Energy-Optimal Asymmetrical Gait Selection for Quadrupedal Robots

Symmetrical gaits, such as trotting, are commonly employed in quadrupedal robots for their simplicity and stability. However, the potential of asymmetrical gaits, such as bounding and galloping–which are prevalent in their natural counterparts at high speeds or over long distances–is less clear in the design of locomotion controllers for legged machines. This study systematically examines five distinct asymmetrical quadrupedal gaits on a legged robot, aiming to uncover the fundamental differences in footfall sequences and the consequent energetics across a broad range of speeds. Utilizing a full-body model of a quadrupedal robot (Unitree A1), we developed a hybrid system for each gait, incorporating the desired footfall sequence and rigid impacts. To identify the most energy-optimal gait, we applied optimal control methods, framing it as a trajectory optimization problem with specific constraints and a work-based cost of transport as an objective function. Our results show that, in the context of asymmetrical gaits, when minimizing cost of transport across the entire stride, the front leg pair primarily propels the system forward, while the rear leg pair acts more like an inverted pendulum, contributing significantly less to the energetic output. Additionally, while bounding–characterized by two aerial phases per cycle–is the most energy-optimal gait at higher speeds, the energy expenditure of gaits at speeds below 1 m/s depend heavily on the robot's specific design.