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The estimation of external joint torque and contact wrench is essential forachieving stable locomotion of humanoids and safety-oriented robots. Althoughthe contact wrench on the foot of humanoids can be measured using aforce-torque sensor (FTS), FTS increases the cost, inertia, complexity, andfailure possibility of the system. This paper introduces a method for learningexternal joint torque solely using proprioceptive sensors (encoders and IMUs)for a floating base robot. For learning, the GRU network is used and randomwalking data is collected. Real robot experiments demonstrate that the networkcan estimate the external torque and contact wrench with significantly smallererrors compared to the model-based method, momentum observer (MOB) withfriction modeling. The study also validates that the estimated contact wrenchcan be utilized for zero moment point (ZMP) feedback control, enabling stablewalking. Moreover, even when the robot's feet and the inertia of the upper bodyare changed, the trained network shows consistent performance with amodel-based calibration. This result demonstrates the possibility of removingFTS on the robot, which reduces the disadvantages of hardware sensors. Thesummary video is available at https://youtu.be/gT1D4tOiKpo.

Proprioceptive External Torque Learning for Floating Base Robot and its Applications to Humanoid Locomotion