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：我们考虑一种非抓取操作任务，其中移动机械臂需在不抓取物体的前提下（即经典的“服务员问题”）在末端执行器上平衡物体，并避开静态与动态障碍物到达目标位置。与现有方法不同，我们聚焦于针对新环境和动态变化场景的快速在线规划。主要贡献在于提出了面向移动机械臂的全身约束模型预测控制器（MPC），可实现物体平衡与碰撞规避。此外，我们提出采用最小静力学可行摩擦系数进行规划，该方法既能提升对摩擦不确定性及其他力扰动的鲁棒性，又能大幅缩短MPC策略更新所需的计算时间。在速度控制型移动机械臂上开展的仿真与硬件实验（涉及最多7个平衡物体、叠放物体及多种障碍物）表明：本方法能处理此前未验证的多种工况，末端执行器速度与加速度分别可达2.0 m/s和7.9 m/s²。值得注意的是，我们还演示了抛射物规避任务——机械臂在平衡高瓶的同时避开了抛来的球体。