Much of the dry landmass on Earth remains impassible to wheeled and tracked machines, the stability of which can be severely compromised on challenging terrains. Quadrupedal animals, on the other hand, can access some of the most remote parts of Earth. They can choose safe footholds within their kinematic reach and rapidly change their kinematic state in response to the environment. Legged robots have the potential to traverse any terrains that their animal counterparts are able to traverse.

Dynamic locomotion in diverse, complex natural environments as shown in Fig. 1 has been a grand challenge in legged robotics. These environments have highly irregular profiles, deformable terrains, slippery surfaces, and overground obstructions. Under such conditions, existing published controllers manifest frequent foot slippage, loss of balance, and ultimately catastrophic failure. The challenge is exacerbated by the inaccessibility of accurate information about the physical properties of the terrain. Exteroceptive sensors such as cameras and LiDAR cannot reliably measure physical characteristics such as friction and compliance; are impeded by obstructions such as vegetation, snow, and water; and may not have the coverage and temporal resolution to capture changes induced by the robot itself, such as the crumbling of loose ground under the robot’s feet. Under these conditions, the robot must rely crucially on proprioception—the sensing of its own bodily configuration at high temporal resolution. In response to unforeseen events such as unexpected ground contact, terrain deformation, and foot slippage, the controller must rapidly produce whole-body trajectories subject to multiple objectives: balancing, avoiding self-collision, counteracting external disturbances, and locomotion. Although animals solve this complex control problem instinctively, it remains an open challenge in robotics.