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This paper introduces a hierarchical control framework for quadrupedal robots transporting unknown payloads, combining model predictive control (MPC) with a gradient-descent-based adaptive law to estimate payload parameters online. The estimated parameters are used within the MPC to plan stable trajectories for a reduced-order locomotion model, which are then tracked by a whole-body controller. Experimental results demonstrate successful payload transportation, even with significant unmodeled payloads (up to 109% of robot mass on flat terrain) and disturbances, outperforming standard MPC and L1 adaptive MPC.
Quadrupedal robots can now robustly carry payloads exceeding their own mass on rough terrain, thanks to a novel adaptive MPC framework that learns the payload online.
This letter formally develops a novel hierarchical planning and control framework for robust payload transportation by quadrupedal robots, integrating a model predictive control (MPC) algorithm with a gradient-descent-based adaptive updating law. At the framework's high level, an indirect adaptive law estimates the unknown parameters of the reduced-order (template) locomotion model under varying payloads. These estimated parameters feed into an MPC algorithm for real-time trajectory planning, incorporating a convex stability criterion within the MPC constraints to ensure the stability of the template model's estimation error. The optimal reduced-order trajectories generated by the high-level adaptive MPC (AMPC) are then passed to a low-level nonlinear whole-body controller (WBC) for tracking. Extensive numerical investigations validate the framework's capabilities, showcasing the robot's proficiency in transporting unmodeled, unknown static payloads up to 109% in experiments on flat terrains and 91% on rough experimental terrains. The robot also successfully manages dynamic payloads with 73% of its mass on rough terrains. Performance comparisons with a normal MPC and an $\mathcal {L}_{1}$ MPC indicate a significant improvement. Furthermore, comprehensive hardware experiments conducted in indoor and outdoor environments confirm the method's efficacy on rough terrains despite uncertainties such as payload variations, push disturbances, and obstacles.