Multi-agent Planning

Amin Atrash

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

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.

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.

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.

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.

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.

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.

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.

x1

x2

1 0

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.

NADL ExampleVariables

nat(4) posbool robot_works

systemagt: Robot

Lift-Blockcon: pospre: pos<3eff: robot_works -> pos' = pos+1, pos' = pos

Lower-Blockcon: pospre: pos>0eff: robot_works -> pos' = pos+1, pos' = pos

environmnetagt: Baby

Hit-Robotcon: robot_workspre: trueeff: robot_works robot_works’

initiallypos = 0 and robot_works

goalpos = 3

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.

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.

ODBB-based Planning

Goalpre1

pre2

Initial

pre3

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.

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

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.

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.

Conclusions

• Developed expressive description language

• Applied OBDD planning

• Proposed “optimistic planning.”

• Showed use in multiagent non-deterministic domains