NURBS Based Multi-objective Path Planning

Jalel, Sawssen; Marthon, Philippe; Hamouda, Atef

doi:10.1007/978-3-319-19264-2_19

Cited by 4 publications

(5 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Further work includes extending the framework to other Lie manifolds, specifically SE(3). This is feasible with little modification, since (12)(13)(14)(15)(16)(17)(18) are group-agnostic, simply employing the appropriate exp(•) and log(•) functions. Such 3D planner would typically be interesting for optimizing the trajectory of e.g.…”

Section: Discussionmentioning

confidence: 99%

“…a smooth rigid-body motion on SE(3) [6] presented as early as twenty years ago. Most methods rely on estimating piecewise-smooth curves, based on piecewise polynomial function [7]- [9] or B-spline [10], [11] or Non-Uniform Rational B-Splines (NURBS) [12], [13]. Other methods model the trajectory using Bezier Curves geometrically constructed on Manifold [14].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Timed-Elastic Smooth Curve Optimization for Mobile-Base Motion Planning

Deray

Magyar²,

Solà

et al. 2019

2019 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)

View full text Add to dashboard Cite

This paper proposes the use of piecewise C n smooth curve for mobile-base motion planning and control, coined Timed-Elastic Smooth Curve (TESC) planner. Based on a Timed-Elastic Band, the problem is defined so that the trajectory lies on a spline in SE(2) with non-vanishing n-th derivatives at every point. Formulated as a multi-objective nonlinear optimization problem, it allows imposing soft constraints such as collision-avoidance, velocity, acceleration and jerk limits, and more. The planning process is realtime-capable allowing the robot to navigate in dynamic complex scenarios.The proposed method is compared against the state-of-the-art in various scenarios. Results show that trajectories generated by the TESC planner have smaller average acceleration and are more efficient in terms of total curvature and pseudo-kinetic energy while being produced with more consistency than stateof-the-art planners do.

show abstract

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Timed-Elastic Smooth Curve Optimization for Mobile-Base Motion Planning

Deray

Magyar²,

Solà

et al. 2019

2019 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)

View full text Add to dashboard Cite

show abstract

“…For the sake of simplicity, a double infinite sequence of simple nodes a i is considered such that a i <a i+1 for all i. Then, the B-splines N i,k are then defined through the recurrence relationships (10) and (11).…”

Section: ð9þmentioning

confidence: 99%

“…More recently, in [9][10][11][12] a predefined NURBS curve is used to improve its properties adjusting the weights.…”

Section: Trajectories Of Mobile Robots Defined By Nurbsmentioning

confidence: 99%

See 1 more Smart Citation

Path Planning Based on Parametric Curves

Pérez¹,

Aguilar²,

MontésSánchez³

et al. 2018

Advanced Path Planning for Mobile Entities

View full text Add to dashboard Cite

Parametric curves are extensively used in engineering. The most commonly used parametric curves are, Bézier, B-splines, (NURBSs), and rational Bézier. Each and every one of them has special features, being the main difference between them the complexity of their mathematical definition. While Bézier curves are the simplest ones, B-splines or NURBSs are more complex. In mobile robotics, two main problems have been addressed with parametric curves. The first one is the definition of an initial trajectory for a mobile robot from a start location to a goal. The path has to be a continuous curve, smooth and easy to manipulate, and the properties of the parametric curves meet these requirements. The second one is the modification of the initial trajectory in real time attending to the dynamic properties of the environment. Parametric curves are capable of enhancing the trajectories produced by path planning algorithms adapting them to the kinematic properties of the robot. In order to avoid obstacles, the shape modification of parametric curves is required. In this chapter, an algorithm is proposed for computing an initial Bézier trajectory of a mobile robot and subsequently modifies it in real time in order to avoid obstacles in a dynamic environment.

show abstract

Hybrid Evolutionary Approach to Multi-objective Path Planning for UAVs

Hohmann

Bujny

Adamy

et al. 2021

2021 IEEE Symposium Series on Computational Intelligence (SSCI)

View full text Add to dashboard Cite

The goal of Multi-Objective Path Planning (MOPP) is to find Pareto-optimal paths for autonomous agents with respect to several optimization goals like minimizing risk, path length, travel time, or energy consumption. In this work, we formulate a MOPP for Unmanned Aerial Vehicles (UAVs). We utilize a path representation based on Non-Uniform Rational B-Splines (NURBS) and propose a hybrid evolutionary approach combining an Evolution Strategy (ES) with the exact Dijkstra algorithm. Moreover, we compare our approach in a statistical analysis to state-of-the-art exact (Dijkstra's algorithm), gradient-based (L-BFGS-B), and evolutionary (NSGA-II) algorithms with respect to calculation time and quality features of the obtained Pareto fronts indicating convergence and diversity of the solutions. We evaluate the methods on a realistic 2D urban path planning scenario based on real-world data exported from OpenStreetMap. The examination's results indicate that our approach is able to find significantly better solutions for the formulated problem than standard Evolutionary Algorithms (EAs). Moreover, the proposed method is able to obtain more diverse sets of trade-off solutions for different objectives than the standard exact approaches. Thus, the method combines the strengths of both approaches.

show abstract

NURBS Based Multi-objective Path Planning

Cited by 4 publications

References 12 publications

Timed-Elastic Smooth Curve Optimization for Mobile-Base Motion Planning

Timed-Elastic Smooth Curve Optimization for Mobile-Base Motion Planning

Path Planning Based on Parametric Curves

Hybrid Evolutionary Approach to Multi-objective Path Planning for UAVs

Contact Info

Product

Resources

About