Ground test of terrain relative navigation based on crater matching algorithm for precise lunar landing

Abstract

Recent lunar exploration missions require precise landing navigation to succeed in missions. GPS is not available in the Moon, a lunar lander basically uses inertial navigation and corrects inertial navigation errors by observing stars or measuring lunar terrain data. When the lander arrives at the lunar parking orbit (100km altitude), nominal delivery error from translunar coast (TLC) to lunar orbit initiation (LOI) is known as $\pm$ 12 km (3 sigma error). Even if the lander can perform precise relative navigation in further landing phases, it is more important to get rid of initial errors. This paper focused on eliminating such initial errors by using a crater matching algorithm. The lunar lander can estimate its absolute position by taking an image of craters and comparing it with databases. Because the lander cannot always take images of craters in directly vertical to a lunar surface, a crater matching algorithm requires to be robust on the lander’s attitude changes. Therefore, the purpose of this research was to propose the crater matching algorithm robust on attitude changes and verify that terrain relative navigation (TRN) based on the algorithm could eliminate initial errors effectively. The algorithm adopted a projective invariant which is an algebraic number that does not change even when taken at any angle. The proposed algorithm was verified by actual camera tests and numerical simulations. The actual camera tests were performed to determine a matching threshold by calculating the invariants of the specific crater configurations taken at various angles. The matching rates were also investigated with the real crater database, LU78287GT. Moreover, TRN based on the algorithm was applied to computer simulations for the lunar landing and turned out to effectively remove initial errors. Finally, real ground tests were performed with a optical camera and IMU to estimate the position of the ground vehicle. In the computer simulations, the proposed crater matching algorithm showed approximately 99% and 90% of matching rates at 0.3-pixel noise ($1 \sigma$) with a local database and the whole lunar database, respectively. The TRN based on the algorithm also eliminated the initial errors effectively. In addition, the ground test showed the proposed algorithm based TRN was successfully reduced initial errors. After verifying the algorithm by flight tests and real platform tests in the future.