in the differential game approach to formation control

On the finite horizon Nash equilibrium solution in the differential game approach to formation control

Directed Formation Control of n Planar Agents with Distance and Area Constraints

Formation Tracking of Heterogeneous Mobile Agents Using Distance and Area Constraints

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