The ability to accomplish manipulation and locomotion tasks in the presence of significant time-varying external loads is a remarkable skill of humans that has yet to be replicated convincingly by humanoid robots. Such an ability will be a key requirement in the environments we envision deploying our robots: dull, dirty, and dangerous. External loads constitute a large model bias, which is typically unaccounted for. In this work, we enable our humanoid robot to engage in loco-manipulation tasks in the presence of significant model bias due to external loads. We propose an online estimation and control framework involving the combination of a physically consistent extended Kalman filter for inertial parameter estimation coupled to a whole-body controller. We showcase our results both in simulation and in hardware, where weights are mounted on Nadia's wrist links as a proxy for engaging in tasks where large external loads are applied to the robot.

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