Energy-Efficient Driving for Distributed Drive Electric Vehicles via Lagrangian-Constrained Deep Reinforcement Learning with Adaptive Safety Critics

The energy-efficient driving of Distributed Drive Electric Vehicles (DDEVs) presents a complex optimization challenge: exploiting over-actuated torque distribution capabilities to minimize energy consumption while strictly adhering to high-dimensional safety constraints, specifically individual tire slip ratios. Existing Deep Reinforcement Learning (DRL) methods often struggle to balance these conflicting objectives, typically relying on scalar penalties that fail to guarantee safety in dynamic scenarios. This paper proposes a contribution-oriented framework, LagCriticSAC, which introduces a novel dual-critic architecture to decouple safety assessment from reward maximization. Unlike standard Lagrangian approaches that rely on global cost signals, our method employs dedicated cost-critics to provide state-aware predictions of long-term constraint violations for each wheel. This mechanism dynamically adjusts learnable Lagrange multipliers, creating a closed-loop feedback system that autonomously shifts between risk-averse and efficiency-priority modes. Experiments demonstrate that this approach not only achieves superior energy efficiency, outperforming Soft Actor-Critic (SAC) and Model Predictive Control (MPC) benchmarks by 6.2% and 12.4% respectively, but also strictly enforces per-wheel longitudinal slip constraints within ±0.1, ensuring operational safety even in high-density traffic environments. • A constrained DRL framework is proposed for energy-efficient driving of DDEVs. • Longitudinal slip constraints are explicitly enforced via a dual-critic network. • Enhanced generalization capability is validated in high-density traffic scenarios.