INTERNATIONAL JOURNAL OF LATEST TECHNOLOGY IN ENGINEERING,  
MANAGEMENT & APPLIED SCIENCE (IJLTEMAS)  
ISSN 2278-2540 | DOI: 10.51583/IJLTEMAS | Volume XIV, Issue XI, November 2025  
Optimizing Lunar Descent Efficiency Using Reinforcement earning:  
A Computational Physics Investigation of Fuel-Constrained Landing  
Dynamics  
Akshey Sharma Kasibhatla  
Trio World Academy  
DOI : https://doi.org/10.51583/IJLTEMAS.2025.1411000088  
Received: 03 December 2025; Accepted: 08 December 2025; Published: 18 December 2025  
ABSTRACT  
Planetary landings can only be autonomous by having control systems that are able to balance accuracy and  
efficiency under nonlinear conditions.  
This research project examines the use of reinforcement learning (RL) which in this case is Proximal Policy  
Optimization (PPO) algorithm to simulate and optimize the dynamics of lunar descent in a one dimensional  
environment with Newtonian physics.  
The agent was trained to successfully complete soft landings at different fuel and thrust-cost settings, where a  
reward function punished the use of fuel and high terminal velocity.  
On 40 000 training episodes, the agent always shared similar stable policies that reduced fuel usage and yet  
reached safe touchdown speeds (less than 2 m/s-1).  
Quantitative analysis showed the existence of a strong negative correlation between available fuel and final  
velocity and unique dual-phase kinetics of fuel-use patterns were found which were similar to real-world  
powered-descent sequences.  
These findings confirm that reinforcement learning is a physically consistent, adaptive control technique to  
optimize descent, and has the potential to be useful in autonomous guidance systems in future trips to the moon  
and other planets.  
Primary Keywords (Core Concepts):  
1.  
2.  
3.  
4.  
5.  
6.  
7.  
8.  
Reinforcement Learning (RL)  
Proximal Policy Optimization (PPO)  
Lunar Landing Simulation  
Autonomous Spacecraft Descent  
Fuel-Efficient Landing Control  
Newtonian Physics Simulation  
Rocket Descent Dynamics  
Soft Landing Optimization  
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INTRODUCTION  
Space missions require fine control during descent and landing - a stage in which the slightest miscalculation  
can result in disaster. The 2019 Vikram lander crash as well as the precision landing of Chandrayaan-3, were  
both examples of how the physics behind control of a descent is one of the most complex of problems in modern  
aerospace engineering. Of the total factors affecting a successful lunar landing, fuel efficiency and stability are  
two steps on the safe steps, two sides of the coin of achieving a successful landing. The spacecraft must slow  
down enough to make a soft landing without drawing on its limited volumes of fuel. This trade-off is the basis  
of descent optimization -- a problem that using deterministic models of control, based on the Newtonian version  
of mechanical laws coupled with the Tsiolkovsky equation for rockets, traditionally has been.  
However, such traditional models rely on specifically defined control laws and they also tend not to adapt to  
dynamic, nonlinear environments. But reinforcement learning (RL), a subset of artificial intelligence based on  
the trial-and-error optimization approach of artificial intelligence, can learn thrust strategies entirely on its own  
that will allow it to minimize fuel consumption while still maintaining stability. By playing in a simulated lunar  
environment modeling classical mechanics, an RL agent can grade up its control policy based on feedback from  
reward signals determined by smoothness of landing, fuel consumption, and by velocity at landing (or the RL  
policy informs designers of where to test such a lander). This approach very well turns a physical control  
problem into a computational learning process.  
