AllMacros.tex

%--- New Commands and Definitions

\newcommand{\bb}[1]{\mathbf{#1}}
\newcommand{\bs}[1]{\pmb{#1}}

\newcommand{\low}[1]{_{\scriptscriptstyle #1}}
\newcommand{\high}[1]{^{\scriptscriptstyle #1}}
\newcommand{\mat}[1]{\bb{#1}}
\newcommand{\gmat}[1]{\bs{#1}}
\newcommand{\Gmat}[1]{\pmb{\cal #1}}
\newcommand{\bvec}[1]{\bb{#1}}
\newcommand{\gvec}[1]{\bs{#1}}
\newcommand{\blkmat}[1]{\begin{bmatrix} #1 \end{bmatrix}}

\newcommand{\stx}[1]{\bvec{x}\low{#1}}
\newcommand{\stxU}[1]{\bvec{x}_{#1}}
\newcommand{\stxT}[1]{\bvec{x}^T\low{#1}}
\newcommand{\hstx}[1]{\hat{\bvec{x}}\low{#1}}
\newcommand{\bstx}[1]{\bar{\bvec{x}}\low{#1}}
\newcommand{\dstx}[1]{\dot{\bvec{x}}\low{#1}}
\newcommand{\dstxU}[1]{\dot{\bvec{x}}_{#1}}

\newcommand{\ctr}[1]{\bvec{u}\low{#1}}
\newcommand{\ctrU}[1]{\bvec{u}_{#1}}
\newcommand{\ctrT}[1]{\bvec{u}^T\low{#1}}
\newcommand{\hctr}[1]{\hat{\bvec{u}}\low{#1}}
\newcommand{\bctr}[1]{\bar{\bvec{u}}\low{#1}}
\newcommand{\dctr}[1]{\dot{\bvec{u}}\low{#1}}
\newcommand{\dctrU}[1]{\dot{\bvec{u}}_{#1}}


\newcommand{\vel}[1]{\bvec{v}\low{#1}}
\newcommand{\velU}[1]{\bvec{v}_{#1}}
\newcommand{\velT}[1]{\bvec{v}^T\low{#1}}
\newcommand{\hvel}[1]{\hat{\bvec{v}}\low{#1}}
\newcommand{\bvel}[1]{\bar{\bvec{v}}\low{#1}}
\newcommand{\bvelT}[1]{\bar{\bvec{v}}^T\low{#1}}
\newcommand{\dvel}[1]{\dot{\bvec{v}}\low{#1}}
\newcommand{\dvelU}[1]{\dot{\bvec{v}}_{#1}}

\newcommand{\om}[1]{\gvec{\omega}\low{#1}}
\newcommand{\omU}[1]{\gvec{\omega}_{#1}}
\newcommand{\omT}[1]{\gvec{\omega}^T\low{#1}}
\newcommand{\hatom}[1]{\hat{\gvec{\omega}}\low{#1}}
\newcommand{\bom}[1]{\bar{\gvec{\omega}}\low{#1}}
\newcommand{\dom}[1]{\dot{\gvec{\omega}}\low{#1}}
\newcommand{\domU}[1]{\dot{\gvec{\omega}}_{#1}}

\newcommand{\lbd}[1]{\gvec{\lambda}\low{#1}}
\newcommand{\lbdU}[1]{\gvec{\lambda}_{#1}}
\newcommand{\lbdT}[1]{\gvec{\lambda}^T\low{#1}}
\newcommand{\hlbd}[1]{\hat{\gvec{\lambda}}\low{#1}}
\newcommand{\dlbd}[1]{\dot{\gvec{\lambda}}\low{#1}}
\newcommand{\dlbdU}[1]{\dot{\gvec{\lambda}}_{#1}}

