Overview
Configuration-Space Obstacle Construction is a motion planning method for configuration-space construction. It works by expanding obstacles by the robot shape to convert motion to point navigation.
SpecializedSource checked
Configuration-Space Obstacle Construction
Configuration-Space Obstacle Construction addresses configuration-space construction by expanding obstacles by the robot shape to convert motion to point navigation.
Quick Facts
Compact metadata for implementation and discovery.
- Category
- Geometry
- Difficulty
- Advanced
- Family
- Motion Planning
- Tier
- Specialized
- Status
- Verified
- Review
- Source Checked
- Sources
- 2
- Formulas
- 0
- Relationships
- 5
- Code example
- Not ready
- Visualization
- Ready
Core Concepts
configuration-space constructionmotion planninggeometric primitivesgeometry
Quick facts
Complexity
Runtime and memory behavior at a glance.
Best
O(n)
Average
O(n log n)
Worst
O(n^2)
Space
O(n)
When to Use
- Use Configuration-Space Obstacle Construction when solving configuration-space construction and you want to benefit from expanding obstacles by the robot shape to convert motion to point navigation.
- Choose it when O(n log n) average/worst-case time and O(n) memory match your workload profile.
- Prefer it over RRT* or Lazy PRM when the problem structure favors configuration-space construction.
When Not to Use
- Avoid when coordinate precision is too low for the required geometric decisions.
- Avoid when degenerate cases dominate and the implementation has no robustness strategy.
What It Does
- Computes configuration-space construction within Motion Planning workloads (O(n log n) time, O(n) space).
- Works by expanding obstacles by the robot shape to convert motion to point navigation.
- Maintains key invariants across configuration-space construction, motion planning, geometric primitives.
Use Cases
- Production and research workloads requiring configuration-space construction via expanding obstacles by the robot shape to convert motion to point navigation.
- Motion Planning pipelines where O(n log n) time and O(n) space fit system constraints.
- Engineering comparisons against RRT* and Lazy PRM when tuning configuration-space construction.
Inputs
- Points, segments, polygons, or geometric primitives
- Query or construction parameters
Outputs
- Geometric decision, measurement, or constructed structure
Pseudocode
- 1.Normalize input coordinates, primitives, or pixel buffers and initialize spatial data structures for configuration-space construction.
- 2.Establish the sweep event queue, hierarchy, or scale-space pyramid required by Configuration-Space Obstacle Construction.
- 3.Process geometric predicates or pixel neighborhoods by expanding obstacles by the robot shape to convert motion to point navigation.
- 4.Resolve boundary degeneracies, occlusions, or threshold suppressions to maintain consistency.
- 5.Output the final configuration-space construction primitives, descriptors, or composited buffer.
Canonical Example
- Input
- Points, segments, polygons, or geometric primitives configured for a representative configuration-space construction test case
- Output
- Geometric decision, measurement, or constructed structure satisfying Configuration-Space Obstacle Construction invariants
- Explanation
- Configuration-Space Obstacle Construction processes the input by expanding obstacles by the robot shape to convert motion to point navigation, tracking configuration-space construction and motion planning to produce the verified configuration-space construction result.
Implementation Notes
- Normalize orientation and coordinate conventions at module boundaries.
- Add degenerate cases such as collinear points and touching edges.
- Use robust predicates where sign errors change topology.
Common Pitfalls
- Ignoring collinear, coincident, or nearly degenerate geometry.
- Relying on floating-point signs without a robustness strategy.
- Mixing coordinate systems or orientation conventions.
Interactive Mechanism Walkthrough
Spatial Primitive & Sweep-Line CanvasShow expanding obstacles by the robot shape to convert motion to point navigation on a small configuration-space construction example.
Step 1 of 5: Normalize input coordinates, primitives, or pixel buffers and initialize spatial data structures for configuration-space construction.
geometry-mechanismNotes
Configuration-Space Obstacle Construction operates in O(n log n) time and O(n) space within the Motion Planning family. Often compared with RRT* and Lazy PRM.
Sources (2)
What each reference supports for this entry.
Computational Geometry: Algorithms and Applications
BookTextbook support for Configuration-Space Obstacle Construction's computational geometry problem family, predicates, structures, or geometric construction.
Open sourceThe Algorithm Design Manual
BookAlgorithm catalog support for Configuration-Space Obstacle Construction in the computational geometry benchmark area.
Open sourceExplore Next
Good next jumps from the relationship graph, ranked for useful discovery.
AlternativesRRT-Connect
Pathfinding · Extended
RRT-Connect and Configuration-Space Obstacle Construction are practical alternatives within motion planning, with different assumptions and tradeoffs.
Compare with thisRelationships
View full relationship pageUsesRRT*
Configuration-Space Obstacle Construction uses RRT* as a subroutine, representation, or supporting idea while expanding obstacles by the robot shape to convert motion to point navigation.
UsesLazy PRM
Configuration-Space Obstacle Construction uses Lazy PRM as a subroutine, representation, or supporting idea while expanding obstacles by the robot shape to convert motion to point navigation.
Tags
GeometryComputational Geometry