icra_2014_initial.sty

\newcommand{\authorone}{Jordan Lack}
\newcommand{\authortwo}{Matthew J. Powell}
\newcommand{\authorthree}{Aaron D. Ames}

\newcommand{\ds}{\mathrm{oa}}
\newcommand{\oa}{\mathrm{oa}}
\newcommand{\fa}{\mathrm{fa}}
\newcommand{\ua}{\mathrm{ua}}

\newcommand{\Vfa}{V_{\mathrm{FA}}}
\newcommand{\Vua}{V_{\mathrm{UA}}}
\newcommand{\Voa}{V_{\mathrm{OA}}}

\newcommand{\ts}{e_{\mathrm{ts}}}
\newcommand{\hl}{e_{\mathrm{hl}}}
\newcommand{\hs}{e_{\mathrm{hs}}}

\newcommand{\cwf}{\mathrm{cwf}}
\newcommand{\ecwf}{\mathrm{ecwf}}

%%% Robot
\newcommand{\robot}{r}
\newcommand{\lengthofcalf}{L_c}
\newcommand{\lengthofthigh}{L_t}

%%% dimensionality
\newcommand{\dimensionu}{m}
\newcommand{\dimensionx}{n}
\newcommand{\dimensioncontacts}{k}

%%% General Math Notation
% Common Number Sets
\newcommand{\Reals}{\mathbb{R}}
\newcommand{\Integers}{\mathbb{Z}}
\newcommand{\Naturals}{\mathbb{N}}

% Zero vector
\newcommand{\zm}{\mathbf{0}}

%%% General Physics Notation
\newcommand{\frictioncoefficient}{\mu}

%%% Hybrid Systems
% Graphs and Cycles
\newcommand{\cycle}{\ell}
\newcommand{\Graph}{\Gamma}
\newcommand{\vertex}{v}
\newcommand{\VertexSet}{V}
\newcommand{\edge}{e}
\newcommand{\EdgeSet}{E}
\newcommand{\sore}{\text{sor($\edge$)}}
\newcommand{\tare}{\text{tar($\edge$)}}

% Hybrid Control Systems
\newcommand{\HC}{\mathscr{HC}}
\newcommand{\domain}{D}
\newcommand{\admissiblecontrol}{U}
\newcommand{\guard}{S}
\newcommand{\resetmap}{\Delta}
\newcommand{\controlsystem}{FG}

% Indexing
\newcommand{\indexbyvertex}[1]{#1_\vertex}
\newcommand{\indexbyedge}[1]{#1_\edge}
\newcommand{\indexbysource}[1]{#1_{\sore}}
\newcommand{\indexbytarget}[1]{#1_{\tare}}
\newcommand{\indexbycontact}[1]{#1_{\contact}}
\newcommand{\indexbyhuman}[1]{#1^\human}
\newcommand{\indexbyrobot}[1]{#1_\robot}
\newcommand{\indexbyfullactuation}[1]{#1_{\fullactuation}}
\newcommand{\indexbyunderactuation}[1]{#1_{\underactuation}}
\newcommand{\indexbydoublesupport}[1]{#1_{\doublesupport}}

% Robot
\newcommand{\x}{x}
\newcommand{\xdot}{\dot \x}
\newcommand{\control}{u}


\newcommand{\Lagrangian}{L}
\newcommand{\KineticEnergy}{T}
\newcommand{\PotentialEnergy}{V}

\newcommand{\GeneralizedInertia}{M(\q)}
\newcommand{\CoriolisGravity}{N(\q,\dq)}
\newcommand{\Coriolis}{C(\q,\dq) \dq}
\newcommand{\Gravity}{G(\q)}
\newcommand{\TorqueDistribution}{B(\q)}
\newcommand{\Jacobian}{J}
\newcommand{\ContactWrench}{F}

\newcommand{\q}{q}
\newcommand{\dq}{\dot \q}
\newcommand{\ddq}{\ddot \q}
\newcommand{\ConfigurationSpace}{Q}

