  This article considers $G$-Anosov representations of a fixed closed oriented
Riemann surface $\Sigma$ of genus at least $2$. Here, $G$ is the Lie group
$\text{PSp}(2n,\mathbb{R}$), $\text{PSO}(n,n)$ or $\text{PSO}(n,n+1)$. It
proves that Reidemeister torsion (R-torsion) associated to $\Sigma$ with
coefficients in the adjoint bundle representations of such representations is
well-defined. Moreover, by using symplectic chain complex method, it
establishes a novel formula for R-torsion of such representations in terms of
the Atiyah-Bott-Goldman symplectic form corresponding to the Lie group $G$.
Furtermore, it applies the results to Hitchin components, in particular,
Teichm\"{u}ller space.
