Overview
Lazy PRM is a sampling-based motion planning method for motion planning. It works by building a probabilistic roadmap while deferring expensive collision checks.
ExtendedSource checked
Lazy PRM
Lazy PRM addresses motion planning by building a probabilistic roadmap while deferring expensive collision checks.
Quick Facts
Compact metadata for implementation and discovery.
- Category
- Pathfinding
- Difficulty
- Intermediate
- Family
- Sampling-Based Motion Planning
- Tier
- Extended
- Status
- Verified
- Review
- Source Checked
- Sources
- 2
- Formulas
- 0
- Relationships
- 6
- Code example
- Ready
- Visualization
- Ready
Core Concepts
motion planningsampling-based motion planningrandom samplingpathfinding
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 Lazy PRM when solving motion planning and you want to benefit from building a probabilistic roadmap while deferring expensive collision checks.
- Choose it when O(n log n) average/worst-case time and O(n) memory match your workload profile.
- Prefer it over RRT* or RRT-Connect when the problem structure favors motion planning.
When Not to Use
- Avoid when path costs or obstacles change in ways the method cannot update efficiently.
- Avoid when approximate paths are unacceptable and the method does not guarantee optimality.
What It Does
- Computes motion planning within Sampling-Based Motion Planning workloads (O(n log n) time, O(n) space).
- Works by building a probabilistic roadmap while deferring expensive collision checks.
- Maintains key invariants across motion planning, sampling-based motion planning, random sampling.
Use Cases
- Production and research workloads requiring motion planning via building a probabilistic roadmap while deferring expensive collision checks.
- Sampling-Based Motion Planning pipelines where O(n log n) time and O(n) space fit system constraints.
- Engineering comparisons against RRT* and RRT-Connect when tuning motion planning.
Inputs
- Start state q_init, goal region Q_goal, and collision-check oracle in configuration space
Outputs
- Collision-free trajectory or roadmap connecting q_init to Q_goal
Pseudocode
- 1.Initialize the search space, start/goal states, and cost/priority tables for Lazy PRM.
- 2.Insert the initial state into the open frontier or roadmap with its baseline cost and heuristic estimate.
- 3.Expand or sample candidate transitions by building a probabilistic roadmap while deferring expensive collision checks.
- 4.Update path costs, parent pointers, or conflict constraints whenever an improved trajectory is found.
- 5.Reconstruct and return the collision-free path from start to goal once the termination criterion holds.
Canonical Example
- Input
- Start state q_init, goal region Q_goal, and collision-check oracle in configuration space configured for a representative motion planning test case
- Output
- Collision-free trajectory or roadmap connecting q_init to Q_goal satisfying Lazy PRM invariants
- Explanation
- Lazy PRM processes the input by building a probabilistic roadmap while deferring expensive collision checks, tracking motion planning and sampling-based motion planning to produce the verified motion planning result.
Implementation Notes
- Separate search state from world state so changes can be tested.
- Use small maps with known optimal answers before large scenarios.
- Track whether returned paths are optimal, bounded, or heuristic.
Common Pitfalls
- Using an inadmissible heuristic where optimality is expected.
- Ignoring dynamic obstacles, time-dependent costs, or changing edge weights.
- Testing only open grids and missing narrow-passage cases.
Interactive Mechanism Walkthrough
2D Grid Wavefront & TrajectoryShow building a probabilistic roadmap while deferring expensive collision checks on a small motion planning example.
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Step 1 of 5: Initialize the search space, start/goal states, and cost/priority tables for Lazy PRM.
pathfinding-mechanismNotes
Lazy PRM operates in O(n log n) time and O(n) space within the Sampling-Based Motion Planning family. Often compared with RRT* and RRT-Connect.
Sources (2)
What each reference supports for this entry.
Planning Algorithms
BookMotion-planning reference for PRM roadmaps, sampling, and deferred collision checking.
Open sourcePath Planning Using Lazy PRM
PaperOriginal Lazy PRM reference for deferring roadmap collision checks until candidate paths are needed.
Open sourceExplore Next
Good next jumps from the relationship graph, ranked for useful discovery.
Alternative toRRT-Connect
Pathfinding · Extended
Lazy PRM and RRT-Connect are practical alternatives within motion planning, with different assumptions and tradeoffs.
Compare with thisRelationships
View full relationship pageAlternative toRRT*
Lazy PRM and RRT* are practical alternatives within motion planning, with different assumptions and tradeoffs.
Alternative toRRT-Connect
Lazy PRM and RRT-Connect are practical alternatives within motion planning, with different assumptions and tradeoffs.
Alternative toConfiguration-Space Obstacle Construction
Lazy PRM and Configuration-Space Obstacle Construction are practical alternatives within motion planning, with different assumptions and tradeoffs.
Related Algorithms
Tags
PathfindingGraphRandomness