  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
robot dynamics and whole-body optimal control as a coupled system to
investigate energy consumption during balance recovery. We developed a 2-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. Despite the
complexity of this nonlinear process, we show that near-minimal effort stepping
locations fall within a region of attractions, rather than a narrow solution
space suggested by a simple model. This provides new insights into the
non-uniqueness of near-optimal solutions in robot motion planning and control,
and the diversity of stepping behavior in humans.
