Necessary and sufficient LMI conditions for constraints satisfaction within a B-spline framework

Prodan, Ionela; Stoican, Florin; Louembet, Christophe

doi:10.1109/cdc40024.2019.9030240

Cited by 12 publications

(9 citation statements)

References 18 publications

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“…This section presents the notions of B-spline curves and their equivalent Bézier representations. The focus is on their definitions, transformations, and further geometrical properties, while more details on both types of curves could be found in the literature [ 11 , 12 , 15 , 18 , 20 , 21 ]. The same notations as in some of the previous work [ 8 , 9 ] is used intentionally, for easy reference.…”

Section: B-spline and Equivalent Bézier Curvesmentioning

confidence: 99%

“…B-splines have been chosen for their local convexity : Each interval is bounded by the convex hull of the local control points [ 8 , 11 , 12 ]. This leads to the simple rule that the B-spline control boundary , i.e., the convex hull of the B-spline control point, must be fully contained inside the feasible area of the polytope map [ 13 , 14 , 15 ]. The rule has been applied widely in the literature to solve different types of motion planning problems.…”

Section: Introductionmentioning

confidence: 99%

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Navigation with Polytopes: A Toolbox for Optimal Path Planning with Polytope Maps and B-spline Curves

Nguyen

Gangavarapu

Kompe

et al. 2023

Sensors

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To deal with the problem of optimal path planning in 2D space, this paper introduces a new toolbox named "Navigation with Polytopes" and explains the algorithms behind it. The toolbox allows one to create a polytopic map from a standard grid map, search for an optimal corridor, and plan a safe B-spline reference path used for mobile robot navigation. Specifically, the B-spline path is converted into its equivalent Bézier representation via a novel calculation method in order to reduce the conservativeness of the constrained path planning problem. The conversion can handle the differences between the curve intervals and allows for efficient computation. Furthermore, two different constraint formulations used for enforcing a B-spline path to stay within the sequence of connected polytopes are proposed, one with a guaranteed solution. The toolbox was extensively validated through simulations and experiments.

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Section: B-spline and Equivalent Bézier Curvesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Navigation with Polytopes: A Toolbox for Optimal Path Planning with Polytope Maps and B-spline Curves

Nguyen

Gangavarapu

Kompe

et al. 2023

Sensors

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“…A well known problem of discrete-time systems coming from the sampling of continuous-time ones is how to ensure the feasibility of the solutions of the latter by only imposing constraints on the former [8,29,25]. In the case of ICS, this problem is even more difficult to overcome because of the discontinuities in the state trajectories, and it remains still open, although some control strategies were developed to formally tackle the problem [30].…”

Section: Feasibility For Impulsive Control Systemsmentioning

confidence: 99%

On stability of nonzero set-point for nonlinear impulsive control systems

D’Jorge

Anderson

Ferramosca

et al. 2022

Systems & Control Letters

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“…(5) The final objective of this process is to generate profiles, equivalently stated, to find the control points which meet the constraints (5) and minimize the cost function as in [10]:…”

Section: B Trajectory Generation Problemmentioning

confidence: 99%

“…In [2] and [6] a flat representation and subsequent Bspline parameterization [10] are exploited to construct an optimization problem which, simultaneously, minimizes trajectory length and satisfies various constraints.…”

Section: Introductionmentioning

confidence: 99%

Analysis of alternative flat representations of a UAV for trajectory generation and tracking

Huu-Thinh

Prodan

Stoican

2021

2021 25th International Conference on System Theory, Control and Computing (ICSTCC)

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Motion planning problems benefit greatly from the properties of differential flatness, which are widely employed for trajectory generation and controller design. This paper aims to highlight the fact that various flat representations of a system can have different implications in the trajectory generation and tracking objectives. In particular, we consider a fixedwing UAV (Unmanned Aerial Vehicle) and analyze various flat representations. We reformulate the trajectory generation and tracking problem in terms of different flat outputs and analyze the optimal cost, constraints satisfaction, tracking error and computational complexity. Insights on the future work complete the analysis. The research shows promising directions, especially in the area of disturbance rejection and robust control.

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Necessary and sufficient LMI conditions for constraints satisfaction within a B-spline framework

Cited by 12 publications

References 18 publications

Navigation with Polytopes: A Toolbox for Optimal Path Planning with Polytope Maps and B-spline Curves

Navigation with Polytopes: A Toolbox for Optimal Path Planning with Polytope Maps and B-spline Curves

On stability of nonzero set-point for nonlinear impulsive control systems

Analysis of alternative flat representations of a UAV for trajectory generation and tracking

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