Decentralized and Prioritized Navigation and Collision Avoidance for Multiple Mobile Robots

Roussos, Giannis; Kyriakopoulos, Kostas J.

doi:10.1007/978-3-642-32723-0_14

Cited by 27 publications

(21 citation statements)

References 10 publications

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“…In this section we consider m elliptical obstacles in R n , where β i (x) is of the form (22), with n = 2 and n = 3. We set the number of obstacle to be m = 2 n and we define the external boundary to be a spherical shell of center x 0 and radius r 0 .…”

Section: Numerical Experimentsmentioning

confidence: 99%

“…These efforts have proven successful but can be used only when the space is globally known since this information is needed to design shuch dif-feomorphism. Alternative solutions that are applicable without global knowledge of the environment are the use of polynomial navigation functions [20] for n-dimensional configuration spaces with spherical obstacles and [21] for 2-dimensional spaces with convex obstacles, as well as adaptations used for collision avoidance in multiagent systems [22], [24], [25].…”

Section: Introductionmentioning

confidence: 99%

“…Spherical quadratic potentials appear in some specific applications but are most often the result of knowing the goal configuration. Thus, the methods in [11]- [22] are applicable, for the most part, when the goal is known a priori and not when potential gradients are measured during deployment. To overcome this limitation, this work extends the theoretical convergence guarantees of Koditscheck-Rimon functions to problems in which the attractive potential is an arbitrary strongly convex function and the free space is a convex set with a finite number of nonintersecting smooth and strongly convex obstacles (Section II) under mild conditions (Section III).…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Navigation Functions for Convex Potentials in a Space With Convex Obstacles

Paternain

Koditschek

Ribeiro

2018

IEEE Trans. Automat. Contr.

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Given a convex potential in a space with convex obstacles, an artificial potential is used to navigate to the minimum of the natural potential while avoiding collisions. The artificial potential combines the natural potential with potentials that repel the agent from the border of the obstacles. This is a popular approach to navigation problems because it can be implemented with spatially local information that is acquired during operation time. Artificial potentials can, however, have local minima that prevent navigation to the minimum of the natural potential. This paper derives conditions that guarantee artificial potentials have a single minimum that is arbitrarily close to the minimum of the natural potential. The qualitative implication is that artificial potentials succeed when either the condition number-the ratio of the maximum over the minimum eigenvalue-of the Hessian of the natural potential is not large and the obstacles are not too flat or when the destination is not close to the border of an obstacle. Numerical analyses explore the practical value of these theoretical conclusions.

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Section: Numerical Experimentsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Navigation Functions for Convex Potentials in a Space With Convex Obstacles

Paternain

Koditschek

Ribeiro

2018

IEEE Trans. Automat. Contr.

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“…In the papers [1,20], and [19] navigation function was used to control multiple mobile robots. Authors of these publications adress the problem of collision avoidance in multiagent robotic systems.…”

Section: Introductionmentioning

confidence: 99%

Set-point Control of Mobile Robot with Obstacle Detection and Avoidance Using Navigation Function - Experimental Verification

Kowalczyk

Przybyla

Kozłowski

2016

J Intell Robot Syst

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This paper presents the results of an experimental verification of mobile robot control algorithm including obstacle detection and avoidance. The controller is based on the navigation potential function that was proposed in work (Urakubo, Nonlinear Dyn. 1475-1487 2015). Conducted experiments considered the task of reaching and stabilization of robot in point. The navigation potential agregates information of robot position and orientation but also the repelling potentials of obstacles. The obstacle detection is performed solely with the use of laser scanner. The experiments show that the method can easily handle environments with one or two obstacles even if they instantly hide or show-up due to the scanner range limits. The experiments also indicate that the utilized control method has a good potential for being used in parallel parking task. 81(3),

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“…This behavior is modeled by a planar Dubins vehicle [1], which gives a good approximation for feasible UAV trajectories, but this yields a nonlinear system. The Lyapunov stability-based control design is commonly used to develop feedback controllers for problems of this type [2][3] [4], but constructing a Lyapunov function may not be a straightforward task.…”

Section: Introductionmentioning

confidence: 99%

A stochastic approach to Dubins feedback control for target tracking

Anderson

Milutinović

2011

2011 IEEE/RSJ International Conference on Intelligent Robots and Systems

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A nonlinear system gives rise to many inherent difficulties when designing a feedback control. Motivated by a fixed-speed, fixed-altitude Unmanned Aerial Vehicle (UAV) that tracks an unpredictable target, we seek to control the turning rate of a planar Dubins vehicle. We introduce stochasticity in the problem by assuming the target performs a random walk, which both aides in the computation of a smooth value function and further accounts for all realizations of target kinematics. A Bellman equation based on an approximating Markov chain that is consistent with the stochastic kinematics is used to compute a control policy that minimizes the expected value of a cost function based on a nominal UAV-target distance. Our results indicate how uncertainty in the target motion affects the control law, and simulations illustrate that the control can further be applied to any continuous, smooth trajectory with no need for further computation.

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Decentralized and Prioritized Navigation and Collision Avoidance for Multiple Mobile Robots

Cited by 27 publications

References 10 publications

Navigation Functions for Convex Potentials in a Space With Convex Obstacles

Navigation Functions for Convex Potentials in a Space With Convex Obstacles

Set-point Control of Mobile Robot with Obstacle Detection and Avoidance Using Navigation Function - Experimental Verification

A stochastic approach to Dubins feedback control for target tracking

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