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74.419 Artificial Intelligence 2004
Planning 2: Partially Ordered Plans
Partially Ordered Plans - or:
"How Do You Put Your Shoes On?"
Partially Ordered Plans:
• no strict sequence
• partly parallel
• observe threats
Least Commitment Strategy
Partially Instantiated Plans
Least Commitment Strategy
In general, make as little concrete as possible,
i.e. leave things undetermined until you have to
determine them and become concrete.
Partially Instantiated Plans
During planning, variables have not necessarily
to be instantiated immediately.
Instantiation can wait, until binding becomes
Partial Order Planning 1
Start with a rough plan and refine iteratively.
First plan consists only of start and finish actions:
• start - T as precondition, initial world state
as effect
• finish - goal as precondition, NIL as effect
Select actions to achieve sub-goals separately,
quasi in parallel  partial-order plan
Fulfill open preconditions (sub-goals), until no
more unsatisfied preconditions are left (last one
is T of start)
Partial Order Planning 2
Add causal links to connect effects from actions to
matching preconditions for plan.
Causal links specify a partial order.
Recognize threats - the effect of an action A
negates the precondition of another action B.
Add threats as partial order to plan: B<A (do B
before A).
Partial Order Planning - Threats
partial order plan = set of action strings (partial plans)
Detect and resolve threats, i.e. conflicts between
actions – where the precondition of one action is
deleted by another action – by choosing an adequate
ordering of actions: if action b is a threat to action a,
then a<b, i.e. a has to occur before b.
(see also Russell/Norvig textbook, The POP Planner)
Partial Order Planning - Overall
Use plan transformation operators to refine the
partial plan and construct a complete plan:
• add an action (operator),
• reorder actions (operators),
• instantiate actions (operators).
A partial order plan consists of a set of action
sequences (partial plans; action strings) which
together achieve the complete set of goal
Threats induce an additional partial order of these
action sequences.
Hierarchical Planning
Hierarchical Planning / Plan Decomposition
Plans are organized in a hierarchy. Links between
nodes at different levels in the hierarchy denote a
decomposition of a “complex action” into more
primitive actions (operator expansion).
move (x, y, z)
pickup (x, y)
putdown (x, z)
The lowest level corresponds to executable actions
of the agent.
Hierarchical Planning
Hierarchical Planning / Plan Decomposition
• hierarchical organisation of 'actions'
• complex and less complex (or: abstract) actions
• lowest level reflects directly executable actions
• planning starts with complex action on top
• plan constructed through action decomposition
• substitute complex action with plan of less
complex actions (pre-defined plan schemata; or
learning of plans/plan abstraction, cf. ABSTRIPS)
• overall plan must generate effect of complex
Abstract Planning
Consider different criticality values of preconditions
in planning.
Start with global, abstract plan.
Then refine plan by trying to fulfill preconditions of
abstract plan:
• Choose preconditions with highest criticality
values first ( = most difficult to achieve).
• Then lower criticality value and continue with
Other Issues in Planning
Disjunctive Preconditions
Conditional Effects
– change is due to specific condition
– integrate into partial planning with threats
Disjunctive Effects
– parallel future worlds to consider
All-Quantified Variables (in preconditions and effects)
– only for finite, static Universe of objects
Real World Agents 1
• Consider Sensors and Effectors
– perception of environment, e.g. vision
– ensure correspondence between internal map of
robot and environment, e.g. locating robot
– low-level body control, e.g. Motion Control (behaviour
routines, e.g. Fuzzy or Neural Network Controller)
– other sensor information for body control and
environment mapping, e.g. bumpers, radar
– sensors for other information channels and cognitive
processes, e.g. speech – language
Real World Agents 2
• Low-level Processing and Control
– Motion Control
– Audio Recording and low-level analysis
• Medium-level Processing
– Navigation / Route Planning
– Robot Location
• Higher-level Processing
– Speech Recognition, NLP, ...
– Strategies, Planning
– BDI (Belief-Desire-Intention) - Architecture
Real World Agents 3
• Multi-Agents
– Language / Communication →
communicating agents
– mental Models of other Agents
cooperating agents
– Strategies
cooperating agents
– Deontic Systems
– Trust
Additional References
Nils J. Nilsson: Artificial Intelligence – A New Synthesis.
Morgan Kaufmann, San Francisco, 1998.
Konolidge, K. and K. Myers: The Saphira Architecture
for Autonomous Mobile Robots (Robot Soccer Class
Guzzoni, D. et al.: Many Robots Make Short Work.
(AAAI’96 Robot Competition - Meeting Scheduling)
Martina Veloso, MIT (RoboCup)
Web Links
RoboCup official web page –
Active Media Robotics (pioneer, Saphira) –
SONY’s RoboDog AIBO –
PBS Videos –
Robots Alive, 04-09-97 (AAAI’96, Maze/Meeting
Scheduling Robot Competition)
Games Machines Play, 05-21-2002 (RoboCup, Seattle