6. Two vectors $\overrightarrow{O A}, \overrightarrow{O B}$ on a plane satisfy $|\overrightarrow{O A}|=a,|\overrightarrow{O B}|=b$, and $a^{2}+b^{2}=4, \overrightarrow{O A} \cdot \overrightarrow{O B}=0$. If the vector $\overrightarrow{O C}=\lambda \overrightarrow{O A}+\mu \overrightarrow{O B}(\lambda, \mu \in \mathbf{R})$, and $\left(\lambda-\frac{1}{2}\right)^{2} a^{2}+\left(\mu-\frac{1}{2}\right)^{2} b^{2}=1$, then the maximum value of $|\overrightarrow{O C}|$ is . $\qquad$