\newcommand{\qsa}{\q_{sa}}
\newcommand{\qsk}{\q_{sk}}
\newcommand{\qsh}{\q_{sh}}
\newcommand{\qnsh}{\q_{nsh}}
\newcommand{\qnsk}{\q_{nsk}}
\newcommand{\qnsa}{\q_{nsa}}

% Contacts and Constraints
\newcommand{\Terrain}{\mathcal{T}}
\newcommand{\contact}{c}
\newcommand{\ContactSet}{\mathcal{C}}
\newcommand{\holonomic}{\eta}
\newcommand{\unilateral}{h}
\newcommand{\ConstraintMatrix}{A}

% Domain Breakdowns
\newcommand{\DomainBreakdown}{\mathcal{B}}

% Human-Inspired Control
\newcommand{\pzero}{d_{\vertex}}
\newcommand{\fullactuation}{fa}
\newcommand{\underactuation}{ua}
\newcommand{\doublesupport}{oa}
\newcommand{\controlgain}{\varepsilon}
\newcommand{\param}{\alpha}
\newcommand{\humanoutputcombo}{Y_{\vertex}}
\newcommand{\OutputSet}{O}
\newcommand{\youtput}{o}
\newcommand{\controloutput}{y}
\newcommand{\human}{H}
%\newcommand{\vhip}{v_{hip,v}}
\newcommand{\vhip}{\mathrm{vel}_v}
\newcommand{\phip}{p_{hip,v}}
\newcommand{\phipL}{\delta p_{hip,v}}
\newcommand{\timeparameterization}{\tau}
\newcommand{\yone}{\controloutput_{1,\vertex}}
\newcommand{\yonefa}{\controloutput_{1,\fullactuation}}
\newcommand{\yoneua}{\controloutput_{1,\underactuation}}
\newcommand{\yoneds}{\controloutput_{1,\doublesupport}}
\newcommand{\yaone}{\controloutput^a_{1,\vertex}}
\newcommand{\yatwo}{\controloutput^a_{2,\vertex}}
\newcommand{\ydone}{\controloutput^d_{1,\vertex}}
\newcommand{\ydtwo}{\controloutput^d_{2,\vertex}}
\newcommand{\ytwo}{\controloutput_{2,\vertex}}
\newcommand{\ydottwo}{{\dot \controloutput}_{2,\vertex}}
\newcommand{\ytwofa}{\controloutput_{2,\fullactuation}}
\newcommand{\ytwoua}{\controloutput_{2,\underactuation}}
\newcommand{\ytwods}{\controloutput_{2,\doublesupport}}
\newcommand{\dyonedq}{c}
\newcommand{\dytwodq}{H}

%IO Linearization
\newcommand{\decouplingmatrix}{\mathcal{A}}

%%% Zero Dynamics and Partial
\newcommand{\ZeroDynamics}{\mathbf{Z}}
\newcommand{\PartialZeroDynamics}{\mathbf{PZ}}
% Motion Transitions
\newcommand{\paramtransition}{\gamma}
% Reconstruction
\newcommand{\qreconstruction}{\Phi}
\newcommand{\dqreconstruction}{\Psi}
% Inverse Kinematics
\newcommand{\thetaalpha}{\vartheta(\indexbydoublesupport{\param})}
\newcommand{\thetaalphadot}{{\dot \vartheta}(\indexbydoublesupport{\param})}

%%% Optimization
\newcommand{\HDBC}{\mathrm{Cost}_{\mathrm{HD}}}
\newcommand{\costoa}{\mathrm{Cost}_{\mathrm{oa}}}
\newcommand{\costfa}{\mathrm{Cost}_{\mathrm{fa}}}
\newcommand{\costua}{\mathrm{Cost}_{\mathrm{ua}}}
\newcommand{\st}{\quad \mathrm{s.t} \quad}

%%% Formatting
\newcommand{\takespace}{\vspace{-5mm}}
\newcommand{\gap}{\vspace{0.1cm}}
\newcommand{\newsec}[1]{\gap \noindent {\bf #1}}