Runtime Learning of Quadruped Robots in Wild Environments Yihao Cai 1, Y anbing Mao 1, Lui Sha 2, Hongpeng Cao 3, and Marco Caccamo 3 This paper presents a runtime learning framework for quadruped robots, enabling them to learn and adapt safely in dynamic wild environments. The core novelty of this framework lies in two interactive and complementary components within the control module: the high-performance (HP)-Student and the high-assurance (HA)-Teacher. HP-Student is a deep reinforcement learning (DRL) agent that engages in self-learning and teaching-to-learn to develop a safe and high-performance action policy. HA-Teacher is a simplified yet verifiable physics-model-based controller, with the role of teaching HP-Student about safety while providing a backup for the robot's safe locomotion. HA-Teacher is innovative due to its real-time physics model, real-time action policy, and real-time control goals, all tailored to respond effectively to real-time wild environments, ensuring safety. The framework also includes a coordinator who effectively manages the interaction between HP-Student and HA-Teacher. Experiments involving a Unitree Go2 robot in Nvidia Isaac Gym and comparisons with state-of-the-art safe DRLs demonstrate the effectiveness of the proposed runtime learning framework. I NTRODUCTION Quadruped robots have become a promising solution for navigating challenging wild environments, such as forests, disaster zones, and mountainous regions [1], [2].

This paper proposes the SeC-Learning Machine: Simplex-enabled safe continual learning for safety-critical autonomous systems. The SeC-learning machine is built on Simplex logic (that is, ``using simplicity to control complexity'') and physics-regulated deep reinforcement learning (Phy-DRL). The SeC-learning machine thus constitutes HP (high performance)-Student, HA (high assurance)-Teacher, and Coordinator. Specifically, the HP-Student is a pre-trained high-performance but not fully verified Phy-DRL, continuing to learn in a real plant to tune the action policy to be safe. In contrast, the HA-Teacher is a mission-reduced, physics-model-based, and verified design. As a complementary, HA-Teacher has two missions: backing up safety and correcting unsafe learning. The Coordinator triggers the interaction and the switch between HP-Student and HA-Teacher. Powered by the three interactive components, the SeC-learning machine can i) assure lifetime safety (i.e., safety guarantee in any continual-learning stage, regardless of HP-Student's success or convergence), ii) address the Sim2Real gap, and iii) learn to tolerate unknown unknowns in real plants. The experiments on a cart-pole system and a real quadruped robot demonstrate the distinguished features of the SeC-learning machine, compared with continual learning built on state-of-the-art safe DRL frameworks with approaches to addressing the Sim2Real gap.