glossary.tex

% Add term explanations. As the package auto-arranges, order is irrelevant
% ftp://ftp.funet.fi/pub/TeX/CTAN/macros/latex/contrib/glossaries/glossariesbegin.pdf

% Define some convenience macros
\newcommand{\glosentry}[3][]{ % name, description
	\newglossaryentry{#2}{%
		name={#2},
		description={#3},
		parent=glossary,
		#1}
	\glsadd{#2}
}
\newcommand{\acrentry}[4][]{ % short, long, description
	\newacronym[description={#3\ifthenelse{\equal{#4}{}}{}{, {#4}}},parent=glossary,#1]{#2}{#2}{#3}
	\glsadd{#2}
}
\newcommand{\notentry}[4][]{ % sort, name, description
    \newglossaryentry{#2}{%
        sort={#2},
        name={#3},
        description={#4},
        parent=romanletter,
        #1}
    \glsadd{#2}
}

% Add notation categories
\newglossaryentry{glossary}{sort=1,name={},description={}}
\newglossaryentry{symbol}{sort=2,name={},description={}}
\newglossaryentry{greekletter}{sort=3,name={},description={}}
\newglossaryentry{romanletter}{sort=4,name={},description={}}

% Add glossary entries (name, description)
\glosentry{C++}{Programming language}
\glosentry{tick}{Foo}

% Add acronyms (short, long, description)
\acrentry{QR}{quick response}{(code), a two-dimensional bar-code}
\acrentry[\glslongpluralkey={Markov decision processes}]{MDP}{Markov decision process}{}
\acrentry[\glslongpluralkey={partially observable Markov decision processes}]{POMDP}{partially observable Markov decision process}{}
\acrentry{GMM}{Gaussian mixture model}{}
\acrentry{ROS}{Robot Operating System}{an open source framework for robotics software development}
\acrentry{PBVI}{point-based value iteration}{}
\acrentry{pdf}{probability density function}{}
\acrentry{MI}{mutual information}{}
\acrentry{EKF}{extended Kalman filter}{}
\acrentry{KL}{Kullback-Leibler}{(divergence)}
\acrentry{SLAM}{simultaneous localization and mapping}{}
\acrentry{PID}{proportional-integral-derivative}{(controller)}
\acrentry{PWLC}{piecewise linear and convex}{}
\acrentry{IMU}{inertial measurement unit}{}

% Special notations to appear on top
\notentry[parent=symbol,sort=0]{emptyline}{}{}
\notentry[parent=symbol]{oplus}{$\oplus$}{cross-sum between sets}
\notentry[parent=symbol]{cup}{$\cup$}{union of arbitrary sets}

% Add notations (name, notation, description)
% Greek letters can be sorted according to english alphabets (which is wrong)
% or by arranging by hand with the sort key
\notentry[parent=greekletter,sort=01]{alpha}{$\alpha$}{vector containing the value of a policy tree for all states}
\notentry[parent=greekletter,sort=02]{beta}{$\beta$}{camera angle of view}
\notentry[parent=greekletter,sort=03]{Gamma}{$\Gamma(b,a,b')$}{belief transition function}
\notentry[parent=greekletter,sort=04]{gamma}{$\gamma$}{discount factor}
\notentry[parent=greekletter,sort=05]{delta}{$\delta$}{measured angle}
\notentry[parent=greekletter,sort=06]{epsilon}{$\epsilon$}{magnitude of the Bellman error}
\notentry[parent=greekletter,sort=07]{theta}{$\theta_t$}{robot's heading}
\notentry[parent=greekletter,sort=08]{vartheta}{$\vartheta$}{weighing factor for information gain on current target}
\notentry[parent=greekletter,sort=09]{kappa}{$\kappa$}{constant positive scalar penalty}
\notentry[parent=greekletter,sort=10]{Lambda}{$\Lambda$}{set of all $\alpha$-vectors}
\notentry[parent=greekletter,sort=11]{mu}{$\mu$}{mean of belief}
\notentry[parent=greekletter,sort=12]{pi}{$\pi$}{policy}
\notentry[parent=greekletter,sort=13]{rho}{$\rho(b,a)$}{reward for executing action $a$ in belief $b$}
\notentry[parent=greekletter,sort=14]{Sigma}{$\Sigma$}{covariance of belief}
\notentry[parent=greekletter,sort=15]{tau}{$\tau(b,a,z')$}{belief update function}
\notentry[parent=greekletter,sort=16]{varphi}{$\varphi$}{weighing factor for information gain on next target}
\notentry[parent=greekletter,sort=17]{chi}{$\chi_n$}{the best $n$-step $\alpha$-vector}
\notentry[parent=greekletter,sort=18]{omega}{$\omega_t$}{rotational velocity}