\newcommand{\pos}[2]{{}\high{#1}\bvec{p}\low{#2}}
\newcommand{\posU}[2]{{}^{#1}\bvec{p}_{#2}}
\newcommand{\bposU}[2]{{}^{#1}\bar{\bvec{p}}_{#2}}
\newcommand{\dltpos}[2]{{}\high{#1}\delta\bvec{p}\low{#2}}
\newcommand{\posT}[2]{{}\high{#1}\bvec{p}^T\low{#2}}
\newcommand{\hpos}[2]{{}\high{#1}\hat{\bvec{p}}\low{#2}}
\newcommand{\hposT}[2]{{}\high{#1}\hat{\bvec{p}}^T\low{#2}}
\newcommand{\dpos}[2]{{}\high{#1}\dot{\bvec{p}}\low{#2}}
\newcommand{\dposU}[2]{{}\high{#1}\dot{\bvec{p}}_{#2}}
\newcommand{\ddpos}[2]{{}\high{#1}\ddot{\bvec{p}}\low{#2}}

\newcommand{\angdir}[2]{{}\high{#1}\alpha\low{#2}}
\newcommand{\dangdir}[2]{{}\high{#1}\dot{\alpha}\low{#2}}

\newcommand{\dir}[2]{{}\high{#1}\bvec{d}\low{#2}}
\newcommand{\bdir}[2]{{}\high{#1}\bar{\bvec{d}}\low{#2}}
\newcommand{\dirT}[2]{{}\high{#1}\bvec{d}^T\low{#2}}
\newcommand{\hdir}[2]{{}\high{#1}\hat{\bvec{d}}\low{#2}}
\newcommand{\ddir}[2]{{}\high{#1}\dot{\bvec{d}}\low{#2}}

\newcommand{\lm}[2]{{}\high{#1}\bvec{m}\low{#2}}
\newcommand{\lmT}[2]{{}\high{#1}\bvec{m}^T\low{#2}}
\newcommand{\hlm}[2]{{}\high{#1}\hat{\bvec{m}}\low{#2}}
\newcommand{\dlm}[2]{{}\high{#1}\dot{\bvec{m}}\low{#2}}

\newcommand{\out }[1]{\bvec{y}\low{#1}}
\newcommand{\dout }[1]{\dot{\bvec{y}}\low{#1}}
\newcommand{\outT }[1]{\bvec{y}^T\low{#1}}
\newcommand{\outp }[1]{\bvec{y}\low{p_#1}}
\newcommand{\doutp}[1]{\dot{\bvec{y}}\low{p_#1}}
\newcommand{\ddoutp}[1]{\ddot{\bvec{y}}\low{p_#1}}
\newcommand{\outpT}[1]{\bvec{y}^T\low{p_#1}}
\newcommand{\outd }[1]{\bvec{y}\low{d_#1}}
\newcommand{\doutd}[1]{\dot{\bvec{y}}\low{d_#1}}
\newcommand{\ddoutd}[1]{\ddot{\bvec{y}}\low{d_#1}}
\newcommand{\outdT}[1]{\bvec{y}^T\low{d_#1}}

%\newcommand{\xxi}[0]{\gvec{\xi}}

%\newcommand{\DDelta}[0]{\mathfrak{D}}

\newcommand{\rot}[2]{{}\high{#1}\low{#2}\mat{R}}
\newcommand{\rotT}[2]{{}\high{#1}\low{#2}\mat{R}^T}
\newcommand{\dltrot}[2]{{}\high{#1}\low{#2}\delta\mat{R}}
\newcommand{\drot}[2]{{}\high{#1}\low{#2}\dot{\mat{R}}}
\newcommand{\hrot}[2]{{}\high{#1}\low{#2}\hat{\mat{R}}}
\newcommand{\trot}[2]{{}\high{#1}\low{#2}\tilde{\mat{R}}}

\newcommand{\covar}[1]{\gmat{\Sigma}\low{#1}}
\newcommand{\covarBIG}[1]{\gmat{\Sigma}_{#1}}