The physics involved in the moon fall is well understood, but rainy. Since in a lunar landing mission the lander  
is accelerated with the lunar gravitational force at about 1.62 m s-2, it is necessary to develop a high thrust to  
overcome the gravitational force to control the vertical velocity during the landing. département de G-fluidique  
et de Thermeerts 린 'Acceleration due to  
thrust in comparison with the vehicle's mass' - is based on Newton's Second Law and fuel burn, creating a  
relationship between thrust, fuel and motion. The appropriate form of climb therefore is a complex result of  
mechanical performance as well as real-time decision making. The RL framework offers a chance for simulating  
these dynamics under controlled conditions, and allows to establish quantitative analysis of the effects of various  
fuel constraints and thrust-cost penalties to the final landing results.  
This is an investigation through simulation of a computational physics simulation of lunar descent using the  
Python's Gymnasium simulation environment, and the Proximal Policy Optimization (PPO) algorithm. The  
simulation is based off a one axis lander with activation of lunar gravity, discrete thrust control and fluctuating  
fuel stores. Learning Controller training under different fuelthrust combinations: The study is done by training  
control policies on different combinations of fuel and thrust, also observing how the learned control policy leads  
to an optimization between efficiency and stability. Measurable outputs/outcomes are landing  
velocity, remaining fuel, and reward convergence - results that clearly show the success of the system to learn  
to save fuel resulting in a soft landing.  
The aim of this paper is to show that reinforcement learning can be used as a physically consistent and  
quantitatively verifiable model for real-world descent optimization problems. Besides its computational novelty,  
the study illustrates the interdisciplinarity of AI to simulate and optimize classical physical systems, which  
establish a milestone between traditional mechanics to a modern algorithmic control. By using machine learning  
with a physics-based descending lunar landing, this research will discover general scientific principles of low-  
fuel landing while being part of the new landscape of data-driven modeling in aerospace.  
METHODOLOGY  
Overview  
A one-dimensional computational model of lunar landing was developed for studying the use of reinforcement  
learning (RL) to optimize fuel consumption while ensuring a stable landing.  
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The simulation was coded using the Python programming language using the Gymnasium physics environment  
and the Stable-Baselines3 library, and the Proximal Policy Optimization (PPO) algorithm as the learning model.  
Each training episode was a full descent from rest at an altitude of 100 m to the surface or until the end of fuel  
supply.  
Physical Model  
The virtual lunar lander was modelled as a vertically descending mass point with gravitational acceleration  
(1.62 m/s^2) and thrusting engine acceleration that changed.  
Each time step (Dt = 0.05 s) the velocity and the altitude of the lander were updated by the second law of  
Newton, which involves the gravity and the acceleration of thrust.  
The fuel was used up by the application of thrust, which dynamically contributed to the reduction of total mass  
and coupled the fuel consumption with acceleration.  
Key model parameters:  
Parameter  
Symbol  
G
Value  
Lunar gravity  
Initial altitude  
Initial velocity  
Dry mass  
1.62 m/s²  
h₀  
100 m  
v₀  
0 m/s  
m₀  
150 kg  
Maximum fuel  
Maximum thrust  
Time step  
400–800 units (variable)  
3 000 N  
f◻  
T◻  
Δt  
0.05 s  
Each run had been stopped when either altitude 0 m (touchdown) or fuel 0.  
This simplified single-axis model separated dynamics on vertical descent with the focus on the trade off between  
the control of thrust and fuel economy.  
Reinitiation Learning Framework.  
The system was implemented as an agent-environment cycle.  
In each time step, the environment gave out the state vector as follows:  
-
-
-
-
Altitude  
Vertical velocity  
Remaining fuel fraction  
Previous thrust value  
The RL agent made a continuous thrust choice from 0 to T_m.  
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The environment then updated the lander's state (in response to applied thrust) and gave it a corresponding  
reward signal.  
Reward Function  
The optimization problem had a trade-off between hard landing (soft landing goal) and fuel consumption (lowest  
fuel consumption).  
At each step:  
-
-
-
-
The long descent times had a small negative reward (-0.01) associated with them.  
To deter too much burns, a thrust penalty (-0.0002 x thrust) was imposed.  
