L2-PPO: Recurrent Mobile Robot Navigation with Closed-form Continuous-time Networks and Lyapunov Auxiliary Learning

Autonomous mobile robot navigation in partially observable dynamic environments remains challenging because single-frame observations cannot fully capture obstacle motion and because policy and value representations must be learned under time-varying conditions. This paper proposes L2-PPO, a hierarchical local navigation framework that combines closed-form continuous-time (CfC) neural networks with a Lyapunov-inspired auxiliary loss applied only to the critic. Separate CfC backbones are used for the actor and critic to encode the temporal evolution of dynamic obstacles from partial sensor observations. The auxiliary loss imposes a monotonic-decrease constraint on the distance between current-state and virtual-goal embeddings without modifying the environment reward or directly backpropagating into the actor. Observation normalization, action mapping, and recurrent-state handling are kept consistent between training and ROS 2 deployment, enabling zero-shot sim-to-real deployment and real-time control. In 50 independent simulation runs in the complex dynamic scenario, L2-PPO achieved a 100% navigation success rate. Compared with standard PPO, it reduced the average navigation time by 20.0% (from 34.5 ± 2.6 s to 27.6 ± 1.1 s) and the average path length by 1.82 m (from 14.72 ± 0.82 m to 12.90 ± 0.38 m). Repeated physical robot experiments further achieved a 95%-100% success rate, with a single-step onboard ONNX inference latency of 2.38 ± 0.31 ms (99th percentile 3.18 ms), well below the 50 ms control interval. This result confirms that policy inference satisfies the real-time requirement of the deployed controller.