1. Multi-agent Planning Amin Atrash

2. Papers Dynamic Planning for Multiple Mobile Robots –Barry L. Brummit, Anthony Stentz OBDD-based Universal Planning: Specifying and Solving Planning Problems for Synchronized Agents in Non- Deterministic Domains –Rune M. Jensen, Manuela M. Veloso

3. Dynamic Mission Planning for Multiple Mobile Robots Goal: Coordinate the actions of multiple robots to achieve a goal. Dynamically reassign goals to robots as information about the environment is updated. Handle multiple robots, multiple goals, and dynamic environments.

4. Architecture Local Navigator – Takes local information and chooses steering direction for robot. (obstacle avoidance). Dynamic Planner – Updates path of robot to goal based on updated maps (D*). Mission Planner – Updates goal assignments to robots.

5. Scenario Multiple Travelling Salesman Problem. M goals with N robots. M dynamic planners running, each maintaining a path from each robot to the planner's assigned goal (D* planners). Robots moving in randomly generated environment. As environment is updated, D* planners update path to all goals, and mission planners reassign goals to robots. Mission Planner uses exhaustive search of possible combinations.

6. Results/Conclusions With 3 robots and 6 goals, there was 25% improvement using dynamic mission planner compared to baseline planner which never changed initial goal assignments. Shown that complex missions can be performed with using reasonable computation.

7. OBDD-based Universal Planning: Special and Solving Planning Problems for Synchronized Agents in Non- deterministic Domains Uses Ordered Binary Decision Diagrams (OBDDs) to encode a domain as a non- deterministic finite automaton then apply fast model checking. Develop NADL.

8. Idea Given a domain. Generate NFA. Transitions defined by OBDD. Use model checking to find solution. Should generate universal plans – set of state- action rules which cover all possible situations in non-deterministic environment. All planning is done prior to execution. NADL – language for encoding a domain. –Non-deterministic Agent Domain Language.

9. ODBB Ordered Binary Decision Diagrams. Represent boolean functions. Efficient representation because number of nodes is often much smaller than number of truth assignments. Operation complexity bound by number of nodes. x1x1 x2x2 10

10. NADL State variables, system agents, environment agents, initial conditions, goal conditions. Each action has fixed equal duration. All agents each perform one action. –All agents together for action tuple: Joint action. Actions defined as set of state variables, precondition formula, and effect formula. Non-determinism occurs when actions do not restrict all variables to a specific value and with non-deterministic selection of actions.

11. NADL Example Variables nat(4) pos bool robot_works system agt: Robot Lift-Block con: pos pre: pos<3 eff: robot_works -> pos' = pos+1, pos' = pos Lower-Block con: pos pre: pos>0 eff: robot_works -> pos' = pos+1, pos' = pos environmnet agt: Baby Hit-Robot con: robot_works pre: true eff:  robot_works  robot_works’ initially pos = 0 and robot_works goal pos = 3

12. NADL, NFAs, and OBDDs Given an NADL description, a Non- deterministic Finite Automata (NFA) can be generated. OBDD used to represent transition function. Define set of variables to represent current states, joint actions, and next state. Generate OBDD.

13. OBDD-based Planning Preimage(V) – all states, s', such that there exists action, a, in s' which will lead to a state, s in V. Strong planning. – For a state belonging to the preimage of a set of states, V, there exists at least one input, i, where all transitions from s associated to i lead into V. –Start with set of goal states. –Iterate a backwards BFS. –Stop when all initial states are included in set of visited states. Strong cyclic planning – similar to strong planning but also considers plans with loops.

14. ODBB-based Planning Goal pre1 pre2 Initial pre3

15. Optimistic Planning Strong planning is pessimistic. –Will avoid short path with chance of entering failed state for longer safer path. Usually not feasible in real world. –Especially with non-deterministic domains. Optimistic planning – In scenarios where a strong plan cannot be found, an optimistic plan can be used. –Considers actions which can lead to failed states.

16. Results – Deterministic Domains Gripper Domain - Able to solve larger problems than other planners Movie Domain – Outperformed other traditional planners and returned optimal plan Logistics Domain – Unable to solve problem. –Possibly due to bad representation or variable ordering Obstacle Domain

17. Results – Power Plant Power Plant Domain – 4 heat exchangers, 4 turbines, 1 reactor. Good, bad, and failed state. Heat exchangers can fail and need to be blocked. Turbines can fail and need to be stopped. Need at least on heat exchanger and turbine working.

18. Results – Soccer Domain Two teams of players in grid world. Players can move or pass ball. Goal: Have player in front of opponent goal without any opponents in area.

19. Conclusions Developed expressive description language Applied OBDD planning Proposed “optimistic planning.” Showed use in multiagent non-deterministic domains