  In this research, we address the complex task of developing versatile and
agile quadrupedal gaits for robotic platforms, a domain predominantly governed
by model-based trajectory optimization methods. We propose an innovative,
reference-free reinforcement learning framework that exploits the intrinsic
symmetries of dynamic systems to synthesize a broad array of naturalistic
quadrupedal locomotion patterns. By capitalizing on distinct symmetry
characteristics - namely temporal, morphological, and time-reversal - our
approach efficiently facilitates the generation and transition among diverse
gaits such as pronking, bounding half-bounding and galloping, across a spectrum
of velocities, circumventing the necessity for expert-generated trajectories or
complex reward structures. Implemented on the Petoi Bittle robotic model, our
methodology illustrates robust and adaptable gait generation capabilities,
significantly broadening the scope for robotic mobility and speed adaptability.
This contribution not only advances our comprehension of quadrupedal locomotion
mechanisms but also underscores the pivotal role of symmetry in the development
of scalable and effective robotic gait strategies. Our findings hold
substantial implications for robotic design and control, potentially enhancing
operational versatility and efficiency across a variety of deployment
environments.
