  We present a method for humanoid robot walking on partial footholds such as
small stepping stones and rocks with sharp surfaces. Our algorithm does not
rely on prior knowledge of the foothold, but information about an expected
foothold can be used to improve the stepping performance. After a step is
taken, the robot explores the new contact surface by attempting to shift the
center of pressure around the foot. The available foothold is inferred by the
way in which the foot rotates about contact edges and/or by the achieved center
of pressure locations on the foot during exploration. This estimated contact
area is then used by a whole body momentum-based control algorithm. To walk and
balance on partial footholds, we combine fast, dynamic stepping with the use of
upper body angular momentum to regain balance. We applied this method to the
Atlas humanoid designed by Boston Dynamics to walk over small contact surfaces,
such as line and point contacts. We present experimental results and discuss
performance limitations.
