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.
최근 달 착륙 임무에서 임무를 성공적으로 마치기 위해서는 정밀한 착륙 항법 기술이 필수적이다. 달 착륙선은 기본적으로 관성항법을 이용하고, 누적되는 관성항법 오차를 별 추적기나 달의 표면 정보를 이용하여 보정한다. 착륙선이 달 주차궤도에 도착하면, 12 km의 공분산 오차를 가진다. 나머지 달 착륙과정에서 아무리 정확한 상대항법을 수행한다고 하더라도, 초기 오차를 수정하는 것이 중요하다. 따라서, 이 논문에서는 누적오차를 수정하기 위해 크레이터 매칭 알고리즘을 제안하고, 그 알고리즘을 기반으로 한 항법을 수행한다. 실제 카메라 테스트를 통해 매칭 경계값을 결정했고, 지상플랫폼 검증에 반영했다. 또한, 실제 달 크레이터 데이터베이스를 사용하여 제안한 알고리즘의 매칭성능을 조사하였다. 매칭성능은 어느정도 착륙선의 위치를 알고 있다는 가정 하에, 지역적인 데이터베이스와, 완전히 위치를 모르고 있을 때 전체 달에 대한 데이터베이스를 사용하여 수행되었다. 마지막으로, 지상시험을 통해 알고리즘을 통해 초기 오차를 보정할 수 있음을 검증하였다. 이 알고리즘은 비행시험, 실제 플랫폼 검증을 통해 달 뿐만 아니라 크레이터를 보유한 다른 행성착륙 임무에서도 적용될 수 있을 것으로 보인다.
