1. What is the primary purpose of a Probabilistic Roadmap (PRM) in robotics?
A) Localization
B) Path Planning
C) Object Detection
D) Motion Control
Answer: B) Path Planning
2. In a Probabilistic Roadmap, what is the main strategy used to generate the roadmap?
A) Grid-based sampling
B) Deterministic sampling
C) Random sampling
D) Sequential sampling
Answer: C) Random sampling
3. What are the two main phases of the PRM algorithm?
A) Sampling and Path Optimization
B) Roadmap Construction and Query Phase
C) Path Generation and Execution
D) Collision Detection and Avoidance
Answer: B) Roadmap Construction and Query Phase
4. Which of the following is not a step in the roadmap construction phase of PRM?
A) Node Generation
B) Edge Generation
C) Collision Checking
D) Path Execution
Answer: D) Path Execution
5. What is the purpose of the query phase in a PRM?
A) To create nodes in the environment
B) To find a path from start to goal
C) To optimize the generated roadmap
D) To detect obstacles
Answer: B) To find a path from start to goal
6. What type of environment is PRM particularly effective in?
A) Fully structured environments
B) Highly dynamic environments
C) Large, complex, and high-dimensional spaces
D) Low-dimensional, simple environments
Answer: C) Large, complex, and high-dimensional spaces
7. Which of the following is true about the nodes in PRM?
A) They are deterministically placed
B) They represent the obstacles in the environment
C) They are randomly sampled configurations
D) They are dynamically changing over time
Answer: C) They are randomly sampled configurations
8. In PRM, what does an edge between two nodes represent?
A) The shortest path between the nodes
B) A collision-free path between the nodes
C) The distance between the nodes
D) The obstacle density between the nodes
Answer: B) A collision-free path between the nodes
9. What does the “probabilistic” aspect of PRM refer to?
A) The certainty of finding a solution
B) The use of probabilistic models for motion
C) The random nature of node sampling
D) The likelihood of avoiding obstacles
Answer: C) The random nature of node sampling
10. Which of the following is a common application of PRM?
A) Weather forecasting
B) Autonomous vehicle navigation
C) Human-computer interaction
D) Image recognition
Answer: B) Autonomous vehicle navigation
11. What is the role of collision detection in PRM?
A) To optimize the path
B) To ensure nodes are placed in free space
C) To determine the shortest path
D) To dynamically update the roadmap
Answer: B) To ensure nodes are placed in free space
12. Which of the following techniques can be used to improve the quality of a PRM?
A) Increasing the number of nodes
B) Decreasing the number of edges
C) Reducing collision detection accuracy
D) Limiting the roadmap size
Answer: A) Increasing the number of nodes
13. In PRM, how are start and goal positions incorporated into the roadmap?
A) They are pre-defined in the roadmap
B) They are randomly generated as nodes
C) They are connected to the nearest roadmap nodes
D) They are excluded from the roadmap
Answer: C) They are connected to the nearest roadmap nodes
14. Which algorithm is often combined with PRM to refine the final path?
A) A* algorithm
B) Dijkstra’s algorithm
C) Genetic algorithm
D) Greedy algorithm
Answer: A) A* algorithm
15. What is the main advantage of using PRM in high-dimensional spaces?
A) Faster computation time
B) Reduced memory usage
C) Scalability to complex environments
D) Guaranteed solution
Answer: C) Scalability to complex environments
16. Why might PRM not be suitable for highly dynamic environments?
A) It cannot handle real-time changes
B) It requires too many nodes
C) It is too slow to compute
D) It depends on deterministic paths
Answer: A) It cannot handle real-time changes
17. In PRM, what happens if a sampled node lies within an obstacle?
A) The node is included in the roadmap
B) The node is discarded
C) The node is moved to the nearest free space
D) The roadmap is recalculated
Answer: B) The node is discarded
18. What is the typical representation of a PRM?
A) A binary tree
B) A graph
C) A matrix
D) A list
Answer: B) A graph
19. Which factor is critical in determining the success of a PRM?
A) Node density
B) Roadmap size
C) Sampling method
D) Collision detection speed
Answer: A) Node density
20. What is one of the main limitations of PRM?
A) It requires too much memory
B) It is not suitable for high-dimensional spaces
C) It does not guarantee the shortest path
D) It is unable to handle obstacles
Answer: C) It does not guarantee the shortest path
21. How can the computational efficiency of a PRM be improved?
