Constraint-Enhanced Reinforcement Learning Based on Dynamic Decoupled Spherical Radial Squashing

When deploying reinforcement learning policies to physical robots, actuator rate constraints -- hard limits on how fast each joint can move per control step -- are unavoidable. These limits vary substantially across joints due to differences in motor inertia, power bandwidth, and transmission stiffness, creating pronounced heterogeneity that existing methods fail to handle geometrically: the per-joint feasible region forms a high-dimensional box in action-increment space, yet QP projection and spherical parameterization methods impose isotropic ball-shaped constraints, exponentially under-covering the true feasible set as heterogeneity grows. This paper proposes Dynamic Decoupled Spherical Radial Squashing (DD-SRad), which resolves this mismatch by computing a position-adaptive radius independently for each actuator, achieving tight alignment with the true per-joint feasible region. DD-SRad satisfies per-step hard constraints with probability~1, preserves well-conditioned gradients throughout training, and admits exact policy gradient backpropagation with zero runtime solver overhead. MuJoCo benchmark experiments demonstrate the highest task return at zero constraint violation -- matching the unconstrained upper bound -- with 30%--50% improvement in constraint-space coverage over spherical baselines. High-fidelity IsaacLab simulations with Unitree H1 and G1 humanoid robots confirm end-to-end optimality parameterized directly from official joint specifications, validating a systematic pathway from hardware datasheets to safe deployment.

Hybrid Energy-Aware Reward Shaping: A Unified Lightweight Physics-Guided Methodology for Policy Optimization

Deep reinforcement learning excels in continuous control but often requires extensive exploration, while physics-based models demand complete equations and suffer cubic complexity. This study proposes Hybrid Energy-Aware Reward Shaping (H-EARS), unifying potential-based reward shaping with energy-aware action regularization. H-EARS constrains action magnitude while balancing task-specific and energy-based potentials via functional decomposition, achieving linear complexity O(n) by capturing dominant energy components without full dynamics. We establish a theoretical foundation including: (1) functional independence for separate task/energy optimization; (2) energy-based convergence acceleration; (3) convergence guarantees under function approximation; and (4) approximate potential error bounds. Lyapunov stability connections are analyzed as heuristic guides. Experiments across baselines show improved convergence, stability, and energy efficiency. Vehicle simulations validate applicability in safety-critical domains under extreme conditions. Results confirm that integrating lightweight physics priors enhances model-free RL without complete system models, enabling transfer from lab research to industrial applications.