The field of autonomous systems and legged locomotion is witnessing significant developments, with a focus on advanced optimal trajectory planning, gait optimization, and compliant robot design. Researchers are exploring innovative methods to improve the efficiency and adaptability of autonomous systems, including the use of mixed Bernstein-Fourier approximations and Lie group integrators. Noteworthy papers in this area include the introduction of a novel mixed Bernstein-Fourier approximation framework for optimal trajectory generation, and a geometric gait optimization method for kinodynamic systems using a Lie group integrator. Additionally, the development of tensegrity-based robot leg designs with variable stiffness and deformable multibody modeling for model predictive control are showcasing promising results in achieving more resilient and adaptable legged robots. The introduction of novel robotic platforms, such as the 10-DOF flexible bipedal wheeled robot, is also pushing the boundaries of locomotion capabilities. Overall, these advancements are paving the way for more sophisticated and efficient autonomous systems.