We consider the nonprehensile object transportation task known as the waiter's problem - in which a robot must move an object balanced on a tray from one location to another - when the balanced object has uncertain inertial parameters. In contrast to existing approaches that completely ignore uncertainty in the inertia matrix or which only consider small parameter errors, we are interested in pushing the limits of the amount of inertial parameter uncertainty that can be handled. We first show how balancing constraints robust to inertial parameter uncertainty can be incorporated into a motion planning framework to balance objects while moving quickly. Next, we develop necessary conditions for the inertial parameters to be realizable on a bounding shape based on moment relaxations, allowing us to verify whether a trajectory will violate the balancing constraints for any realizable inertial parameters. Finally, we demonstrate our approach on a mobile manipulator in simulations and real hardware experiments: our proposed robust constraints consistently balance a 56 cm tall object with substantial inertial parameter uncertainty in the real world, while the baseline approaches drop the object while transporting it.

翻译：我们研究了被称为"服务员问题"的非抓取物体运输任务——即机器人必须将托盘上保持平衡的物体从一个位置移动到另一个位置——当平衡物体具有不确定惯性参数时的情形。与现有完全忽略惯性矩阵不确定性或仅考虑小参数误差的方法不同，我们关注的是探索可处理的惯性参数不确定性的极限。我们首先展示了如何将抵抗惯性参数不确定性的平衡约束纳入运动规划框架，以实现快速移动过程中的物体平衡。接着，我们基于矩松弛方法推导了惯性参数在边界形状上可实现性的必要条件，从而能够验证轨迹是否会在任何可实现惯性参数下违反平衡约束。最后，我们在移动机械臂上通过仿真和真实硬件实验验证了所提方法：我们提出的鲁棒约束在现实世界中始终能平衡具有显著惯性参数不确定性的56厘米高物体，而基线方法在运输过程中均导致物体掉落。