  Pivoting gait is efficient for manipulating a big and heavy object with
relatively small manipulating force, in which a robot iteratively tilts the
object, rotates it around the vertex, and then puts it down to the floor.
However, pivoting gait can easily fail even with a small external disturbance
due to its instability in nature. To cope with this problem, we propose a
controller to robustly control the object motion during the pivoting gait by
introducing two gait modes, i.e., one is the double-support mode, which can
manipulate a relatively light object with faster speed, and the other is the
quadruple-support mode, which can manipulate a relatively heavy object with
lower speed. To control the pivoting gait, a graph model predictive control is
applied taking into account of these two gait modes. By adaptively switching
the gait mode according to the applied external disturbance, a robot can stably
perform the pivoting gait even if the external disturbance is applied to the
object.
