I need to create a PDA that accepts by empty stack and accepts the language formed by strings over the alphabet $\{a, b\}$ of the form: $uw$, where $w$ is the string $u$ reversed and doubled. So, for example, if $u=ab$ then $w=bbaa$ (the $ab$ is reversed then its characters are doubled).
Examples of strings in the language: $\epsilon$, $aaa$, $baaabb$, $abbbbbbaa$, etc.
I'm really struggling with setting up a PDA that satisfies the criteria. Any help is appreciated.