From 02f75ae8497089e2088ead6e919e6d1d945e631f Mon Sep 17 00:00:00 2001 From: NotXia <35894453+NotXia@users.noreply.github.com> Date: Thu, 16 Nov 2023 22:18:11 +0100 Subject: [PATCH] Add FAIKR1 non-linear planning --- .../module1/img/_nonlinear_plan_example.pdf | Bin 0 -> 31706 bytes .../module1/img/_pop_example1.pdf | Bin 0 -> 26050 bytes .../module1/img/_pop_example2.pdf | Bin 0 -> 29010 bytes .../module1/img/_pop_example3.pdf | Bin 0 -> 29466 bytes .../module1/img/_pop_example4.pdf | Bin 0 -> 28659 bytes .../module1/img/_pop_example5.pdf | Bin 0 -> 30278 bytes .../module1/img/_pop_example6.pdf | Bin 0 -> 30518 bytes .../module1/img/_pop_example7.pdf | Bin 0 -> 30448 bytes .../module1/img/_threat_example.pdf | Bin 0 -> 22595 bytes .../module1/img/nonlinear_plan_example.drawio | 112 ++++ .../module1/img/pop_example.drawio | 567 ++++++++++++++++++ .../module1/img/threat_example.drawio | 65 ++ .../module1/sections/_generative_planning.tex | 240 +++++++- 13 files changed, 983 insertions(+), 1 deletion(-) create mode 100644 src/fundamentals-of-ai-and-kr/module1/img/_nonlinear_plan_example.pdf create mode 100644 src/fundamentals-of-ai-and-kr/module1/img/_pop_example1.pdf create mode 100644 src/fundamentals-of-ai-and-kr/module1/img/_pop_example2.pdf create mode 100644 src/fundamentals-of-ai-and-kr/module1/img/_pop_example3.pdf create mode 100644 src/fundamentals-of-ai-and-kr/module1/img/_pop_example4.pdf create mode 100644 src/fundamentals-of-ai-and-kr/module1/img/_pop_example5.pdf create mode 100644 src/fundamentals-of-ai-and-kr/module1/img/_pop_example6.pdf create mode 100644 src/fundamentals-of-ai-and-kr/module1/img/_pop_example7.pdf create mode 100644 src/fundamentals-of-ai-and-kr/module1/img/_threat_example.pdf create mode 100644 src/fundamentals-of-ai-and-kr/module1/img/nonlinear_plan_example.drawio create mode 100644 src/fundamentals-of-ai-and-kr/module1/img/pop_example.drawio create mode 100644 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zX<{8F>9Vh@X5Hf|+~oQEEUy+*dv-~8T9-7>p>Dm>R_@sL0YvK^0R(n%aH06ie8A`+ zS$lH_iodd6_5b5RT3|Et|8^Wc9(0f*gb^dqQF6|f$ zD?kiKLe(3ljGHhE=K{cGghQJE!s`xBvhE literal 0 HcmV?d00001 diff --git a/src/fundamentals-of-ai-and-kr/module1/img/nonlinear_plan_example.drawio b/src/fundamentals-of-ai-and-kr/module1/img/nonlinear_plan_example.drawio new file mode 100644 index 0000000..f6f029b --- /dev/null +++ b/src/fundamentals-of-ai-and-kr/module1/img/nonlinear_plan_example.drawio @@ -0,0 +1,112 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/src/fundamentals-of-ai-and-kr/module1/img/pop_example.drawio b/src/fundamentals-of-ai-and-kr/module1/img/pop_example.drawio new file mode 100644 index 0000000..fb37bbb --- /dev/null +++ b/src/fundamentals-of-ai-and-kr/module1/img/pop_example.drawio @@ -0,0 +1,567 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/src/fundamentals-of-ai-and-kr/module1/img/threat_example.drawio b/src/fundamentals-of-ai-and-kr/module1/img/threat_example.drawio new file mode 100644 index 0000000..9504f5c --- /dev/null +++ b/src/fundamentals-of-ai-and-kr/module1/img/threat_example.drawio @@ -0,0 +1,65 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/src/fundamentals-of-ai-and-kr/module1/sections/_generative_planning.tex b/src/fundamentals-of-ai-and-kr/module1/sections/_generative_planning.tex index 1997716..6d78d99 100644 --- a/src/fundamentals-of-ai-and-kr/module1/sections/_generative_planning.tex +++ b/src/fundamentals-of-ai-and-kr/module1/sections/_generative_planning.tex @@ -18,6 +18,7 @@ \end{description} + \section{Linear planning} \marginnote{Linear planning} Formulates the planning problem as a search problem where: @@ -325,4 +326,241 @@ Heuristics may be used to avoid this. Conjunction of goals are solved separately, but this could lead to the \marginnote{Sussman anomaly} \textbf{Sussman anomaly} where a sub-goal destroys what another sub-goal has done. For this reason, when a conjunction is encountered, it is not immediately popped from the goal stack -and is left as a final check. \ No newline at end of file +and is left as a final check. + + + +\section{Non-linear planning} +\marginnote{Non-linear planning} +Non-linear planning finds a plan as a search problem in the space of plans (instead of states as in linear planning). +Each node of the search tree is a partial plan. Edges represent plan refinement operations. + +A non-linear plan is represented by: +\begin{descriptionlist} + \item[Actions{\normalfont.}] \marginnote{Actions set} + \item[Orderings] \marginnote{Orderings set} + between actions. + \item[Causal links] \marginnote{Causal links} + triplet $\langle S_i, S_j, c \rangle$ where $S_i$ and $S_j$ are actions and $c$ is a sub-goal. + $c$ should be the effect of $S_i$ and precondition of $S_j$. + + Causal links represent causal relations between actions (i.e. interaction between sub-goals): + to execute $S_j$, the effect $c$ of $S_i$ is required first. +\end{descriptionlist} + +The initial plan is an empty plan with two fake actions \texttt{start} and \texttt{stop} +with ordering $\texttt{start} < \texttt{stop}$: +\begin{descriptionlist} + \item[\texttt{start}] has no preconditions and the effects match the initial state. + \item[\texttt{stop}] has no effects and the preconditions match the goal. +\end{descriptionlist} +At each step, one of the following refinement operations can be applied until the goal is reached: +\begin{itemize} + \item Add an action to the set of actions. + \item Add an ordering to the set of orderings. + \item Add a causal link to the set of causal links. +\end{itemize} + +\begin{figure}[h] + \centering + \includegraphics[width=0.4\textwidth]{img/_nonlinear_plan_example.pdf} + \caption{Example of search tree in non-linear planning} +\end{figure} + + +\begin{description} + \item[Least commitment planning] \marginnote{Least commitment planning} + Only strictly necessary restrictions (e.g. ordering) are imposed. + Non-linear planning is a least commitment planning. + + \item[Linearization] \marginnote{Linearization} + At the end, the partially ordered actions should be linearized, + respecting the ordering constraints, to obtain the final plan. +\end{description} + + +\begin{description} + \item[Threat] \marginnote{Threat} + An action $S_k$ is a threat to a causal link $\langle S_i, S_j, c \rangle$ + if its effects cancel $c$. + $S_k$ should not be executed in between $S_i$ and $S_j$. + + \begin{figure}[H] + \centering + \includegraphics[width=0.3\textwidth]{img/_threat_example.pdf} + \caption{Example of threat. Causal links are represented using thick arrows.