Announcements. Exam #2 next Thursday (March 13) Covers material from Feb. 11 through March 6

Transcription

1 Multi-Robot Path Planning and Multi-Robot Traffic Management March 6, 2003 Class Meeting 16

2 Announcements Exam #2 next Thursday (March 13) Covers material from Feb. 11 through March 6

3 Up to Now Swarm-Type Cooperation Topics addressed dealt with: Simple cooperative control strategies Homogeneous robots Frequent biological inspirations Issues included: Swarming / flocking Search / coverage Herding Formations Tracking Distributed sensing Unit-modular reconfigurable robots

4 Next several classes Higher-Level Reasoning More complex reasoning Often involves: Heterogeneous robots Primary issues: Today: Path Planning More focus: Task allocation / action selection

5 Much of what we ve studied: Motion Coordination Objective: enable robots to navigate collaboratively to achieve spatial positioning goals Issues studied: Dispersion / Aggregation / Homing Search / Coverage Formation-keeping Target tracking Reconfigurable robot shapes Wrap-up motion coordination today: Multi-robot Path Planning Multi-robot Traffic management

6 Student Paper Presentation A distributed and optimal motion planning approach for multiple mobile robots, by Guo and Parker, Proceedings of IEEE International Conference on Robotics and Automation, Presented by Ben Birch

7 Objective: Teams of Robots Operating in Outdoor Environments w/o Significant Setup Time Application of robot teams to site security, surveillance and reconnaissance, etc. ATRV-mini robots at ORNL

8 Overall Highest-Level Schematic Multi-Robot 3D Mapping Multi-Robot Path Planning Execute Mission Objective Multi-Robot Localization

9 Robot Team and Experimental Setup Robot Team: 4 ATRV-mini robots (Manuf: RWI/iRobot) Named (after Roman Emperors): Augustus, Constantine, Theodosius, Vespasian Sensors: 2 robots: PTZ camera 2 robots: SICK laser Compass/inclinometer DGPS Sonar

10 Multi-Robot Motion Planning: Background Motion planning in dynamic environment with moving obstacles is NP-hard. Simple reactive motion planning strategies cannot be guaranteed to be deadlock free and to converge. Previous results either obtain optimal solutions through centralized and exhaustive computing, or achieve distributed implementations without considering optimization issues. Outdoor environment is more challenging with terrain features and requires online re-planning.

11 Multi-Robot Motion Planning: General Approach Approach to 3D multi-robot motion planning: Distributed; Capable of outdoor environment and real time re-planning; Uses global performance measurement for minimization Uses D* searching (Stentz, ICRA 94) to facilitate local search

12 Assumptions for Distributed and Optimal Motion Planning Premises: Each robot has an assigned goal, and knows its start and goal; Pre-defined map available indoor: static polygonal obstacles outdoor: terrain elevation and traversability based on grid representation; Onboard sensors detect discrepancy, and revise map online; Communication devices broadcast messages; Robots move at constant fixed speeds; Robots switch instantaneously between fixed speed and halting.

13 Overall Approach to Multi-Robot Path Planning Calculating optimal paths for all robots simultaneously is computationally expensive For now, path planning issue: Given assigned starting and goal positions, find optimal path to goal Approach: Plan optimal independent paths for each robot Cost is function of obstacles, distance, terrain slope, path smoothness Search for inter-robot collisions along paths Define optimal velocity profiles to enable robots to follow paths while eliminating collisions Cost is function of collisions, N-dimensional distance, robot idle time, prioritized penalty for giving way

14 Distributed and Optimal Motion Planning Algorithm Step 1: Path planning D* search in free space to produce optimal path P i for each robot from the start to the goal minimizing a cost function based on distance, slope, turning, obstacles Generated paths communicated to all robots Collision (time-space) check produces a set of collision region; Coordination diagram constructed: Each path P i is a continuous mapping that denotes the set of points that place robot along path P i ; Coordination space is defined Collision regions marked as obstacles in coordination diagram.

15 Distributed and Optimal Motion Planning Algorithm (con t.) Step 2: Velocity planning D* search in coordination diagram, minimizing cost function of distance, idle time, obstacles, penalty for giving way Produces velocity profile VP i and performance index K i ; Communicate VP i and K i across robots; Step 3: Global performance evaluation Find the minimal K l, select corresponding VP l as the optimal solution for velocity.

16 Search Result in Coordination Diagram For 3 robot path coordination: Coordination diagram parameterized by non-decreasing path length Returned trajectory: interpreted as a velocity profile for each robot

17 Multi-Robot Motion Planning Algorithm for Robot A i D* search in free space Path P i Get P j broadcast From Robot A j motion planning Inter-robot communications st broadca D* search CD for collision-free trajectory optimizing rule F i Performance index K i Velocity profile VP i Collision check for paths P i and P j Get K j and VP j No Collisions if robots move simultaneously? Performance evaluation: find K min = K i Yes Construct coordination diagram (CD) Set velocity V i = VP i Robot A i motion control move robot on P i according to V i

18 Results of Multi-Robot Path Planning In 3D simulation: Planned paths: Velocity Profiles:

19 3D Simulation in Mars-like Terrain Environment Online replanning function (red obstacles not in prior map)

20 Nomad 200 Indoor Robots Simulation Robot 1 Robot 2 Robot 3 Indoor paths and velocity profile

21 Nomad 200 Indoor Robots Experiments Problems met in real run experiments: Localization errors; Motion uncertainties Robot does not take equal unit time to track a unit distance; Robot does not switch instantaneously between moving and stopping. Robustness design: Safety margin defined in path searching for localization errors; Safety margin defined in velocity planning for motion uncertainties.

22 Nomad 200 Indoor Robots Experiments Pre-defined map, Robots at run, Encoder trajectories.

23 Coordinating Multiple Robots Through Traffic Rules Kato et al, Japan Issues: Collisions Deadlocks Congestion Possible approaches: Communication Local collision avoidance Traffic rules

24 Typical Problem Situation for Traffic Rules

25 Traffic Rule Application System (TRAS) Traffic Rule : imposes a certain level of order on mobile objects, such as mobile robots and people, and work environments Rules constructed by considering: Work environment Performance of mobile objects Quantity of mobile objects Robots must know: Current position Current sensory information Global map information

26 Traffic Rules Keep sufficient space in front Keep sufficient side space Maintain passage zone Intersection crossing: Preference to right turn Preference toward a right-side mobile object Collision avoidance Deadlock avoidance: Preference at intersections Replan if route blocked

27 Control of Robots in Traffic Management 1. Plan shortest route to goal 2. Extract local maps from global map for route and intersections 3. Move along planned path 4. Determine sensor-detecting range re: traffic rules 5. Observe workspace, using sensors 6. Detect obstacles 7. Judge, according to traffic rules, whether collision will occur 8. Decide how to act 9. Move or stop 10. Return to step 2

28 Summary of Motion Coordination Research Many issues studied by the field: Multi-robot path planning Traffic control Formation generation Formation keeping Target tracking Target search Multi-robot docking Approaches are usually specific to given application

29 Summary of Motion Coordination Research Objective: enable robots to navigate collaboratively to achieve spatial positioning goals Issues studied: Dispersion / Aggregation / Homing Search / Coverage Formation-keeping Target tracking Reconfigurable robot shapes Multi-robot Path Planning Multi-robot Traffic management

30 Next Time Topic: Taxonomies Two student presentations: Lan Lin Xiaoquan Fu