Singular　perturbation　adaptive　control　only　with　angular　position　measurements　and　flexible　Jeformation　is　designed　for　free-floating　space　manipulators　with　multiple　flexible　links　and　unknown　physical　parameters.　The　dynamical　Lagrange　equation　is　established　based　on　assumed　mode　technique.　A　singular　perturbation　model　has　been　formulated　and　useJ　for　designing　a　reduced-order　controller.　This　controller　consists　of　a　slow　control　component　and　a　fast　control　component.　High-precision　measurements　of　base　attitude　and　joint　Jisplacements　anJ　link　coordinate　are　available　on　flexible　space　robot　manipulators.　In　contrast,　base　attitude　angular　velocity　and　joint　velocity　and　link　coordmate　rate　measurements　which　increase　the　cost　are,　in　many　cases,　contaminated　by　noise　A　sliding　velocity　observer　based　augmented　adaptive　control　law　is　constructed　for　the　slow　counterpart　of　the　flexible　manipulator.　The　fast　subsystem　controller　is　designed　with　the　estimateJ　velocity　by　linear　observer　to　damp　out　the　vibration　of　the　flexible　link　by　optimal　Linear　Quadratic　Regulator　(LQR)　method.　Copyright　©　2014　by　the　International　Astronautical　Federation.　All　rights　reserved.