} + \end{figure} + + Possible solutions to a threat $S_k$ to $\langle S_i, S_j, c \rangle$ are: + \begin{descriptionlist} + \item[Demotion] \marginnote{Demotion} + Add the ordering constraint $S_k < S_i$ (i.e. threat executed before). + \item[Promotion] \marginnote{Promotion} + Add the ordering constraint $S_k > S_i$ (i.e. threat executed after). + \end{descriptionlist} +\end{description} + +\begin{algorithm} +\caption{Partial order planning (POP)} +\begin{lstlisting}[mathescape=true] +def pop(initial_state, goal, actions): + plan = init_empty_plan(initial_state, goal) + while not plan.isSolution(): + try: + sn, c = selectSubgoal(plan) + chooseOperator(plan, actions, sn, c) + resolveThreats(plan) + except PlanFailError: + plan.backtrack() + return plan + +def selectSubgoal(plan): + sn, c = random([sn, c in plan.steps if c in sn.unsolved_preconditions]) + return sn, c + +def chooseOperator(plan, actions, sn, c): + s = random([s in (actions + plan.steps) if c in s.effects]) + if s is None: raise(PlanFailError) + plan.addCausalLink($\langle$s, sn, c$\rangle$) + plan.addOrdering(s < sn) + if s not in plan.steps: + plan.addAction(s) + plan.addOrdering(start < s < stop) + +def resolveThreats(plan): + for s_k, s_i, s_j in plan.threats(): + resolution = random([ DEMOTION, PROMOTION ]) + if resolution == DEMOTION: + plan.addOrdering(s_k < s_i) + elif resolution == PROMOTION: + plan.addOrdering(s_k > s_j) + if plan.isNotConsistent(): raise(PlanFailError) +\end{lstlisting} +\end{algorithm} + +\begin{example}[Purchasing schedule] + The initial state is: + \[ \texttt{at(home)}, \texttt{sells(hws, drill)}, \texttt{sells(sm, milk)}, \texttt{sells(sm, banana)} \] + where $\texttt{hws}$ means "hardware store" and $\texttt{sm}$ means "supermarket". + + The goal is: + \[ \texttt{at(home)}, \texttt{have(drill)}, \texttt{have(milk)}, \texttt{have(banana)} \] + + The possible actions are:\\[0.5em] + \begin{minipage}{.5\linewidth} + \begin{descriptionlist} + \item[\texttt{GO(X, Y)}] \phantom{} + \begin{description} + \item[Preconditions] $\texttt{at(X)}$ + \item[Effects] $\texttt{at(Y)}$, $\lnot \texttt{at(X)}$ + \end{description} + \end{descriptionlist} + \end{minipage} + \begin{minipage}{.5\linewidth} + \begin{descriptionlist} + \item[\texttt{BUY(S, Y)}] \phantom{} + \begin{description} + \item[Preconditions] $\texttt{at(S)}$, $\texttt{sells(S, Y)}$ + \item[Effects] $\texttt{have(Y)}$ + \end{description} + \end{descriptionlist} + \end{minipage}\\[0.5em] + + Partial order planning steps are: + \begin{enumerate} + \item Define the initial plan: + \begin{center} + \includegraphics[width=0.7\textwidth]{img/_pop_example1.pdf} + \end{center} + + \item The loop of POP is: + \begin{itemize} + \item Choose an action $a_i$ and one of its unsolved preconditions $c$. + \item Select an action $a_j$ with the precondition $c$ in its effects. + \item Add the ordering constraint $\texttt{start} < a_j < \texttt{stop}$. + \item Add the causal link $\langle a_j, a_i, c \rangle$ (and ordering $a_j < a_i$). + \item Solve threats. + \end{itemize} + + We choose the action $a_i = \texttt{stop}$ and the precondition $c = \texttt{have(drill)}$. + We choose as action with $c$ in its effects $a_j = \texttt{BUY(X, drill)}$. + We therefore add to the plan the ordering $\texttt{start} < \texttt{BUY(X, drill)} < \texttt{stop}$ and + the causal link $\langle \texttt{BUY(X, drill)}, \texttt{stop}, \texttt{have(drill)} \rangle$: + \begin{center} + \includegraphics[width=0.7\textwidth]{img/_pop_example2.pdf} + \end{center} + + \item Repeat the previous point for the preconditions $\texttt{have(milk)}$ and $\texttt{have(banana)}$: + \begin{center} + \includegraphics[width=0.7\textwidth]{img/_pop_example3.pdf} + \end{center} + + \item Now, we choose as action $\texttt{BUY(X, drill)}$ and as unsolved precondition $\texttt{sells(X, drill)}$. + This can be solved from the action $\texttt{start}$ with effect $\texttt{sells(hws, drill)}$. + We make the substitution $\texttt{X}/\texttt{drill}$ and + add $\langle \texttt{start}, \texttt{BUY(hws, drill)}, \texttt{sells(hws, drill)} \rangle$ to the causal links. + The same process can be repeated for $\texttt{BUY(X, milk)}$ and $\texttt{BUY(X, banana)}$: + \begin{center} + \includegraphics[width=0.7\textwidth]{img/_pop_example4.pdf} + \end{center} + + \item Now, we choose as action $\texttt{BUY(hws, drill)}$ and as unsolved precondition $\texttt{at(hws)}$. + This can be solved using the action $\texttt{GO(X, hws)}$. + We add $\langle \texttt{GO(X, hws)}, \texttt{BUY(hws, drill)}, \texttt{at(hws)} \rangle$ to the causal links. + + We continue by choosing as action $\texttt{GO(X, hws)}$ and as unsolved precondition $\texttt{at(X)}$. + This can be solved from $\texttt{start}$ with effect $\texttt{at(home)}$. + We therefore make the substitution $\texttt{X}/\texttt{home}$ and + add $\langle \texttt{start}, \texttt{GO(home, hws)}, \texttt{at(home)} \rangle$ to the causal links. + + The same process can be repeated for the $\texttt{milk}$ and $\texttt{banana}$ branch: + \begin{center} + \includegraphics[width=0.7\textwidth]{img/_pop_example5.pdf} + \end{center} + + \item We have a threat between $\texttt{GO(home, hws)}$ and $\texttt{GO(home, sm)}$ as they both + require the precondition $\texttt{at(home)}$ and both have as effect $\lnot\texttt{at(home)}$. + It can be easily seen that neither promotion nor demotion solves the conflict. + We are therefore forced to backtrack. + + We backtrack at the previous point, where we chose as action $\texttt{GO(X, sm)}$ and as precondition $\texttt{at(X)}$ + (this step has been implicitly done in the previous point). + \begin{itemize} + \item Instead of choosing the action $\texttt{start}$, we choose $\texttt{GO(home, hws)}$ with the effect $\texttt{at(hws)}$. + We therefore make the substitution $\texttt{X}/\texttt{hws}$ and update the causal links. + \item We also resolve the threat $\texttt{GO(hws, sm)}$ to $\texttt{BUY(hws, drill)}$ + (it removes the precondition $\texttt{at(hws)}$) + by promoting $\texttt{GO(hws, sm)}$ + and adding the ordering constraint $\texttt{BUY(hws, drill)} < \texttt{GO(hws, sm)}$: + \end{itemize} + \begin{center} + \includegraphics[width=0.7\textwidth]{img/_pop_example6.pdf} + \end{center} + + \item Now, we choose as action $\texttt{stop}$ and as precondition $\texttt{at(home)}$. + We choose as action $\texttt{GO(sm, home)}$ and update the causal links. + + Finally, we solve the threat $\texttt{GO(sm, home)}$ to + both $\texttt{BUY(sm, milk)}$ and $\texttt{BUY(sm, banana)}$ (it removes the required precondition $\texttt{at(sm)}$) + by promoting $\texttt{GO(sm, home)}$. + The newly added ordering constraints are + $\texttt{BUY(sm, milk)} < \texttt{GO(sm, home)}$ and + $\texttt{BUY(sm, banana)} < \texttt{GO(sm, home)}$. + + The final plan is: + \begin{center} + \includegraphics[width=0.7\textwidth]{img/_pop_example7.pdf} + \end{center} + By considering the ordering constraints, a linearization could be: + \[ + \begin{split} + \texttt{GO(home, hws)} &\rightarrow + \texttt{BUY(hws, drill)} \rightarrow + \texttt{GO(hws, sm)} \rightarrow\\ + &\texttt{BUY(sm, milk)} \rightarrow + \texttt{BUY(sm, banana)} \rightarrow + \texttt{GO(sm, home)} + \end{split} + \] + \end{enumerate} +\end{example} \ No newline at end of file