The field of legged robot locomotion is rapidly advancing, with a focus on developing scalable and adaptive control frameworks that can navigate complex and dynamic environments. One of the key innovations in this area is the integration of iterative learning control with biologically inspired torque libraries, which enables rapid adaptation to changes in terrain and gravitational conditions. Another significant development is the use of Koopman operator theory to create linear models of nonlinear systems, allowing for more efficient and effective control. Additionally, researchers are exploring the use of reinforcement learning and model-based approaches to improve the robustness and efficiency of legged locomotion. Notable papers in this area include:

• Iteratively Learning Muscle Memory for Legged Robots to Master Adaptive and High Precision Locomotion, which presents a scalable and adaptive control framework for legged robots.
• Koopman Operator Based Linear Model Predictive Control for 2D Quadruped Trotting, Bounding, and Gait Transition, which demonstrates the use of Koopman operator theory for online optimal control of quadrupedal robots.
• Guided Reinforcement Learning for Omnidirectional 3D Jumping in Quadruped Robots, which introduces a novel guided reinforcement learning approach for efficient and explainable jumping in quadruped robots.