Disturbance rejection in space applications: Problems and solutions

Navigation, control and guidance of the propulsive phase of planetary landing, e.g. on Mars (or the Moon), with a soft landing being the only target, are driven by Inertial Measurement Units and a radar altimeter/velocimeter. Their measurements are affected by bias and scale errors. The latter ones are aggravated by the attitude navigation error as it accumulates during the ballistic (and aerodynamic) flight after orbiter separation and couples for most of the descent trajectory with the vehicle axis inclination from the local vertical direction. By complementing the center-of-mass dynamics with appropriate disturbance state equations driven by noise vectors and estimating the noise from the model error (plant measurements minus model output), scale errors and bias can be retrieved in real time in the form of disturbance state variables. Although a similar complement is adopted in the standard navigation algorithms, it takes the form of an output disturbance, which may lead to unobservability. In this paper instead, the disturbance complement is designed to be fully observable, which may require that the derivatives of smooth systematic errors be pushed up to the command channel (a form of back-stepping). It is then viable, unlike standard navigation, to eliminate them from position and velocity tracking errors through disturbance rejection, under appropriate convergence conditions and sensor layout. It will, however, be demonstrated in this paper that the same result cannot be achieved under pure feedback control. Since constant errors (bias) become zero through back-stepping, a well known fact derives: bias can only be eliminated by disposing of supplementary sensors.To further enlighten and solve the question of bias rejection, a further case study is treated. The attitude control of drag-free satellites is considered, where fine accelerometers allow for the rejection of wide-band aerodynamic torques (think of low-Earth orbit spacecrafts) at the price of attitude divergence because of accelerometer bias and drift. The spacecraft attitude can be made bounded and accurate, if bias and drift are modeled as angular accelerations, affecting the attitude. They are estimated by attitude sensors like star trackers and then are rejected by the attitude control. The results in the soft landing and drag free case studies are illustrated by simulated runs and Monte Carlo trials.

► Navigation sensors affected by bias and scale errors.
► Disturbance model part of embedded model control allows estimation and cancellation.
► Bias cancellation needs supplementary sensors.
► Scale errors need back-stepping and trajectory convergence.
► Application to soft planetary landing and fine attitude control.