\newcommand{\fI}[0]{I}
\newcommand{\fE}[0]{E}
\newcommand{\fB}[0]{B}
\newcommand{\fCM}[0]{CM}
\newcommand{\fH}[0]{H}
\newcommand{\fL}[0]{L}
\newcommand{\fLB}[0]{LB}
\newcommand{\frames}[1]{\ensuremath{\{#1\}}}
\newcommand{\frameI}[0]{\frames{\fI}}
\newcommand{\frameE}[0]{\frames{\fE}}
\newcommand{\frameB}[0]{\frames{\fB}}
\newcommand{\frameCM}[0]{\frames{\fCM}}
\newcommand{\frameH}[0]{\frames{\fH}}
\newcommand{\frameL}[0]{\frames{\fL}}
\newcommand{\frameLB}[0]{\frames{\fLB}}

\newcommand{\zero}[0]{\mat{0}}
\newcommand{\one}[0]{\mat{1}}
\newcommand{\zeros}[2]{\zero_{{#1}\times{#2}}}
\newcommand{\ones}[2]{\one_{{#1}\times{#2}}}
\newcommand{\eyefunc}[0]{\mat{I}}
\newcommand{\eye}[1]{\eyefunc_{#1}}

\newcommand{\trsps}[0]{^T}
\newcommand{\set}[1]{\mathcal{#1}}
\newcommand{\setunion}[0]{\oplus}

\newcommand{\ColVec}[2]{\left[\begin{array}{#1} #2 \end{array}\right]}
\newcommand{\RowVec}[2]{\left[\begin{array}{#1} #2 \\\end{array}\right]}

\newcommand{\sk}[0]{\textrm{skew}}
\newcommand{\symm}[0]{{\rm symm}}
\newcommand{\abs}[1]{\left|#1\right|}
\newcommand{\diag}[1]{{\rm diag}\left(#1\right)}
\newcommand{\norm}[1]{\left\|#1\right\|}
\newcommand{\normL}[2]{\norm{#2}_{\set{L}_{#1}} }
\newcommand{\normH}[2]{\norm{#2}_{\set{H}_{#1}} }
\newcommand{\determ}[1]{\left|#1\right|}
\newcommand{\eigmax}[1]{\lambda_{max}\left(#1\right)}
\newcommand{\eigmin}[1]{\lambda_{min}\left(#1\right)}
\newcommand{\svd}[1]{\rm{svd}\left(#1\right)}
\newcommand{\tr}[1]{{\rm tr}\left(#1\right)}
\newcommand{\vc}[1]{{\rm vec}\left(#1\right)}
\newcommand{\convhull}[1]{ {\rm co}\left(#1\right) }
%\newcommand{\dotp}[2]{\langle#1,#2\rangle}
\newcommand{\intprod}[2]{\langle#1,#2\rangle}
\newcommand{\extprod}[2]{#1 \times #2}
\newcommand{\expo}[1]{\textrm{exp}\left[#1\right]}
\newcommand{\expect}[1]{\langle#1\rangle}
\newcommand{\sign}[1]{{\rm sign}\left({#1}\right)}
\newcommand{\matskewfunc}[0]{\mat{S}}
\newcommand{\matunskewfunc}[0]{\mat{S}\high{-1}}
\newcommand{\symmcompfunc}[0]{{\rm symm}}
\newcommand{\skewcompfunc}[0]{{\rm skew}}
\newcommand{\matskew}[1]{\matskewfunc(#1)}
\newcommand{\matunskew}[1]{\matunskewfunc(#1)}
\newcommand{\matskewPow}[2]{\matskewfunc^{#2}(#1)}
\newcommand{\symmcomp}[1]{\symmcompfunc\left(#1\right)}
\newcommand{\skewcomp}[1]{\skewcompfunc\left(#1\right)}

