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\newtheorem{thm}{Theorem}[section]

\newtheorem{lem}[thm]{Lemma}

\newtheorem{prop}[thm]{Proposition}

\newtheorem*{cor}{Corollary}

\theoremstyle{definition}

\newtheorem{defn}{Definition}[section]

\newtheorem{conj}{Conjecture}[section]

\newtheorem{exmp}{Example}[section]

\theoremstyle{remark}

\newtheorem*{rem}{Remark}

\newtheorem*{note}{Note}

\begin{document}

 \begin{defn}

     For a $N-$robotic arm system with $J_1,\ldots,J_N$ joints and $J_0$ is base joint, the cost of rotation at every joint denote $c(J_i), i=1,\ldots,N$. We assume that $c(\cdot)$ is decreasing as $J_i$ increase. And we call a path is an {\em optimal end configuration} \rm if $ C^* = \min \{\sum_{i=1}^N (c(J_i))\}$, $i = 1,\ldots,N$.

     \label{define:optimal_end_configuration}

 \end{defn}