Stable Coordination in Mobile Robot Platooning: A New Approach

1. Stable Coordinated Platooning by a Group of Mobile RobotsAnjan Kumar Ray , Martin McGinnity , Laxmidhar Behera, Sonya Coleman Anjan Kumar Ray Research Associate, ISRC UKIERI Workshop on the Fusion of BCI and Assistive Robotics, 7-8 July, 2011

2. Presentation Outline • Background developments for collaboration • Network model and services of individual robot • Understanding environment • Platoon formation • Stable platoon coordination • Results • Addition of new members • Results • Conclusion

3. Network model of individual robot

4. Network Services Each robot acts as a server of different information for other robots. Each robot can request information from other robots. A robot can be connected by an individual robot or a group of robots. A robot can connect to an individual robot or a group of robots. A robot can switch among server robots depending on requirements.

5. Experiment on network services (b) A group of robots turn (a) Linear velocity control The objective : Robots can share information in a decentralized way

6. Understanding environment: an example • A robot understands its environment using different sensors. • An example shows a laser based human tracking by a robot. • Objective: A robot can decide its motion as per environmental situation and application.

7. Scenario : Column formation and Platoon • If a robot decides its motion, it can pass this information to other robots. • Subsequently, other robots can follow the leader. • They should maintain safe separation distances among each others. • A column formation is generated in this way. • Similarly, multiple columns generate a platoon of robots. • So, any front member can be the leader. • Assumption: The leader knows its motion initiative. Figure 1: Column of robots Figure 2: Platoon of robots

8. Stable platoon coordination: Model • A robot is given an ID Acr where ‘c’ and ‘r’ refer to the corresponding column and row. • The position and orientation at thek-th time instance are denoted by • where, • Linear and angular velocities of each robot are represented by V cr and ωcr.

9. Stable platoon coordination: Constraints • General constraints • for front members: • General constraint for column members: • Relative positional constraints: • Front members may be at the left, right or both sides of the leader. • Navigational constrains imposed by the leader: • The leader may move straight, turn right or left or move with any combinations. • Further constraints imposed on column members: • They should not imitate velocity profile of the leader rather decide their own velocities as per the impending situation.

10. Stable platoon coordination: Velocity Control Velocities of the front members satisfying all constraints are defined by Similarly, the velocities of the column members are defined by Where,

11. Results: Simulation Proposed method: front members remain same Same velocity profile: Change of front members

12. Results: Simulation Resuming straight path Continuous turning sequences

13. Results: Experimental (two robots) Continuous left turns Continuous right turns

14. Results: Experimental (4 robots)

15. Results: contd. Coordination along straight path Linear velocities

16. Results Coordination during turning Linear velocities

17. Results: contd. Angular velocities Resuming straight path after turning Linear velocities

18. Results: contd. Relative heading with respect to the leader

19. Addition of new members • Previous method ensures cohesion of an existing formation. • Next, we studied the possibility of expanding an existing formation. • In this method, external robots can join the existing formation. • These robots gradually adapt to the existing formation. • They are able to decide their velocities as per the changes in the leader. • This method enhances scalability of an existing formation.

20. Addition of new members • An external robotis assigned with an ID Acr+1 within the formation. • A reference trajectory is initialized at the k-thtime which puts the reference trajectory at the desired separation distance. • The reference trajectory for each external robot is defined as per the kinematic constraints of an existing formation.

21. Addition of new members: • We proposed a model predictive control method to define the velocities of these • external robots. • It minimizes reference trajectory tracking errors. • The cost function is given by • where, • Ueis error input vector • is error state matrix • is error input matrix • and are weighting matrices

22. The control law is obtained by minimizing the cost function as Finally, velocity inputs to the external robot are given by

23. Results: Adaptation to an existing formation Angular velocities Paths of an existing formation along with an external robot Linear velocities

24. Addition of new members: different phases Two robots (blue) One robot (blue)

25. Conclusion • Experimental verifications of a multi-robot platoon coordination is presented. • Members follow motion patterns of the leader while maintaining safe separation distances among each other. • Furthermore, the front members keep their relative heading with respect to the • leader. • We tested the proposed method in different navigational situations. • We included the facility of adding additional members to the formation. • Results are shown to validate the method. • This method can be explored in different application areas including distributed • sensing of the environment, satellite formation, UAV formation for wide area • surveillance and UGV formation. 25

26. Thank you