Experimental results of a Terrain Relative Navigation algorithm using a simulated lunar scenario

Abstract

This paper deals with the problem of the navigation of a lunar lander based on the Terrain Relative Navigation approach. An algorithm is developed and tested on a scaled simulated lunar scenario, over which a tri-axial moving frame has been built to reproduce the landing trajectories. At the tip of the tri-axial moving frame, a long-range and a short-range infrared distance sensor are mounted to measure the altitude. The calibration of the distance sensors is of crucial importance to obtain good measurements. For this purpose, the sensors are calibrated by optimizing a nonlinear transfer function and a bias function using a least squares method. As a consequence, the covariance of the sensors is approximated with a second order function of the distance. The two sensors have two different operation ranges that overlap in a small region. A switch strategy is developed in order to obtain the best performances in the overlapping range. As a result, a single error model function of the distance is found after the evaluation of the switch strategy. Because of different environmental factors, such as temperature, a bias drift is evaluated for both the sensors and properly taken into account in the algorithm. In order to reflect information of the surface in the navigation algorithm, a Digital Elevation Model of the simulated lunar surface has been considered. The navigation algorithm is designed as an Extended Kalman Filter which uses the altitude measurements, the Digital Elevation Model and the accelerations measurements coming from the moving frame. The objective of the navigation algorithm is to estimate the position of the simulated space vehicle during the landing from an altitude of 3 km to a landing site in the proximity of a crater rim. Because the algorithm needs to be updated during the landing, a crater peak detector is conceived in order to reset the navigation filter with a new state vector and new state covariance. Experimental results of the navigation algorithm are presented in the paper

PSO-Based Soft Lunar Landing with Hazard Avoidance: Analysis and Experimentation

“…The experimental facility considered for the practical implementation of the proposed algorithm is located at the School of Aerospace Engineering of Sapienza University of Rome [26,27]. It is basically composed of a Cartesian robotic manipulator, which can move along the three axes x-y-z (only the translational motion can be simulated), and a highfidelity reproduction of a portion of the lunar terrain.…”

“…As already mentioned, the landing is supposed to occur near the equatorial lunar region called "Mare Serenitatis", simulated as in Ref. [27], and represented in Figure 3. The reference frame employed in this work is characterized by the z-axis directed upwards and perpendicular to the surface, and the xand y-axes lying on the surface and mutually perpendicular, in order to have a right-handed frame.…”

“…As already stated, during this control, the goal is still to decrease the velocity along the three axes. Therefore, the system in Equation (27), in which the unknowns are u x , u y , u z , and t 2 , needs to be solved. Since in the system (27) there is no information about the vertical position, this control is considered feasible if the vertical position, computed as…”

“…The sub-optimality is due to the polynomial approximation of the trajectory; however, in general, computing fast and real-time optimal trajectories is always a compromise between the computational time and the optimality of the results. The proposed methodology is practically tested through an experimental facility represented by a simulated lunar terrain and a Cartesian robotic manipulator [26,27] equipped with a camera through which craters could be detected.…”