A bonus reward of +100 was placed for a soft landing (final velocity < 2 m/s).  
A fine (-100) was paid if the lander crashed or ran out of fuel before landing.  
PPO used thousands of training episodes to maximize its neural network policy to find the cumulative reward,  
which is essentially a process of selecting a control strategy that can mimic efficient humanlike descent  
behavior.  
Training Configuration  
Training included six configurations combining variation in fuel capacity and thrust-cost scaling factor as shown  
below:  
Configuration  
Max Fuel (units)  
Thrust Cost Scale  
A
400  
600  
800  
600  
800  
1.0  
1.0  
1.0  
1.5  
1.5  
B
C
D
E
Each policy was trained for 40,000 episodes, with 5,000-step evaluations of the policy. Core PPO  
hyperparameters:  
Setting  
Learning rate  
Discount factor (γ)  
Batch size  
Value  
3 × 10⁻⁴  
0.99  
256  
Clip range  
0.2  
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Random seed  
42  
Activation function  
Hidden layers  
ReLU  
3 × 64 neurons  
These environments guaranteed convergence behavior as well as numerical stability. During the second stage,  
Data Collection and Analysis, data collection and analysis will be performed using SPSS software.  
Data Collection and Analysis  
data will be collected and analysed using SPSS software.  
Measures (metric) of each configuration were time and memory usage:  
-
-
-
-
Final landing velocity (m/s)  
Fuel remaining (%)  
Episode duration (s)  
Total cumulative reward  
To minimize stochastic variance, averaging of results was done across 100 evaluation episodes. Matplotlib was  
used to generate plots that could be used to illustrate:  
-
-
-
-
Altitude vs. time  
Velocity vs. time  
Fuel vs. time  
Average Reward per Training Episode  
Comparative data have been collected in Table 1 (see Section 3).  
The numerical data were then processed to determine the effect that changes in fuel availability and thrust-cost  
penalties had on descent stability, fuel economy, and landing performance.  
Validation  
This simulation's physical accuracy was verified by comparing the simulation and analytical free-fall motion  
for a no-thrust control case.  
The theoretical free-fall impact velocity (18 m/s) agreed with the simulation result. Therefore, the environment  
physics was intact.  
The trajectories of learned control gave the expected smooth deceleration curves, which corresponded to  
behavior in actual descent, which confirmed that the actions of the agent were consistent with the Newtonian  
dynamics and the physically realistic expenditure of energy trends.  
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RESULTS  
Overview  
Different fuel capacity and thrust-cost scaling combinations were used for training runs. Each configuration  
was trained for 40000 episodes with evaluation in steps of 5000 episodes. The final performance metrics of the  
agent, including the landing velocity, remaining fuel, cumulative reward and qualitative outcome are  
summarized in Table 1.  
Table 1 - Performance of Lander Trained by PPO  
Configura  
tion  
Max  
Thrust  
Cost  
Final  
Fuel Remainin g (%) Reward Outcome  
Fuel  
Velocity  
(m/s)  
(units)  
Scale  
A
B
C
D
E
400  
600  
800  
600  
800  
1.0  
1.0  
1.0  
1.5  
1.5  
4.0  
1.7  
1.2  
2.4  
1.8  
3
59  
90  
95  
82  
90  
Partial success  
Soft landing  
Soft landing  
Efficient but slower  
Optimal  
6
12  
10  
15  
balance  
Quantitative Trends  
Fuel availability and stability (FAST).  
Maximum fuel amount was increased from 400 to 800 units, which continuously reduced landing velocity (from  
4.0 m/s to 1.2 m/s) indicating more smooth deceleration when more propellants were available for longer thrust  
modulation.  
Effect of scaling thrust with cost.  
Raising the cost multiplier from 1.0 to 1.5 led to more conservative use of fuel, a slight increase in terminal  
velocity, but a cost-effective use of fuel. Configuration E (800 units,  
1.5x cost) had one of the highest rewards while still having 15 percent of its fuel left over.  
