A Mathematical Framework for Sensor-Aligned Reinforcement Learning and Sim-to-Real Transfer on Resource-Constrained Autonomous Vehicles

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Overview This paper presents Version 1.0 of a proposed mathematical framework for sensor-aligned reinforcement learning and sim-to-real transfer in resource-constrained autonomous ground vehicles. The research investigates the theoretical feasibility of training an autonomous navigation policy in Unreal Engine 5 using Proximal Policy Optimization (PPO) and subsequently deploying the trained neural network on an ESP32-class microcontroller. The proposed framework integrates nonlinear differential-drive vehicle dynamics, physically realizable sensor observations, partially observable Markov decision processes, domain randomization, embedded neural network inference, and numerical error propagation. Particular attention is given to the mathematical relationship between sensor measurement errors, physical dynamics mismatch, neural network quantization, and their combined effects on closed-loop control performance. The paper develops conditional finite-horizon bounds for trajectory deviation and reward degradation, together with a layerwise analysis of neural network quantization errors. A reproducible experimental methodology is proposed to evaluate PPO learning, sensor alignment, observation history, domain randomization, FP32 and INT8 inference, and zero-shot sim-to-real transfer. Research Status Version 1.0 represents the theoretical framework and proposed system architecture. The complete UE5 simulation environment, PPO training pipeline, embedded deployment, and physical experiments have not yet been empirically validated. The mathematical framework and experimental methodology are intended to provide a foundation for subsequent implementation and evaluation. Research Independence This research was conceived and developed independently by Yaroslav Lukianov as a self-directed academic research project. The author is a student at the Faculty of Mathematics and Physics, Charles University, Prague, Czech Republic.