Immersion and Invariance Observers for Gyro-Free Attitude Control Systems

A novel observer-based attitude tracking controller is proposed in the absence of rate measurements. Based on the I&I design method in conjunction with dynamic scaling, an angular velocity observer employing the attitude quaternion measurements is designed. It is shown that the angular velocity estimate globally converges to the true value exponentially fast independently of the choice of control torque. By defining the rate estimate using a direction cosine matrix, the observer structure is far simplified and requires fewer state variables compared to the existing I&I design. A separation property is then established for the PD tracking controller while asymptotic convergence of the tracking errors is shown. To demonstrate the observer performance, numerical simulations are conducted. Tracking results of two observers with relatively high and low gains are provided and compared with the ideal case where true angular velocity is available for feedback control. Robustness properties are also shown through the simulations in the presence of measurement noise.