A) By reducing the number of sampled nodes
B) By increasing the number of edges
C) By parallelizing the sampling and collision detection
D) By using a simpler collision detection algorithm
Answer: C) By parallelizing the sampling and collision detection
22. Which variant of PRM is designed to improve performance in narrow passages?
A) Lazy PRM
B) Gaussian PRM
C) Bridge Test PRM
D) Probabilistic Roadmap of Trees (PRT)
Answer: C) Bridge Test PRM
23. What is a “milestone” in the context of PRM?
A) A critical edge
B) A goal node
C) A sampled node in the roadmap
D) A failed path
Answer: C) A sampled node in the roadmap
24. What does “lazy PRM” refer to?
A) A PRM that uses fewer nodes
B) A PRM that postpones collision checks until the query phase
C) A PRM that only samples nodes close to the goal
D) A PRM that uses deterministic sampling
Answer: B) A PRM that postpones collision checks until the query phase
25. How is a roadmap typically stored in a PRM algorithm?
A) As an adjacency list
B) As a hash table
C) As a binary search tree
D) As a queue
Answer: A) As an adjacency list
26. What is the purpose of the “local planner” in PRM?
A) To generate nodes
B) To check for collisions
C) To connect nodes with edges
D) To optimize the final path
Answer: C) To connect nodes with edges
27. Which of the following is a typical metric used to measure the distance between nodes in PRM?
A) Euclidean distance
B) Manhattan distance
C) Hamming distance
D) Chebyshev distance
Answer: A) Euclidean distance
28. In which of the following scenarios is PRM most likely to fail?
A) Low-dimensional, simple environments
B) Large, open spaces with few obstacles
C) High-dimensional spaces with narrow passages
D) Dynamic environments with moving obstacles
Answer: C) High-dimensional spaces with narrow passages
29. What is the significance of the “roadmap connectivity” in PRM?
A) It determines the number of nodes in the roadmap
B) It affects the ability to find a path from start to goal
C) It influences the collision detection accuracy
D) It optimizes the roadmap construction speed
Answer: B) It affects the ability to find a path from start to goal
30. What does PRM rely on to ensure completeness?
A) Dense sampling
B) Random sampling
C) Deterministic paths
D) Collision avoidance
Answer: A) Dense sampling
31. Which of the following is not an enhancement commonly applied to PRM?
A) Adaptive sampling
B) Biased sampling
C) Deterministic sampling
D) Dynamic sampling
Answer: D) Dynamic sampling
32. In PRM, what is the purpose of using a “sampling strategy”?
A) To ensure nodes are evenly distributed
B) To minimize the number of edges
C) To maximize the number of nodes
D) To ensure a diverse set of nodes
Answer: D) To ensure a diverse set of nodes
33. What is the typical complexity of constructing a PRM?
A) O(n^2)
B) O(n log n)
C) O(n)
D) O(n^3)
Answer: A) O(n^2)
34. Which of the following methods can be used to improve the exploration of narrow passages in PRM?
A) Uniform sampling
B) Gaussian sampling
C) Random sampling
D) Lazy collision checking
Answer: B) Gaussian sampling
35. What does the “roadmap refinement” process in PRM aim to do?
A) Increase the number of nodes
B) Reduce the roadmap size
C) Improve path quality and connectivity
D) Simplify the collision detection process
Answer: C) Improve path quality and connectivity
36. What is a key challenge when implementing PRM in a high-dimensional space?
A) High computational cost
B) Low collision detection accuracy
C) Limited node placement
D) Reduced pathfinding accuracy
Answer: A) High computational cost
37. In PRM, how is the “local planner” typically used?
A) To connect nodes in free space
B) To validate node placement
C) To generate new nodes
D) To detect obstacles
Answer: A) To connect nodes in free space
38. Which technique is often used alongside PRM to refine the path between nodes?
A) Graph Search Algorithms
B) Heuristic Algorithms
C) Local Optimization Algorithms
D) Monte Carlo Methods
Answer: C) Local Optimization Algorithms
39. What is the main advantage of using PRM over grid-based path planning methods?
A) Lower memory usage
B) Guaranteed pathfinding
C) Better handling of high-dimensional spaces
D) Faster computation time
Answer: C) Better handling of high-dimensional spaces
40. How can the accuracy of a PRM be improved when dealing with obstacles?
A) By increasing the number of nodes
B) By using a more precise collision detection method
C) By reducing the number of edges
D) By simplifying the roadmap construction
Answer: B) By using a more precise collision detection method
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