Attitude Tracking for Rigid Bodies Using Vector and Biased Gyro Measurements

The rigid-body attitude tracking using vector and biased gyro measurements with unknown inertia matrix is studied in this note. First, a gyro-bias observer with global exponential stability is designed. Then, an attitude tracking controller based on this observer is devised, ensuring almost global asymptotic stability and almost semiglobal exponential stability. A separation property of the combined observer-controller is proved. Lastly, an adaptive attitude tracking controller relying on a modified gyro-bias observer and with no over-parametrization is developed to deal with the unknown inertia matrix. The proposed control schemes require neither an explicit attitude representation nor any attitude estimation, but only the measurement of at least two non-collinear known inertial reference vectors and biased gyro rate, which can be obtained by common low-cost IMU sensors. Simulations are included to illustrate the proposed adaptive controller under noisy measurements.