Optimal　state　feedback　control　was　studied　for　trajectory　tracking　control　of　a　four-wheel　mobile　robot　in　the　presence　of　measure　noise,　model　noise　and　input　signal　noise.　The　kinematic　and　dynamic　model　and　the　trajectory　generation　of　the　omnidirectional　vehicle　were　established.　The　discrete　state　equations　were　derived.　Then　an　optimal　state　feedback　controller　based　on　Lyapunov　stability　using　the　Kalman　filter　state　with　white　noises　estimation　technique　was　derived.　A　self-adaptive　control　algorithm　was　presented　to　compensate　for　the　effects　of　input　signal　noise.　Simulation　results　demonstrate　that　the　model　measurement　and　input　signal　noises　and　disturbances　of　the　system　can　be　effectively　compensated;　the　tracking　precision　and　dynamic　response　speed　of　the　system　can　be　obviously　increased.