1. Real-Time Support for Mobile Robotics K. Ramamritham (+ Li Huan, Prashant Shenoy, Rod Grupen)

2. Background A team of mobile robots Collaborate with each other to achieve a common goal Search for trapped people in a burning building Sensors Processor Wireless link

3. Motivation To accomplish a search: Sensor tasks : acquire sensor data Processing tasks : process sensor data Motor tasks : drive the movement of robots

4. Problem Dynamic environment Robots move as a team Team may change in the size Hardware constraints for some tasks Sensor tasks are pre-allocated to robots Which robots run which tasks and when? Where to allocate processing tasks? When to run tasks?

5. Outline Motivation System model Allocation and scheduling algorithms Experimental results Related work and conclusions

6. Problem Model Leader Follower Pair-wise relationship to control the movement Leader Follower Two control strategies Push: follower specifies the search area of the leader Pull: leader searches the area, pulls the follower behind him

7. Task Graph (Push) POS Motor IR P2 P1 P3 Leader Follower Push Construct the map of walls Choose search area Compute the next location of the leader

8. Task Graph (Pull) P2 POS Motor P1 Motor Leader IR P3 Follower Pull Construct the map of walls Choose search area Compute the next location of the follower

9. Task Model and Goal Tasks are abstracted using task graphs Periodic tasks with constraints : Deadline : each instance has a relative deadline Location : sensor tasks are pre-assigned to robots Precedence : sensor tasks  processing tasks  motor tasks Goal: Allocate and schedule tasks on robots All constraints are satisfied

10. Why is this a Hard Problem? Possible strategies dynamically change as the size changes  Increase exponentially as the team size scales Need to efficiently find a feasible strategy online Leader Follower Push Follower Leader Pull {Push, Push}, {Push, Pull}, {Pull, Push}, {Pull, Pull}

11. Overall Approach Allocate tasks to appropriate robots Minimize communication Balance processor workload Find a feasible schedule Deadlines are met Precedence constraints are satisfied Can smart allocation improve schedulability?

12. Task Allocation Step 1 : Choose an unallocated task T j Step 2 : Choose an appropriate processor Communication Cost Ratio (CCR): CCR i, j = comm_cost(T i  T j ) E i + E j E i : Execution time of T i

13. Step 1: How to Choose a Task Consider tasks such that all their preceding tasks have been allocated Try to minimize communication cost Two techniques to choose T j : Greedy: consider individual cost Aggressive: consider total cost from the same processor

14. Step2: How to Allocate a Task If T j is chosen, and T i  T j Try to balance and minimize workload Assign T j to the same processor as T i So long as the processor does not become the most heavily loaded processor Network communication between Ti and Tj is eliminated Otherwise, put T j to the processor with the least utilization

15. Allocation Example Step 1: Consider T4,T5 TT1T2T3T4T5 Ei23323 Pi618 T1T3T2 T4T5 Robot 1 Robot 2 1/4 1/5 1/6 Greedy : CCR 1,4 = 1/4  Choose T4 Aggressive: CCR 2,5 +CCR 3,5 =1/3 Choose T5  Step 2: find the robot Currently : U 1 = U 2 = 1/3 Greedy: Assign T4 to Robot 1 Aggressive: Assign T5 to Robot 2 1/3

16. Making Scheduling Decisions Have allocated tasks to processors, need to find a feasible schedule Possible heuristic functions EDF (Min_D) Minimum laxity first (Min_L) Earliest-start-time first (Min_S) Weighted combinations of {deadline, earliest-start-time, laxity}

17. Outline Motivation Problem setting Allocation and scheduling algorithms Experimental results Simulation results Application analysis Related work and conclusions

18. Simulation Settings Homogeneous system Number of processors and tasks are varying Task sets are randomly generated, each Metric: SuccessRatio (SR): N succ : number of successfully scheduled task sets N: total number of tested task sets

19. Scheduling Heuristic Min_S is the best single heuristic Encode precedence constraints Min_D + W×Min_S is the best overall Both deadline and precedence are taken into account

20. Performance of Allocation Algorithms Aggressive outperforms the other methods. The improvement is larger when the resources are tight.

21. Three Robots, period = 220 ms {Push,Pull} is not feasible Metrics to choose the optimal one Min max laxity : {Pull, Push} Prune the infeasible strategies as the team size scales Analysis With Mobile Robots strategy{Push, Push}{Pull, Pull}{Push, Pull}{Pull, Push} Robot 1195205223195 Robot 2203209220206 Robot 3211203231203 Completion time for tasks on each robot

22. Related Work Task allocation and scheduling in distributed environment. Branch-and-bound search [Peng 97] Period-based method of load partitioning and assignment [Abdelzaher 00] Static allocation for tasks with duplication and precedence constraints [Ramamritham 95] Utilization bound for schedulability analysis Uniprocessor, independent tasks [ Liu&Layland 73] Multiprocessor, P-fairness scheduling [Baruah 96] EDF, RMA [Andersson 01], [Baruah 01], [Funk 01], [Goossens 02], [Srinivasan 02]

23. Conclusions and Future Work A team of mobile robots to achieve a goal Allocate and schedule real-time tasks with constraints for dynamic robotic teams Smart allocation of tasks can improve the schedulability of the whole system Future work : Heterogeneous systems http://lass.cs.umass.edu/