  Capturability of a robot determines whether it is able to capture a robot
within a number of steps. Current capturability analysis is based on stance leg
dynamics, without taking adequate consideration on swing leg. In this paper, we
combine capturability-based analysis with swing leg dynamics. We first
associate original definition of capturability with a time-margin, which
encodes a time sequence that can capture the robot. This time-margin
capturability requires consideration of swing leg, and we therefore introduce a
swing leg kernel that acts as a bridge between step time and step length. We
analyze N-step capturability with a combined model of swing leg kernels and a
linear inverted pendulum model. By analyzing swing leg kernels with different
parameters, we find that more powerful actuation and longer normalized step
length result in greater capturability. We also answer the question whether
more steps would give greater capturability. For a given disturbance, we find a
step sequence that minimizes actuation. This step sequence is whether a step
time sequence or a step length sequence, and this classification is based on
boundary value problem analysis.