\newcommand{\N}[0]{\mathbb{N}}
\newcommand{\Z}[0]{\mathbb{Z}}
\newcommand{\R}[0]{\mathbb{R}}
\newcommand{\C}[0]{\mathbb{C}}
\newcommand{\orth}[1]{\set{O}(#1)}
\newcommand{\som}[0]{\set{SO}(3)}
\newcommand{\so}[1]{\set{SO}(#1)}
\newcommand{\se}[1]{\set{SE}(#1)}
\newcommand{\sem}[0]{\set{SE}(3)}
\newcommand{\krm}[0]{\set{K}(3)}
\newcommand{\kr}[1]{\set{K}(#1)}
\newcommand{\mr}[0]{\ensuremath{\set{M}(3,\R)}}
\newcommand{\mrm}[0]{\set{M}(3,\R)}
\newcommand{\mrmn}[1]{\set{M}(#1,\R)}
%\newcommand{\orth}[1]{{\rm O}(#1)}
%\newcommand{\som}[0]{{\rm SO}(3)}
%\newcommand{\so}[1]{{\rm SO}(#1)}
%\newcommand{\mr}[0]{{\rm M}(3,$\R$)}
%\newcommand{\krm}[0]{{\rm K}(3)}
%\newcommand{\kr}[1]{{\rm K}(#1)}
%\newcommand{\mrm}[0]{{\rm M}(3,\R)}
%\newcommand{\mrmn}[1]{{\rm M}(#1,\R)}

\newcommand{\dd}[2]{\frac{d\, #1}{d #2}}
\newcommand{\ddp}[2]{\frac{\partial\,#1}{\partial #2}}
\newcommand{\ddpT}[2]{\frac{\partial\,#1}{\partial #2^T}}
\newcommand{\ddpx}[2]{\frac{\partial\,\hat{#1}}{\partial #2}}
\newcommand{\dds}[3]{\frac{d^2\, #1}{d #2\,d #3^T}}
\newcommand{\ddss}[3]{\frac{d^2\, #1}{d #2^2}}
\newcommand{\ddssp}[2]{\frac{\partial^2\, #1}{\partial #2^2}}
\newcommand{\ddsdp}[3]{\frac{\partial^2\, #1}{\partial #2\,\partial #3}}
\newcommand{\ddsp}[3]{\frac{\partial^2\, #1}{\partial #2\,\partial #3^T}}
\newcommand{\ddspT}[3]{\frac{\partial^2\, #1}{\partial #2\,\partial #3}}
\newcommand{\ddspx}[3]{\frac{\partial^2\, \hat{#1}}{\partial #2\,\partial #3^T}}

\newcommand{\ddi}[3]{\frac{d^{#1}\, #2}{d {#3}^{#1}}}
\newcommand{\ddpi}[3]{\frac{\partial^{#1}\, #2}{\partial {#3}^{#1}}}

\newcommand{\grd}[2]{\nabla #1|_{#2}}
\newcommand{\grds}[2]{\nabla^2 #1|_{#2}}
\newcommand{\grdx}[2]{\nabla \hat{#1}|_{#2}}
\newcommand{\gradx}[2]{\textrm{grad} \hat{#1}|_{#2}}
\newcommand{\grdsx}[2]{\nabla^2 \hat{#1}|_{#2}}
\newcommand{\hess}[3]{\textrm{Hess} #1\left(#2,#3\right)}
\newcommand{\hessx}[3]{\textrm{Hess} \hat{#1}\left(\hat{#2},\hat{#3}\right)}

%to be unified with the previous macros!
\newcommand{\Set}[1]{\mathcal{#1}}
\newcommand{\SetSeq}[1]{\bs{\mathcal{#1}}}
\newcommand{\Rot}[0]{\mat{R}}                         % rotation matrix
\newcommand{\QRot}[0]{\mat{Q}}                         % attitude Q matrix

\newcommand{\suptextregistered}[0]{$^{\textrm{\textregistered}}$}

% Text Format (by PB)
%-------------------------------------------------------------------

% Math Bold Face
\newcommand{\mbf}[1]
	{{\mathbf #1}}

% Math Bold Bold
\newcommand{\mbb}[1]
	{{\mathbb #1}}

% Math Bold Greek
\newcommand{\mbg}[1]
	{{\mbox{\boldmath$#1$}}}
	
%% Low (Script Script Style)
%\newcommand{\low}[1]
%	{_{\scriptscriptstyle #1}}

% Specific Macros
%-------------------------------------------------------------------
% Rotation Matrix
\newcommand{\MR}{{\textbf{R}}}
	
% Skew-symmetric Matrix S
\newcommand{\MS}{{\mathbf{S}}}


% environments
%-------------------------------------------------------------------

