A　bionic　robotic　fish　based　on　compliant　structure　can　excite　the　natural　modes　of　vibration,　thereby　mimicking　the　body　waves　of　real　fish　to　generate　thrust　and　realize　undulate　propulsion.　The　fish　body　wave　is　a　result　of　the　fish　body’s　mechanical　characteristics　interacting　with　the　surrounding　fluid.　Thoroughly　analyzing　the　complex　modal　characteristics　in　such　robotic　fish　contributes　to　a　better　understanding　of　the　locomotion　behavior,　consequently　enhancing　the　swimming　performance.　Therefore,　the　complex　orthogonal　decomposition　(COD)　method　is　used　in　this　article.　The　traveling　index　is　used　to　quantitatively　describe　the　difference　between　the　real　and　imaginary　modes　of　the　fish　body　wave.　It　is　defined　as　the　reciprocal　of　the　condition　number　between　the　real　and　imaginary　components.　After　introducing　the　BCF　(body　and/or　caudal　fin)　the　fish’s　body　wave　curves　and　the　COD　method,　the　structural　design　and　parameter　configuration　of　the　tensegrity　robotic　fish　are　introduced.　The　complex　modal　characteristics　of　the　tensegrity　robotic　fish　and　real　fish　are　analyzed.　The　results　show　that　their　traveling　indexes　are　close,　with　two　similar　complex　mode　shapes.　Subsequently,　the　relationship　between　the　traveling　index　and　swimming　performance　is　expressed　using　indicators　reflecting　linear　correlation　(correlation　coefficient　((Formula　presented.))　and　p　value).　Based　on　this　correlation,　a　preliminary　optimization　strategy　for　the　traveling　index　is　proposed,　with　the　potential　to　improve　the　swimming　performance　of　the　robotic　fish.　©　2023　by　the　authors.