Optimal Control Algorithms for Fuel Efficient Soft- Landing on Lunar Surface
- Paper number
IAC-07-C1.6.06
- Author
Dr. E. Krishna Kumar, Indian Space Research Organisation (ISRO), Astronautical Society of India, India
- Coauthor
Mr. M.P. Rijesh, Indian Space Research Organisation (ISRO), ISAC, India
- Year
2007
- Abstract
Vertical landing in the terminal phase of a lunar landing mission, with very low velocity(soft landing) and using minimum fuel, is formulated as an optimal control problem. The vehicle uses a retro engine system. Soft landing with minimum fuel consumption is established to be equivalent to a minimum time problem. The solution is by switching at some stage from zero-thrust to full thrust and continue until touchdown. The time for switching and firing duration until touchdown are unknowns to be determined. This paper proposes two different control schemes to achieve the objectives. With the vehicle assumed to be in full thrust mode, two state equations (altitude and velocity) are formed as a function of time, which is then approximated by a third order polynomial. This is different from the available published literature, where the problem is solved based on a second order polynomial resulting in poorer accuracy. The proposed solution covers all possible combination of states from which the vehicle can go to full thrust for soft landing. In the first approach, the current navigation data, when available, are used to propagate free fall conditions over to a future time, which satisfies both the equations. At this instant, the full thrust firing is initiated for a definite time interval. The firing duration also is obtained as a solution of the third order polynomial equations. All these are for realisation onboard in real time. In the second approach, the current navigation data is compared to a precomputed state trajectory stored onboard for different full thrust time intervals. When the mean square errors of the current system states with respect to the stored trajectory reaches below a threshold, the full thrust firing is initiated. This approach considerably reduces real time processing. However, it calls for a good strategy for effective locking on to the full thrust trajectory. A novel strategy to realise this scheme also is exposed in this paper.
- Abstract document
- Manuscript document
IAC-07-C1.6.06.pdf (🔒 authorized access only).
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