Curriculum-Based Deep Reinforcement Learning for Robust Autonomous Rocket Landing under Atmospheric Uncertainty
Organizations: Department of Computer Science and Engineering, Indian Institute of Information Technology, Sri City, Andhra Pradesh, India
Abstract
Autonomous far-range rocket landing is a challenging control problem because navigation, descent-rate regulation, attitude management, and fuel use must be coordinated in the presence of uncertain atmospheric and vehicle dynamics. This paper presents a curriculum-driven proximal policy optimization (PPO) framework for three-dimensional rocket landing in a stochastic environment incorporating altitude-dependent aerodynamic drag, wind shear, temporally correlated turbulence, discrete gusts, uncertain propulsion and aerodynamic parameters, thrust-vector misalignment, engine lag, actuator-gain variation, noisy observations, and command latency. Learning is organised into far-range approach, soft descent, and integrated landing stages. Policy transfer, critic warm-up after reward changes, rehearsal of earlier tasks, and progressive expansion of weather severity are used to support learning across these coupled phases. Across 100,000 evaluation episodes, the policy achieves 96,656 successful landings, corresponding to a success rate of 96.656% and a 95% Wilson confidence interval of 96.543--96.766%. Success decreases from 98.84% under zero-disturbance conditions to 88.07% in the highest weather-severity band. Successful touchdowns exhibit small miss distances and low residual horizontal and vertical velocities. An exploratory logistic-regression analysis identifies mean wind speed as the strongest measured correlate of success, with initial distance, initial altitude, initial vertical velocity, and wind-shear exponent also associated with outcomes. The results quantify both the effectiveness of the learned policy over the evaluated disturbance distribution and the degradation that occurs under severe compound atmospheric conditions.
Figures & tables
| Quantity | Range at | Implementation role |
|---|---|---|
| Reference horizontal wind | units/frame | Random direction and altitude shear |
| Horizontal turbulence SD | units/frame | Correlated per-frame perturbation |
| Vertical turbulence innovation | Half the horizontal scale | Vertical atmospheric fluctuation |
| Gust amplitude parameter | units/frame | Intermittent 60–160-frame gusts |
| Gust initiation probability | per frame | Probability of starting a gust |
| Density scale | Scales air density |
| Reward parameter | Stage 2 | Stage 3 |
|---|---|---|
| 0.4 | 0.4 | |
| 0.5 | 0.5 | |
| 0.3 | 0 | |
| 0.3 | 0 | |
| 0.05 | 0.05 | |
| 0.10 | 0.12 |
| Parameter | Stage 1 | Stage 2 | Stage 3 |
| Task | Far approach / hover | Soft descent | Integrated landing |
| Timesteps | |||
| Initial horizontal radius | 1,000–1,500 | 0–15 | 1,000–1,500 |
| Initial altitude | 900–1,300 | 500–800 | 900–1,300 |
| Initial vertical velocity | |||
| Initial tilt offsets |
| Outcome | Episodes | Share of all episodes |
|---|---|---|
| Successful touchdown | 96,656 | 96.656% |
| Touchdown failing one or more criteria | 3,237 | 3.237% |
| Timeout | 107 | 0.107% |
| Left workspace | 0 | 0.000% |
| Total | 100,000 | 100.000% |
| Weather level | Successful | Crashed | Timeout + lost | Success | |
|---|---|---|---|---|---|
| 0 (calm) | 15,218 | 15,041 | 177 | 0 | 98.84% |
| 17,059 | 16,857 | 202 | 0 | 98.82% | |
| 16,936 | 16,780 | 156 | 0 | 99.08% | |
| 16,825 | 16,658 | 167 | 0 | 99.01% | |
| 17,097 | 16,467 | 628 | 2 | 96.32% | |
| 16,865 | 14,853 | 1,907 | 105 | 88.07% |
| Metric | Mean SD | Median | P95 | Criterion / note |
|---|---|---|---|---|
| Miss distance | 6.634 | 13.054 | units | |
| Horizontal speed | 0.0529 | 0.1142 | ||
| Vertical speed | 0.1101 | 0.1470 | ||
| Tilt (descriptive) | 4.390 | 10.149 | Not in success rule | |
| Fuel used | 159.18 | 226.53 | Initial fuel: 1,000 | |
| Flight duration | 24.117 | 36.517 | Descriptive (seconds) |
| Violated criteria | Episodes | Share of crashes |
|---|---|---|
| Missed pad only | 2,677 | 82.7% |
| Missed pad, too fast vertically, and too fast horizontally | 366 | 11.3% |
| Missed pad and too fast horizontally | 69 | 2.1% |
| Missed pad and too fast vertically | 67 | 2.1% |
| Too fast vertically only | 41 | 1.3% |
| Too fast vertically and too fast horizontally | 17 | 0.5% |
| Factor | Bin | Episodes | Successful | Success |
|---|---|---|---|---|
| Mean wind speed | 15,218 | 15,041 | 98.84% | |
| 25,937 | 25,654 | 98.91% | ||
| 25,938 | 25,678 | 99.00% | ||
| 19,771 | 19,264 | 97.44% | ||
| 10,145 | 8,982 | 88.54% | ||
| 2,991 | 2,037 | 68.10% |
| Predictor | OR | 95% CI for OR | Reported -value |
|---|---|---|---|
| Mean wind speed | 0.244 | [0.228, 0.260] | |
| Wind-shear exponent | 1.453 | [1.399, 1.508] | |
| Initial height | 1.210 | [1.167, 1.255] | |
| Initial vertical speed | 1.199 | [1.156, 1.243] | |
| Initial distance | 0.839 | [0.809, 0.871] | |
| Gust amplitude | 1.172 | [1.097, 1.252] |
Reinforcement Learning
Reinforcement learning studies how agents learn sequential decisions from rewards and interaction, balancing exploration, performance, safety, and adaptation.
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