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Glossary |
Automated planning and scheduling, sometimes denoted as simplyAI planning,[1] is a branch ofartificial intelligence that concerns the realization ofstrategies or action sequences, typically for execution byintelligent agents,autonomous robots andunmanned vehicles. Unlike classicalcontrol andclassification problems, the solutions are complex and must be discovered and optimized in multidimensional space. Planning is also related todecision theory.
In known environments with available models, planning can be done offline. Solutions can be found and evaluated prior to execution. In dynamically unknown environments, thestrategy often needs to be revised online. Models and policies must be adapted. Solutions usually resort to iterativetrial and error processes commonly seen inartificial intelligence. These includedynamic programming,reinforcement learning andcombinatorial optimization. Languages used to describe planning and scheduling are often calledaction languages.
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Given a description of the possible initial states of the world, a description of the desired goals, and a description of a set of possible actions, the planning problem is to synthesize a plan that is guaranteed (when applied to any of the initial states) to generate a state which contains the desired goals (such a state is called a goal state).
The difficulty of planning is dependent on the simplifying assumptions employed. Several classes of planning problems can be identified depending on the properties the problems have in several dimensions.
The simplest possible planning problem, known as the Classical Planning Problem, is determined by:
Since the initial state is known unambiguously, and all actions are deterministic, the state of the world after any sequence of actions can be accurately predicted, and the question of observability is irrelevant for classical planning.
Further, plans can be defined as sequences of actions, because it is always known in advance which actions will be needed.
With nondeterministic actions or other events outside the control of the agent, the possible executions form a tree, and plans have to determine the appropriate actions for every node of the tree.
Discrete-timeMarkov decision processes (MDP) are planning problems with:
When full observability is replaced by partial observability, planning corresponds to apartially observable Markov decision process (POMDP).
If there are more than one agent, we havemulti-agent planning, which is closely related togame theory.
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In AI planning, planners typically input a domain model (a description of a set of possible actions which model the domain) as well as the specific problem to be solved specified by the initial state and goal, in contrast to those in which there is no input domain specified. Such planners are called "domain independent" to emphasize the fact that they can solve planning problems from a wide range of domains. Typical examples of domains are block-stacking, logistics, workflow management, and robot task planning. Hence a single domain-independent planner can be used to solve planning problems in all these various domains. On the other hand, a route planner is typical of a domain-specific planner.
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The most commonly used languages for representing planning domains and specific planning problems, such asSTRIPS andPDDL for Classical Planning, are based on state variables. Each possible state of the world is an assignment of values to the state variables, and actions determine how the values of the state variables change when that action is taken. Since a set of state variables induce a state space that has a size that is exponential in the set, planning, similarly to many other computational problems, suffers from thecurse of dimensionality and thecombinatorial explosion.
An alternative language for describing planning problems is that ofhierarchical task networks, in which a set of tasks is given, and each task can be either realized by a primitive action or decomposed into a set of other tasks. This does not necessarily involve state variables, although in more realistic applications state variables simplify the description of task networks.
Creating domain models is difficult, takes a lot of time, and can easily lead to mistakes. To help with this, several methods have been developed to automatically learn full or partial domain models from given observations.[2][3][4]
Temporal planning can be solved with methods similar to classical planning. The main difference is, because of the possibility of several, temporally overlapping actions with a duration being taken concurrently, that the definition of a state has to include information about the current absolute time and how far the execution of each active action has proceeded. Further, in planning with rational or real time, the state space may be infinite, unlike in classical planning or planning with integer time. Temporal planning is closely related toscheduling problems when uncertainty is involved and can also be understood in terms oftimed automata. The Simple Temporal Network with Uncertainty (STNU) is a scheduling problem which involves controllable actions, uncertain events and temporal constraints. Dynamic Controllability for such problems is a type of scheduling which requires a temporal planning strategy to activate controllable actions reactively as uncertain events are observed so that all constraints are guaranteed to be satisfied.[5]
Probabilistic planning can be solved with iterative methods such asvalue iteration andpolicy iteration, when the state space is sufficiently small.With partial observability, probabilistic planning is similarly solved with iterative methods, but using a representation of the value functions defined for the space of beliefs instead of states.
In preference-based planning, the objective is not only to produce a plan but also to satisfy user-specifiedpreferences. A difference to the more common reward-based planning, for example corresponding to MDPs, preferences don't necessarily have a precise numerical value.
Deterministic planning was introduced with theSTRIPS planning system, which is a hierarchical planner. Action names are ordered in a sequence and this is a plan for the robot. Hierarchical planning can be compared with an automatic generatedbehavior tree.[6] The disadvantage is, that a normal behavior tree is not so expressive like a computer program. That means, the notation of a behavior graph contains action commands, but noloops or if-then-statements. Conditional planning overcomes the bottleneck and introduces an elaborated notation which is similar to acontrol flow, known from other programming languages likePascal. It is very similar toprogram synthesis, which means a planner generates sourcecode which can be executed by an interpreter.[7]
An early example of a conditional planner is “Warplan-C” which was introduced in the mid 1970s.[8] What is the difference between a normal sequence and a complicated plan, which contains if-then-statements? It has to do with uncertainty atruntime of a plan. The idea is that a plan can react tosensor signals which are unknown for the planner. The planner generates two choices in advance. For example, if an object was detected, then action A is executed, if an object is missing, then action B is executed.[9] A major advantage of conditional planning is the ability to handlepartial plans.[10] An agent is not forced to plan everything from start to finish but can divide the problem intochunks. This helps to reduce the state space and solves much more complex problems.
We speak of "contingent planning" when the environment is observable through sensors, which can be faulty. It is thus a situation where the planning agent acts under incomplete information. For a contingent planning problem, a plan is no longer a sequence of actions but adecision tree because each step of the plan is represented by a set of states rather than a single perfectly observable state, as in the case of classical planning.[11] The selected actions depend on the state of the system. For example, if it rains, the agent chooses to take the umbrella, and if it doesn't, they may choose not to take it.
Michael L. Littman showed in 1998 that with branching actions, the planning problem becomesEXPTIME-complete.[12][13] A particular case of contiguous planning is represented by FOND problems - for "fully-observable and non-deterministic". If the goal is specified in LTLf (linear time logic on finite trace) then the problem is always EXPTIME-complete[14] and 2EXPTIME-complete if the goal is specified with LDLf.
Conformant planning is when the agent is uncertain about the state of the system, and it cannot make any observations. The agent then has beliefs about the real world, but cannot verify them with sensing actions, for instance. These problems are solved by techniques similar to those of classical planning,[15][16] but where the state space is exponential in the size of the problem, because of the uncertainty about the current state. A solution for a conformant planning problem is a sequence of actions. Haslum and Jonsson have demonstrated that the problem of conformant planning isEXPSPACE-complete,[17] and 2EXPTIME-complete when the initial situation is uncertain, and there is non-determinism in the actions outcomes.[13]
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