We consider a nonprehensile manipulation task in which a mobile manipulator must balance objects on its end effector without grasping them -- known as the waiter's problem -- and move to a desired location while avoiding static and dynamic obstacles. In constrast to existing approaches, our focus is on fast online planning in response to new and changing environments. Our main contribution is a whole-body constrained model predictive controller (MPC) for a mobile manipulator that balances objects and avoids collisions. Furthermore, we propose planning using the minimum statically-feasible friction coefficients, which provides robustness to frictional uncertainty and other force disturbances while also substantially reducing the compute time required to update the MPC policy. Simulations and hardware experiments on a velocity-controlled mobile manipulator with up to seven balanced objects, stacked objects, and various obstacles show that our approach can handle a variety of conditions that have not been previously demonstrated, with end effector speeds and accelerations up to 2.0 m/s and 7.9 m/s$^2$, respectively. Notably, we demonstrate a projectile avoidance task in which the robot avoids a thrown ball while balancing a tall bottle.

翻译：我们研究了一种非抓取操作任务：移动机械臂必须在不抓取物体的情况下将其在末端执行器上保持平衡（即“服务员问题”），同时移动到目标位置并避开静态与动态障碍物。与现有方法不同，我们的研究重点是在新环境与动态变化环境下实现快速在线规划。主要贡献是为移动机械臂设计了一种整机约束的模型预测控制器，该控制器能同时实现物体平衡与避碰。此外，我们提出基于最小静稳定摩擦系数的规划方法，该方法不仅对摩擦不确定性及外部力扰动具有鲁棒性，还能显著减少更新MPC策略所需的计算时间。在速度控制型移动机械臂上进行的仿真与硬件实验中，我们成功平衡了多达七个物体、堆叠物体及各类障碍物，验证了该方法能应对多种此前未展示的复杂工况，末端执行器最高速度达2.0米/秒，加速度达7.9米/秒²。值得注意的是，我们还完成了抛体避障任务：机器人在平衡一个高瓶的同时，成功避开了抛来的球体。