Reward correlation  
Cumulative rewards increased as a function of increased softness of touch down and moderate residual fuel,  
which confirmed the reward design achieved a balance between stability and economy.  
Learning Behavior  
Average reward per episode rose sharply from 10 000 to 25 000 episodes, but flattened out, showing that PPO  
had converged. The results indicated that the initial training runs that were performed produced high-velocity  
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impacts and complete depletion of the fuel, while the last run produced straight thrust curves and consistent soft  
landing.  
Graphical Summaries  
Figure 1. Altitude vs time for Configuration E.  
The lander begins at 100 m and follows an exponentially decreasing trajectory, indicating controlled descent  
and successful throttle modulation  
The altitude drops very quickly in the 'early descent' phase, and then levels off quite close to the ground, while  
showing a nice smooth controlled descent in the velocity as the reinforcement learning agent is throttling back  
the engines just about to land.  
The curvature befriends exponential decays, characteristic of thrust modulated descent under constant  
gravitational acceleration.  
Figure 2. Velocity Vs time for Configuration E  
The lander accelerates due to the presence of lunar gravity amounting to 6m/s in the middle of its descent and  
then does a gentle braking, whereas the PPO trained agent puts to the brakes by reducing thrust to die off to  
1m/s at the time of touchdown.  
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Figure 3. Remaining time of fuel vs. time for Configuration E.  
The fuel quickly reduces during the early part of the descent and flattens out towards landing, so it is clear that  
the RL agent learned how to efficiently modulate thrust to limit excessive fuel burn and provide a controlled  
descent.  
Figure 4. Averaged reward against training step.  
Confirmation of the learning of a convergent and stable landing policy is shown by the sharp improvement in  
the PPO agent during initial training and the convergence around 110.  
Figure 5.  
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The left axis shows the remaining fuel at a particular landing velocity and the right axis shows the final landing  
velocity at a particular landing velocity. The negative correlation confirms that the balancing of the thrust  
efficiency and stability was achieved by the PPO agent as now to ease landings, which lowers remaining fuel.  
Outcome Summary  
Additionally, the configurations B to E yielded physically acceptable soft landings (< 2.5 m/s) The most  
balanced solution was at 800 fuel units and 1.5x thrust cost, which was a good balance of not spending much  
fuel, but staying at a stable terminal velocity.  
Overall, the agent discovered a strategy for thrusting which mimics human-engineered "suicideburn" profiles  
used in real lunar and Mars landers , that is, aggressive early descent and then gradual throttling of thrust to  
achieve a soft landing.  
Overview  
The results of the paper show that, with a reinforcement-learning (RL) model based on physical constraints, one  
can automatically find a set of thrust-control policies that result in almost optimal descent efficiency.The PPO  
agent created a landing strategy that had minimal fuel consumption and terminal velocity , a solution that is  
emergent and has traditionally been obtained either by an analytic optimization or by heuristic tuning.  
The model and the computational learning framework took the problem of simulation-based computational  
learning and the problem of classical mechanics, reducing the descent problem as a deterministic set of  
equations to an adaptive control program.  
Fuel-Velocity Trade-Off  
One of the distinguishing outcomes of this research is the negative correlation between the available fuel and  
the actual final velocity.As the propellant capacity was raised to 800 units, the touchdown velocity of the agent  
was reduced to approximately 1.2m/s at 400 to 800.  
This is the same as the relationship between mass ratio and the achievable Dv under the control of the  
Tsiolkovsky: the higher the fuel mass the larger the deceleration periods and the more precise the thrust  
modulation.  
Nevertheless, over-imposed thrust-penalties caused under-burning at the surface which generated slightly  
higher terminal velocities.  
This nonlinear sensitivity highlights the duality of the descent guidance objective - safety and efficiency are in  
conflict, and the reward system of the RL agent was able to manage this constraint boundary reasonably well.  
