Multi-agent Planning Amin Atrash. Papers Dynamic Planning for Multiple Mobile Robots –Barry L....
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Transcript of Multi-agent Planning Amin Atrash. Papers Dynamic Planning for Multiple Mobile Robots –Barry L....
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