  Step adjustment can improve the gait robustness of biped robots, however the
adaptation of step timing is often neglected as it gives rise to non-convex
problems when optimized over several footsteps. In this paper, we argue that it
is not necessary to optimize walking over several steps to ensure gait
viability and show that it is sufficient to merely select the next step timing
and location. Using this insight, we propose a novel walking pattern generator
that optimally selects step location and timing at every control cycle. Our
approach is computationally simple compared to standard approaches in the
literature, yet guarantees that any viable state will remain viable in the
future. We propose a swing foot adaptation strategy and integrate the pattern
generator with an inverse dynamics controller that does not explicitly control
the center of mass nor the foot center of pressure. This is particularly useful
for biped robots with limited control authority over their foot center of
pressure, such as robots with point feet or passive ankles. Extensive
simulations on a humanoid robot with passive ankles demonstrate the
capabilities of the approach in various walking situations, including external
pushes and foot slippage, and emphasize the importance of step timing
adaptation to stabilize walking.
