In this paper, we present a robust nonprehensile object transportation framework for quadruped robots. An uncertainty-aware trajectory optimization method generates object motions with minimal closed-loop sensitivity to uncertain parameters. The resulting reference trajectory is tracked using a coupled convex model predictive controller that jointly predicts the CoM dynamics of the quadruped and the payload followed by a whole-body QP that enforces ground reaction constraints. The approach is evaluated through extensive simulations and real-world experiments under variations in the object's inertial parameters. Its performance is compared with fixed-orientation and straight-line trajectories as baseline. The results show that the optimized object motion reduces the sliding by approximately 50% compared with the fixed-orientation baseline and 30% compared with the straight-line baseline, while also achieving lower robot CoM tracking errors.

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