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Quality Motion Planning In a Dynamic Environment

This project focuses on generating efficient paths for robots navigating a 2D environment with both static and dynamic obstacles. It implements a path planning algorithm based on the PRM and Zucker-Kant methods, enhanced for higher problem-solving probabilities. With a maximum velocity and time constraints, the robot adapts to cyclically known dynamic obstacles. Developed in C++ using Visual Studio 2008, this project utilizes MFC for GUI and CGAL for computational geometry functions. Key outcomes include new path planning algorithms and insights into working with complex libraries.

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Quality Motion Planning In a Dynamic Environment

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  1. Quality Motion Planning In a Dynamic Environment August 2011

  2. Project Goal  • Generate a path for a Robot in a 2D Environment containing both Static & Dynamic obstacles. • Few assumptions: • The Robot has a maximum velocity and a Time limitation to reach destination. • The dynamic obstacles movement is known and cyclic. • The static Obstacles are simple polygons.

  3. Implementation & development Environment • The project was written in C++ using Visual Studio 2008, with support of the following software packages: • MFC - we used this package to create our GUI. • CGAL - for basic implementations & functions we used in our algorithms.

  4. Algorithm Overview • Based on • PRM • Zucker-Kant Algorithm • Amending the Zucker-Kant Algorithms to achieve higher probability of solving problems

  5. Algorithm – the Assembly Line • The solution at each stage is represented by a directed graph • The final path is a list of edges on graph • The graph is passed to each of the stages of the algorithm • Each stage modifies the graph and brings it closer to solution

  6. User Output Stage 1 A s s e m b l y L i n e Algorithm chart RunAlgorithm MaBakerView Stage 2 User Input Stage 5 Algorithm Support

  7. Beginning

  8. Stage 1 • Sample points on completely free configurations (vertices on the graph) • Use input to determine sample strategy • Use CGAL to determine free configuration

  9. Stage 2 • Connect close points (edges on the graph) • Make sure each edge is in almost free configuration • Use CGAL to determine free configuration

  10. Stage 3 • Transform each edge found in stage 2 into a distance – time graph, considering moving obstacles • Solve using the VGraph method • If unsolvable – give edge an infinite weight • If solvable – give weight indicating the time it takes to pass the edge • If no moving obstacles on edge, just time when moving in max velocity

  11. Edges with light weights Edges with heavy weights

  12. The Zucker Kant Plane • Let’s look at one segment of movement intersecting with one dynamic obstacle: R O O O R Block Start Block End

  13. The Zucker Kant Plane • In Time to distance on path plane, we get: Time R O O O R Distance Block Start Block End

  14. The Zucker Kant Plane • After setting a goal time, we can solve with vGraph: Time R O Dest Time O O R Distance Block Start Block End

  15. Stage 4 • Run Dijkstra on the graph and find the final path • This is the path the robot is going to use, we still don’t know the velocity function • However – it is guaranteed that this path is passable

  16. Stage 5 • Transform the path found in stage 4 into a distance – time graph, considering moving obstacles • Calculate velocity function, which determine the progress velocities on the path we found in stage 4. • This promises the shortest arrival time to destination.

  17. Examples

  18. What did we learn? • New algorithms for path planning • Working with complicated libraries – MFC, CGAL • Analytical geometry when applied in a program • Working on a big project

  19. Possible improvements • Improved sampling strategies • Incremental algorithm • Fix the case we fail (allow sampling almost free places) • 3D?

  20. Additional Reading • K. Kant and S. Zucker. Toward efficient planning: the path-velocity decomposition. International Journal of Robotics Research, 5(3):72–89, 1986 • Path Planning in Dynamic Environments, Jur Pieter van den Berg, May 1981

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