Navigation functions for focally admissible surfaces

Filippidis, Ioannis; Kyriakopoulos, Kostas J.

doi:10.1109/acc.2013.6579966

Cited by 11 publications

(13 citation statements)

References 25 publications

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“…, and W is the free workspace defined in (8). We emphasize that we consider the intersection with W in (15) for convenience, but later we tune the parameters such that H i ( i , ν i ) ⊂ W, which implies J i 0 will equal to H i ( i , ν i ).…”

Section: B Geometric Construction Of the Flow And Jump Setsmentioning

confidence: 99%

“…It allows obtaining artificial potential fields with the nice property that all critical points except one are saddles and the remaining critical point is the desired reference. Since then, the navigation-function-based approach has been extended in many different directions; e.g., for multiagent systems [4]- [6], for unknown sphere words [7], and for focally admissible obstacles [8]. The major drawback of navigation functions is that they are not correct by construction.…”

Section: Obstacle Avoidance Via Hybrid Feedback I Introductionmentioning

confidence: 99%

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Obstacle Avoidance via Hybrid Feedback

Berkane

Bisoffi

Dimarogonas

2022

IEEE Trans. Automat. Contr.

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In this article, we present a hybrid feedback approach to solve the navigation problem in the n-dimensional space containing an arbitrary number of ellipsoidal obstacles. The proposed algorithm guarantees both global asymptotic stabilization to a target position and avoidance of the obstacles. The controller, exploiting hysteresis regions, employs a Zeno-free switching between two modes of control: stabilization and avoidance. Simulation results illustrate the performance of the proposed approach for 2-D and 3-D scenarios.

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Section: B Geometric Construction Of the Flow And Jump Setsmentioning

confidence: 99%

Section: Obstacle Avoidance Via Hybrid Feedback I Introductionmentioning

confidence: 99%

Obstacle Avoidance via Hybrid Feedback

Berkane

Bisoffi

Dimarogonas

2022

IEEE Trans. Automat. Contr.

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“…We evaluate the performance of the local stochastic approximation of the gradient of the navigation function given in (18) in two different scenarios for which the condition (8) is satisfied. In particular, the estimations of the obstacles are done by considering osculating circles at the closest point of the obstacle to the agent as in Section III-A.…”

Section: Numerical Examplesmentioning

confidence: 99%

Stochastic Artificial Potentials for Online Safe Navigation

Paternain

Ribeiro

2020

IEEE Trans. Automat. Contr.

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Consider a convex set of which we remove an arbitrarily number of disjoints convex sets -the obstacles -and a convex function whose minimum is the agent's goal. We consider a local and stochastic approximation of the gradient of a Rimon-Koditschek navigation function where the attractive potential is the convex function that the agent is minimizing. In particular we show that if the estimate available to the agent is unbiased convergence to the desired destination while obstacle avoidance is guaranteed with probability one under the same geometrical conditions than in the deterministic case. Qualitatively these conditions are that the ratio of the maximum over the minimum eigenvalue of the Hessian of the objective function is not too large and that the obstacles are not too flat or too close to the desired destination. Moreover, we show that for biased estimates a similar result holds under some assumptions on the bias. These assumptions are motivated by the study of the estimate of the gradient of a Rimon-Koditschek navigation function for sensor models that fit circles or ellipses around the obstacles. Numerical examples explore the practical value of these theoretical results.

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“…(x−µc) z < 0 implies then z ∈ P < (0, x−µc). 4 Each (in)equality is obtained thanks to the relationship reported over it.…”

Section: A Proof Of Theoremmentioning

confidence: 99%

A Hybrid Controller for Obstacle Avoidance in an $n$-dimensional Euclidean Space

Berkane

Bisoffi

Dimarogonas

2019

2019 18th European Control Conference (ECC)

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For a vehicle moving in an n-dimensional Euclidean space, we present a construction of a hybrid feedback that guarantees both global asymptotic stabilization of a reference position and avoidance of an obstacle corresponding to a bounded spherical region. The proposed hybrid control algorithm switches between two modes of operation: stabilization (motion-to-goal) and avoidance (boundary-following). The geometric construction of the flow and jump sets of the hybrid controller, exploiting a hysteresis region, guarantees robust switching (chattering-free) between the stabilization and avoidance modes. Simulation results illustrate the performance of the proposed hybrid control approach for a 3-dimensional scenario.

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Navigation functions for focally admissible surfaces

Cited by 11 publications

References 25 publications

Obstacle Avoidance via Hybrid Feedback

Obstacle Avoidance via Hybrid Feedback

Stochastic Artificial Potentials for Online Safe Navigation

A Hybrid Controller for Obstacle Avoidance in an $n$-dimensional Euclidean Space

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