Cross-Platform Learnable Fuzzy Gain-Scheduled Proportional-Integral-Derivative Controller Tuning via Physics-Constrained Meta-Learning and Reinforcement Learning Adaptation

Motivation and gap: PID-family controllers remain a pragmatic choice for many robotic systems due to their simplicity and interpretability, but tuning stable, high-performing gains is time-consuming and typically non-transferable across robot morphologies, payloads, and deployment conditions. Fuzzy gain scheduling can provide interpretable online adjustment, yet its per-joint scaling and consequent parameters are platform-dependent and difficult to tune systematically. Proposed approach: We propose a hierarchical framework for cross-platform tuning of a learnable fuzzy gain-scheduled PID (LF-PID). The controller uses shared fuzzy membership partitions to preserve common error semantics, while learning per-joint scaling and Takagi-Sugeno consequent parameters that schedule PID gains online. Combined with physics-constrained virtual robot synthesis, meta-learning provides cross-platform initialization from robot physical features, and a lightweight reinforcement learning (RL) stage performs deployment-specific refinement under dynamics mismatch. Starting from three base simulated platforms, we generate 232 physically valid training variants via bounded perturbations of mass (+/-10%), inertia (+/-15%), and friction (+/-20%). Results and insight: We evaluate cross-platform generalization on two distinct systems (a 9-DOF serial manipulator and a 12-DOF quadruped) under multiple disturbance scenarios. The RL adaptation stage improves tracking performance on top of the meta-initialized controller, with up to 80.4% error reduction in challenging high-load joints (12.36 degrees to 2.42 degrees) and 19.2% improvement under parameter uncertainty. We further identify an optimization ceiling effect: online refinement yields substantial gains when the meta-initialized baseline exhibits localized deficiencies, but provides limited improvement when baseline quality is already uniformly strong.