Related Experiment Video
Updated: Aug 2, 2025
05:55
Modeling the Functional Network for Spatial Navigation in the Human Brain
Published on: October 13, 2023
1.1K
Navigation with Polytopes: A Toolbox for Optimal Path Planning with Polytope Maps and B-spline Curves.
Ngoc Thinh Nguyen1, Pranav Tej Gangavarapu1, Niklas Fin Kompe1
1Institute for Robotics and Cognitive Systems, University of Lübeck, 23562 Lübeck, Germany.
Sensors (Basel, Switzerland)
|April 13, 2023
Summary
This study introduces "Navigation with Polytopes," a new toolbox for optimal path planning. It enables mobile robot navigation by creating polytopic maps and planning safe B-spline paths, reducing planning conservativeness.
Area of Science:
- Robotics
- Computational Geometry
- Artificial Intelligence
Background:
- Optimal path planning is crucial for mobile robot navigation in 2D environments.
- Existing methods can be conservative or computationally intensive.
Purpose of the Study:
- Introduce the "Navigation with Polytopes" toolbox for enhanced path planning.
- Develop algorithms for creating polytopic maps and planning safe B-spline paths.
- Reduce conservativeness in constrained path planning problems.
Main Methods:
- Creation of polytopic maps from grid maps.
- Optimal corridor searching algorithms.
- B-spline path planning with conversion to Bézier representation.
- Novel constraint formulations for path adherence to polytopes.
Main Results:
- A novel method for converting B-spline paths to Bézier curves for efficient computation.
- Two constraint formulations for B-spline paths within polytopes, including one with a guaranteed solution.
- Extensive validation through simulations and experiments.
Conclusions:
- The "Navigation with Polytopes" toolbox offers an effective solution for optimal path planning.
- The proposed methods improve efficiency and reduce conservativeness in mobile robot navigation.
- The toolbox is validated and ready for practical application.
Related Concept Videos
01:24Introduction to Vertical Curves
96
Vertical curves are parabolic transitions that connect different grades on highways and railroads, ensuring a smooth alignment between back and forward tangents. The back tangent represents the initial grade, while the forward tangent defines the subsequent grade. These curves can be symmetrical, with equal tangent lengths, or nonsymmetrical, with varying lengths. The key points defining a vertical curve include the Point of Vertical Intersection (P.V.I.), where the tangents meet; the Point of...
96
01:19Introduction to Horizontal Curves
140
Horizontal curves are essential in highway and railroad design, ensuring smooth and safe transitions between straight path segments, or tangents. These curves allow vehicles to maintain speed without abrupt changes, minimizing accidents and improving travel efficiency.A horizontal curve is typically defined by its geometric relationship to two tangents that meet at an intersection point (P.I.), where a simple curve is introduced to connect them. The back tangent refers to the initial tangent...
140
01:25Design Example: Traverse Angle Computations
115
Traverse angle computations are a critical component of surveying, used to compute the internal angles within a closed traverse. A traverse consists of a series of connected lines forming a closed loop, often used for land boundary delineation or mapping. Calculating the internal angles ensures accuracy in the traverse geometry and is essential for checking survey data integrity.The process begins with known azimuths and bearings of the traverse sides. Internal angles at each vertex are...
115
01:20Elevation of Intermediate Points on Vertical Curves
57
Vertical curves are essential in roadway design because they provide smooth transitions between varying roadway grades. Designing vertical curves involves calculating intermediate elevations and identifying the curve's highest or lowest point, which is essential for optimal roadway performance.Intermediate elevations on a vertical curve are determined using the tangent offset method. This method considers the initial elevation at the start of the curve, the grades, and the curve's geometry. The...
57
01:27Curvilinear Motion: Normal and Tangential Components
435
When a car traverses a curved road, its motion can be elucidated by breaking it down into tangential and normal components. The car-centric coordinates attached to the vehicle move with it.
The positive direction of the t-axis aligns with the increasing position of the car along the curved path, denoted by the unit vector ut. Simultaneously, the n-axis, perpendicular to the t-axis, dissects the curved path into differential arc segments, each forming the arc of a circle with a radius of...
The positive direction of the t-axis aligns with the increasing position of the car along the curved path, denoted by the unit vector ut. Simultaneously, the n-axis, perpendicular to the t-axis, dissects the curved path into differential arc segments, each forming the arc of a circle with a radius of...
435
01:12Adjusting a Traverse
88
In the site survey of a four-sided traverse, internal angles are essential to ensure geometric accuracy. The survey revealed that the sum of the measured internal angles was 359 degrees and 48 minutes, which is 12 minutes less than the expected 360 degrees. This discrepancy signals an error likely arising from measurement inaccuracies during the fieldwork.To rectify this error, the adjustment process involved distributing the 12-minute shortfall equally across the four internal angles. By...
88