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 robots 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.
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