This　study　addresses　a　fully　flexible-link　space　robot　with　uncertain　parameters,　focusing　on　dynamic　modeling,　trajectory　tracking　and　vibration　suppression.　The　system’s　dynamic　model　was　derived　by　employing　the　linear　momentum,　Lagrange’s　equations,　and　the　assumed　mode　method.　An　adaptive　fuzzy　H∞　robust　control　scheme　was　then　designed　to　achieve　precise　tracking　of　the　desired　position.　Subsequently,　a　hybrid　trajectory　was　introduced,　combining　joint　stiffness　motion　and　flexible　link　vibration　through　the　concept　of　virtual　control　and　expected　trajectory.　The　trajectory　was　specifically　formulated　to　address　both　the　motion　and　vibration　characteristics　of　the　space　robot.　An　adaptive　fuzzy　H∞　robust　control　scheme　was　applied　to　track　this　hybrid　trajectory,　ensuring　both　accurate　position　tracking　and　effective　vibration　suppression.　Numerical　simulations　confirmed　the　efficacy　of　the　proposed　control　strategy,　demonstrating　its　ability　to　simultaneously　track　the　position　of　a　two-flexible-link　space　robot　while　suppressing　vibrations　in　the　flexible　links,　thereby　achieving　integrated　control　of　motion　and　vibration.　©　The　Author(s)　2025.