An　approach　is　presented　to　active　vibration　control　of　flexible　robot　manipulators　with　kinematic　redundancy.　The　smart　links　are　fabricated　from　the　flexible　links　to　which　are　bonded　piezoceramic　actuators　and　strain　gage　sensors.　The　state-space　expression　of　the　discrete　time-varying　dynamic　system　is　developed　firstly.　A　LQR　feedback　controller　is　designed　based　on　the　Bellman　dynamic　programming　theory.　Moreover,　an　approximate　method　is　proposed　for　estimating　the　state　information　of　the　system.　Finally,　a　planar　3R　flexible　redundant　manipulator　is　utilized　as　an　illustrative　instance.　The　simulation　results　reveal　that　the　dynamic　characteristic　of　the　manipulator　is　enhanced　significantly.