Path Planning in Dynamic Environments Using Time Warps. S. Farzan and G. N. DeSouza

Transcription

1 Path Planning in Dynamic Environments Using Time Warps S. Farzan and G. N. DeSouza

2 Outline Introduction Harmonic Potential Fields Rubber Band Model Time Warps Kalman Filtering Experimental Results 2

3 Introduction Mobile robot navigation: Localization Map building Path planning: Topological graphs Vertical cell decomposition Grid-based maps 3

4 Introduction Parallel computation Using GPUs 4

5 Definitions Path: a sequence of grid cells with the lowest (minimum) harmonic values. A path to the goal is given by an index matrix, which for every position (x,y) contains the index of the neighbor with the lowest harmonic potential. End-point or Goal: a grid cells with the lowest harmonic value Obstacle: any cluster of cells blocking a possible path towards the goal. The harmonic values are maximum. Free Space: any grid cell that does not contain an obstacle, including the goal. The value is updated at each iteration. 5

6 Harmonic Potential Fields Harmonic Function A harmonic function is a function which satisfies Laplace's equation: This same function can be discretized and the numerical solution of Laplace's equation becomes: 6

7 Harmonic Potential Fields Flowchart 7

8 Rubber Band Model Every cell in the path is affected by two kinds of forces: the internal tension (rubber band) forces ( ) the potential force ( ) The position of a cell in the path is given by the pair (x,y) that leads to the resultant forces to be minimum. That is: 8

9 Rubber Band Model We combine the ideal of rubber band model and harmonic potentials to define the path: 9

10 Rubber Band Model Path smoothening: 10

11 Flowchart: Rubber Band Model 11

12 Handling Moving Objects Prediction: Focus on changes in the environment Analogy: humans crossing streets Harmonic potential based on future grid Reading data and updating obstacle positions 1. The laser readings contain range data referring to both static and dynamic obstacles; 2. A visual system detects humans/moving obstacles; 3. It computes the position of obstacles using its laser range data and the visual system data. 12

13 Time Warps Time-Warped Grid Divide the environment into the circles with the same center point which is the robot; Try to find the warps containing moving objects and assign the warp number to the corresponding object; Predict the future positions of the moving objects based on the time warp using Kalman Filter Mark the predicted collision point as a static obstacle Mark the neighbors of the predicted collision point based on the returned uncertainty from the Kalman Filter 13

14 Time Warps 14

15 Kalman Filtering KF tracks the object and predicts the state vector for each obstacle. The noise from the sensor/processing is reduced by KF. All state vectors are projected into the future according to the time-warped grid. The same Harmonic+Rubber-band model is applied to the time-warped grid. 15

16 Kalman Filtering System Description Time Update Measurement Update 16

17 Time Warps + Kalman Filter Flowchart: 17

18 Time Warps + Kalman Filter 18

19 Experimental Results Static Environment 19

20 Experimental Results Static Environment 20

21 Experimental Results Dynamic Environment 21

22 Experimental Results Dynamic Environment 22

23 Experimental Results Dynamic Environment 23

24 Experimental Results Dynamic Environment 24

25 Experimental Results Dynamic Environment 25

26 References [1] R. Hong and G. DeSouza, A real-time path planner for a smart wheelchair using harmonic potentials and a rubber band model, in Intelligent Robots and Systems (IROS), 2010 IEEE/RSJ International Conference on, pp , oct [2] O. Khatib, Real-time obstacle avoidance for manipulators and mobile robots, in Robotics and Automation. Proceedings IEEE International Conference on, vol. 2, pp , mar [3] H. M. Zhang, Path planning methods of mobile robot based on soft computing technique, Advanced Materials Research, vol. 216, pp , march [4] Y. Hu and S. Yang, A knowledge based genetic algorithm for path planning of a mobile robot, in Robotics and Automation, Proceedings. ICRA IEEE International Conference on, vol. 5, pp Vol.5, april- 1 may [5] G. Antonelli, S. Chiaverini, and G. Fusco, A fuzzy-logic-based approach for mobile robot path tracking, Fuzzy Systems, IEEE Transactions on, vol. 15, pp , april [6] L. Kavraki, P. Svestka, J.-C. Latombe, and M. Overmars, Probabilistic roadmaps for path planning in highdimensional configuration spaces, Robotics and Automation, IEEE Transactions on, vol. 12, pp , aug [7] P. Fiorini and Z. Shillert, Motion planning in dynamic environments using velocity obstacles, International Journal of Robotics Research, vol. 17, pp , [8] N. Tsourveloudis, K. Valavanis, and T. Hebert, Autonomous vehicle navigation utilizing electrostatic potential fields and fuzzy logic, Robotics and Automation, IEEE Transactions on, vol. 17, pp , aug

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