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In legged locomotion, the relationship between different gait behaviors andenergy consumption must consider the full-body dynamics and the robot controlas a whole, which cannot be captured by simple models. This work studies therobot dynamics and whole-body optimal control as a coupled system toinvestigate energy consumption during balance recovery. We developed a 2-phasenonlinear optimization pipeline for dynamic stepping, which generatesreachability maps showing complex energy-stepping relations. We optimize gaitparameters to search all reachable locations and quantify the energy costduring dynamic transitions, which allows studying the relationship betweenenergy consumption and stepping locations given different initial conditions.We found that to achieve efficient actuation, the stepping location and timingcan have simple approximations close to the underlying optimality. Despite thecomplexity of this nonlinear process, we show that near-minimal effort steppinglocations fall within a region of attractions, rather than a narrow solutionspace suggested by a simple model. This provides new insights into thenon-uniqueness of near-optimal solutions in robot motion planning and control,and the diversity of stepping behavior in humans.

Reachability Map for Diverse Balancing Strategies and Energy Efficient Stepping of Humanoids