研究人形机器人搬物时物体质量对平衡的影响，提出动态平衡边界模型。

The demand for humanoid loco-manipulation tasks with an object has recently increased, and most existing control approaches for stability in such tasks rely on heuristics or machine-learning techniques. This study rigorously analyzes and exploits the dynamic effects of the object mass on balance stability. By formulating the object mass parameters in the whole-body dynamics with distributed contact wrenches and centers of pressure at the stance contacts, their nonlinear effects on the system momenta and constraints are quantified. The dynamic models and constraints are incorporated into the construction of the balanced state basin/boundary (BSB), a partition of the center-of-mass state space for a biped system to maintain balance in its desired contacts. The implications of the BSB for prediction and control are highlighted using a humanoid robot and an analytically tractable reduced-order mechanism. The BSBs under different conditions of base of support, actuation capacity, and pose provide systematic analyses of the effects of object mass on the balancing capability of a system. In particular, the trade-off relationships between momentum regulation and limiting factors in balancing are characterized, introducing two key quantities of the object: the critical mass, at which the system's balancing capability is maximum, and the transition mass, which activates different limiting factors. In addition, sufficient conditions for imposing balanced states on a trajectory are established and implemented with BSBs as explicit threshold constraints in the whole-body trajectory optimization for stable object-lifting control of the humanoid, demonstrating the lift-and-hold and lift-and-release tasks with distinct mass properties in simulations and experiments.