% Add notations (name, notation, description)
\notentry{Dkl}{$D_{KL}(\cdot,\cdot)$}{Kullback-Leibler divergence}
\notentry{tr}{$\text{tr}(\cdot)$}{trace}
\notentry{ln}{$\text{ln}(\cdot)$}{natural logarithm}
\notentry{N}{$\mathcal{N}(\mu,\Sigma)$}{multivariate normal distribution with mean $\mu$ and covariance $\Sigma$}
\notentry{E}{$\mathbb{E}[\cdot]$}{expected value}
\notentry{Re}{$\mathbb{R}$}{set of real numbers}
\notentry{S}{$S$}{state space}
\notentry{s}{$s$}{state}
\notentry{A}{$A$}{action space}
\notentry{a}{$a$}{action}
\notentry{C}{$C(a_t,\beta,r_{max})$}{camera cone of observation}
\notentry{T}{$T(s,a,s')$}{state transition model}
\notentry{R}{$R(s,a)$}{reward for executing action $a$ in state $s$}
\notentry{Z}{$Z$}{observation space}
\notentry{z}{$z$}{observation}
\notentry{O}{$O(s',a,z')$}{observation function}
\notentry{B}{$B$}{belief space}
\notentry{b}{$b(s)$}{belief}
\notentry{t}{$t$}{time}
\notentry{Vn}{$V^\pi_n$}{value of policy $\pi$ when there are $n$ steps remaining}
\notentry{V}{$V^\pi$}{value of a stationary policy $\pi$}
\notentry{d}{$d_n$}{decision rule when there are $n$ steps remaining}
\notentry{p}{$p(X)$}{probability of $X$}
\notentry{H}{$H$}{planning horizon}
\notentry{h}{$h_t$}{history of actions and measurements up to time $t$}
\notentry{vt}{$v_t$}{translational velocity}
\notentry{x}{$x_t$}{robot's $x$-coordinate}
\notentry{y}{$y_t$}{robot's $y$-coordinate}
\notentry{u}{$u_t$}{robot control}
\notentry{Q}{$Q$}{covariance of control noise}
\notentry{q}{$q_t$}{control noise}
\notentry{W}{$W$}{covariance of measurement noise}
\notentry{w}{$w_t$}{measurement noise}
\notentry{rmax}{$r_{max}$}{camera maximum range}
\notentry{l}{$l^i$}{location of $i$\textsuperscript{th} landmark}
\notentry{L}{$L^i$}{belief about location of $i$\textsuperscript{th} landmark}
\notentry{f}{$f(\cdot)$}{transition function}
\notentry{m}{$m(\cdot)$}{measurement function}
\notentry{Kp}{$K_p$}{PID controller's proportional gain}
\notentry{Ki}{$K_i$}{PID controller's integral gain}
\notentry{Kd}{$K_d$}{PID controller's derivative gain}
\notentry{I}{$\mathcal{I}(\cdot,\cdot)$}{mutual information}
\notentry{g}{$g(a_t,a_{t-1})$}{cost for taking action $a_t$ when previous action was $a_{t-1}$}
\notentry{VA}{$\mathit{VA}(C_{j=1:3})$}{area from which measurements are obtained}
\notentry{sr}{$s^r_t$}{robot's state at time $t$}