  Multi-legged robots with six or more legs are not in common use, despite
designs with superior stability, maneuverability, and a low number of actuators
being available for over 20 years. This may be in part due to the difficulty in
modeling multi-legged motion with slipping and producing reliable predictions
of body velocity. Here we present a detailed measurement of the foot contact
forces in a hexapedal robot with multiple sliding contacts, and provide an
algorithm for predicting these contact forces and the body velocity. The
algorithm relies on the recently published observation that even while
slipping, multi-legged robots are principally kinematic, and employ a friction
law ansatz that allows us to compute the shape-change to body-velocity
connection and the foot contact forces. This results in the ability to simulate
motion plans for a large number of potentially slipping legs. In homogeneous
environments, this can run in (parallel) logarithmic time of the planning
horizon
