Adaptive PID Control for Robotic Systems via Hierarchical Meta-Learning and Reinforcement Learning with Physics-Based Data Augmentation

Proportional-Integral-Derivative (PID) controllers remain the predominant choice in industrial robotics due to their simplicity and reliability. However, manual tuning of PID parameters for diverse robotic platforms is time-consuming and requires extensive domain expertise. This paper presents a novel hierarchical control framework that combines meta-learning for PID initialization and reinforcement learning (RL) for online adaptation. To address the sample efficiency challenge, a \textit{physics-based data augmentation} strategy is introduced that generates virtual robot configurations by systematically perturbing physical parameters, enabling effective meta-learning with limited real robot data. The proposed approach is evaluated on two heterogeneous platforms: a 9-DOF Franka Panda manipulator and a 12-DOF Laikago quadruped robot. Experimental results demonstrate that the proposed method achieves 16.6\% average improvement on Franka Panda (6.26° MAE), with exceptional gains in high-load joints (J2: 80.4\% improvement from 12.36° to 2.42°). Critically, this work discovers the \textit{optimization ceiling effect}: RL achieves dramatic improvements when meta-learning exhibits localized high-error joints, but provides no benefit (0.0\%) when baseline performance is uniformly strong, as observed in Laikago. The method demonstrates robust performance under disturbances (parameter uncertainty: +19.2\%, no disturbance: +16.6\%, average: +10.0\%) with only 10 minutes of training time. Multi-seed analysis across 100 random initializations confirms stable performance (4.81+/-1.64\% average). These results establish that RL effectiveness is highly dependent on meta-learning baseline quality and error distribution, providing important design guidance for hierarchical control systems.