用反馈策略提升采样效率，让机器人控制更稳定可靠。

Thanks to its parallelizability and flexibility, sampling-based Model Predictive Control (MPC) has become widely popular for controlling real-world robotic systems. However, for high-dimensional and open-loop unstable dynamical systems, the required number of samples to improve the control sequence will grow exponentially with the horizon, leading to poor sample efficiency and numerical instability. This paper investigates the instability of shooting methods in sampling-based MPC and shows that the optimal sampling proposal distribution can be realized by sampling with an optimized feedback policy. We refer to this algorithm as Feedback Sampling MPC (FS-MPC). FS-MPC involves a hybrid sampling design which balances local and global search based on the system stability and the available computation budget. Our theoretical analysis shows that our hybrid sampling approach achieves faster convergence than standard MPPI and better optimality than standard feedback sampling. Empirically, in diverse contact-rich control tasks like humanoid loco-manipulation and dexterous manipulation, we show that FS-MPC successfully tackles dynamically unstable tasks where standard sample-based approaches struggle, and strictly outperforms feedback policies alone. Finally, we validate our method on humanoid robot locomotion and manipulation tasks in the real world.