  In this paper, we present a novel factor graph formulation to estimate the
pose and velocity of a quadruped robot on slippery and deformable terrain. The
factor graph introduces a preintegrated velocity factor that incorporates
velocity inputs from leg odometry and also estimates related biases. From our
experimentation we have seen that it is difficult to model uncertainties at the
contact point such as slip or deforming terrain, as well as leg flexibility. To
accommodate for these effects and to minimize leg odometry drift, we extend the
robot's state vector with a bias term for this preintegrated velocity factor.
The bias term can be accurately estimated thanks to the tight fusion of the
preintegrated velocity factor with stereo vision and IMU factors, without which
it would be unobservable. The system has been validated on several scenarios
that involve dynamic motions of the ANYmal robot on loose rocks, slopes and
muddy ground. We demonstrate a 26% improvement of relative pose error compared
to our previous work and 52% compared to a state-of-the-art proprioceptive
state estimator.