\newtheorem{thm}{Theorem}
\newtheorem{prop}[thm]{Proposition}
\newtheorem{lemma}[thm]{Lemma}
\newtheorem{corol}[thm]{Corollary}
\newtheorem{assum}{Assumption}
\newtheorem{result}[thm]{Result}
%\newtheorem{proposition}[thm]{Proposition}  % To remove
%\newtheorem{theorem}[thm]{Theorem}          % To remove

\newtheorem{define}{Definition}
%\newtheorem{algorithm}{Algorithm}
\newtheorem{criteria}{Criteria}

\theoremstyle{definition}
\newtheorem{remark}{Remark}

% Put chapter number in theorem environments
\numberwithin{thm}{chapter}
\numberwithin{prop}{chapter}
\numberwithin{lemma}{chapter}
\numberwithin{corol}{chapter}
\numberwithin{assum}{chapter}
\numberwithin{remark}{chapter}
\numberwithin{define}{chapter}

%Note environment, for anotating draft version
\newcommand{\note}[1]{{\color{red}\footnotesize\sffamily [#1]}}

% Marco Morgado macros that might be useful:

%\newcommand{\R} {\mathcal{R}}
%\newcommand{\w} {\boldsymbol{\omega}}
%\newcommand{\bi} {\mathbf{b}_{\scriptscriptstyle i}}
%\newcommand{\bj} {\mathbf{b}_{\scriptscriptstyle j}}
%\newcommand{\bn}[1] {\mathbf{b}_{\scriptscriptstyle #1}}
%\newcommand{\p} {\mathbf{p}}
%\newcommand{\dr} {\mathbf{d}}
%\newcommand{\rpb} {\mathbf{r}}
%\newcommand{\s} {\mathbf{s}}
%\newcommand{\vel} {\mathbf{v}}

%\newcommand{\rhoi} {\rho_{\scriptscriptstyle i}}
%\newcommand{\drhoi} {\dot{\rho}_{\scriptscriptstyle i}}
%\newcommand{\rhoj} {\rho_{\scriptscriptstyle j}}
%\newcommand{\drhoj} {\dot{\rho}_{\scriptscriptstyle j}}
%\newcommand{\rhon}[1] {\rho_{\scriptscriptstyle #1}}
%\newcommand{\drhon}[1] {\dot{\rho}_{\scriptscriptstyle #1}}

%\newcommand{\T} {{}^{\scriptscriptstyle T}}

%\newcommand{\DI}[2]{{#1}_{\scriptscriptstyle #2}}

%% Operators
%%\newcommand{\skews}[1]{\mathcal{S}\left(#1\right)}
%%\newcommand{\unskew}[1]{{\mathcal{S}}^{-1}\left(#1\right)}
%\newcommand{\skews}[1]{[#1\times]}

%\DeclareMathOperator{\rank}{rank}
%\DeclareMathOperator{\round}{round}
%\DeclareMathOperator{\trace}{trace}
%\DeclareMathOperator{\diag}{diag}
%\DeclareMathOperator{\blkdiag}{blkdiag}
%\DeclareMathOperator{\rot}{rot}
%\DeclareMathOperator{\eigvec}{eigvec}

%\newcommand{\eye}{\mathbf{I}}
%\newcommand{\zeros}{\mathbf{0}}
%\newcommand{\eyen}[1]{\mathbf{I}_{\scriptscriptstyle #1}}
%\newcommand{\zerosn}[2]{\mathbf{0}_{\scriptscriptstyle #1 \times #2}}
%\newcommand{\ones}{\mathbf{1}}
%\newcommand{\onesn}[2]{\mathbf{1}_{\scriptscriptstyle #1 \times #2}}

%\newcommand{\expectedone}[1]{E\left\{#1\right\}}
%\newcommand{\expectedtwo}[2]{E\left\{#1#2\right\}}

%% Frames
%\newcommand{\ICF}{\{I\}\:}
%\newcommand{\BCF}{\{B\}\:}
%\newcommand{\UCF}{\{U\}\:}
%\newcommand{\ECF}{\{E\}\:}