Learning Dynamics of Ppo  
The graph of Average Reward vs Episode had the canonical S-shaped pattern of learning-reinforcement  
convergence.  
The patterns of thrust of early episodes were exploratory and dissipationful in character; by about 25 000  
episodes PPO equated itself on a steady control policy.  
This trend is indicative of a true course of learning, but not overfitting: reward gains were associated with  
psychologically significant behavioral modifications - less oscillation, slower throttle response, and damping  
velocity more smoothly.  
The outcome justifies the PPO applicability to high dimensional control problems in continuous action space  
systems like those found in aerospace systems.  
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Fuel-Burn Kinetics  
The trend of Fuel Remaining vs Time showed that two kinetic regimes existed.  
The first severe gradient is that of impulse-burn, and this corresponds to the powered-descent phase of the  
Apollo 11 ascent or the rough-braking phase of the Chandrayaan-3.  
The following flattening is an indication of throttle-gated terminal phase in which the thrust output is  
dynamically modified in response to remaining momentum.  
It is interesting to note that such a phased pattern was not forced by code, but rather arose during the optimization  
of the policy, which means that the RL agent learned a physically optimal thrust trajectory.  
Expansive Implications on Autonomous Guidance.  
These findings put reinforcement learning as a plausible substitute to model-predictive control in uncertain  
guidance of descent control.  
The RL agent is adaptive to changing parameter values, unlike the traditional PID controllers that use fixed  
values in the gain parameters; the agent learns an adaptive response based on the feedback, so it is robust to  
changing parameter values, mass variations, or unmodeled perturbations.  
This flexibility might be critical in spaceflight missions where the environmental parameters are stochastic and  
initial control laws with pre-tune-down control are doomed to failure.  
Besides, the high correspondence between trained and desired mechanical behavior confirms that machine-  
learned control laws can be intelligible in physics, instead of black-box outputs.  
The only way the work can be improved is by  
Limitations and Path Forward.  
The present simulation makes the descent a one dimensional vertical motion idealized. This framework should  
be expanded into rotational dynamics, terrain mapping, and sensor noise to future work that can be performed  
up to the 6-DOF.  
To be more real the introduction of stochastic gravity perturbations and time delayed state feedback would be  
more realistic.  
Robustness under condition of higher-dimensional state spaces could be compared to other algorithms by  
comparative tests with Soft Actor-Critic (SAC) or TD3 algorithms.  
These improvements would take this model a step further to conceptual validation into deployable autonomy.  
Synthesis  
Overall, this paper confirms that experience alone can revive physically consistent descent-strategies based on  
reinforcement learning.  
The policies learned by the PPO agent are parallel to the policies which have been learned analytically, by  
applying the optimal-control theory, but are also obtained by organic means of maximizing rewards via an  
iterative procedure.  
This approach of converging algorithmic learning with classical physics can be an example of data-driven  
intelligence and first-principles engineering that could form the basis of the future generation of autonomous  
planetary landing systems.  
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CONCLUSION  
This study will establish that the technique of reinforcement learning (RL) combined with physically realistic  
dynamics can automatically realize fuel-efficient and stable descent strategies that are similar to classical  
optimal-control results.  
By repeatedly acting on a physics-based environment, the PPO agent learnt how to minimize terminal velocity  
with minimal expenditure on propellant, and it can reproduce behavioral patterns of real lunar landers.  
The resulting control curves bore adaptive throttle modulation, smooth braking as well as steady touchdown  
curves - without detailed programming of thrust laws.  
This research paper shows that knowledge-based learning can bring to a convergent state of Newtonian  
consistent control and combine computational intelligence with physical reasoning. These results indicate that  
reinforcement learning can be a suitable model to consider in the development of next-generation autonomous  
spacecraft guidance that can be adaptable in uncertain situations and resilient against the limitations inherent in  
more deterministic controllers.  
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