Reachability Map for Diverse and Energy Efficient Stepping of Humanoids

In legged locomotion, the relationship between different gait behaviors and energy consumption must consider the full-body dynamics and the robot control as a whole, which cannot be captured by simple models. This work studies the totality of robot dynamics and whole-body optimal control as a coupled system to investigate energy consumption during balance recovery. We developed a two-phase nonlinear optimization pipeline for dynamic stepping, which generates reachability maps showing complex energy-stepping relations. We optimize gait parameters to search all reachable locations and quantify the energy cost during dynamic transitions, which allows studying the relationship between energy consumption and stepping locations given different initial conditions. We found that to achieve efficient actuation, the stepping location and timing can have simple approximations close to the underlying optimality, resulting in optimal step positions with a 10.9% lower energy cost than those generated by linear inverted pendulum model. Despite the complexity of this nonlinear process, we found that near-minimal effort stepping locations are within a region of attractions, rather than a narrow solution space suggested by a simple model. This provides new insights into the nonuniqueness of near-optimal solutions in robot motion planning and control, and the diversity of stepping behavior in humans.