用WASP导数替代有限差分，让机器人控制更快更稳

MuJoCo is a powerful and efficient physics simulator widely used in robotics. One common way it is applied in practice is through Model Predictive Control (MPC), which uses repeated rollouts of the simulator to optimize future actions and generate responsive control policies in real time. To make this process more accessible, the open source library MuJoCo MPC (MJPC) provides ready-to-use MPC algorithms and implementations built directly on top of the MuJoCo simulator. However, MJPC relies on finite differencing (FD) to compute derivatives through the underlying MuJoCo simulator, which is often a key bottleneck that can make it prohibitively costly for time-sensitive tasks, especially in high-DOF systems or complex scenes. In this paper, we introduce the use of Web of Affine Spaces (WASP) derivatives within MJPC as a drop-in replacement for FD. WASP is a recently developed approach for efficiently computing sequences of accurate derivative approximations. By reusing information from prior, related derivative calculations, WASP accelerates and stabilizes the computation of new derivatives, making it especially well suited for MPC's iterative, fine-grained updates over time. We evaluate WASP across a diverse suite of MJPC tasks spanning multiple robot embodiments. Our results suggest that WASP derivatives are particularly effective in MJPC: it integrates seamlessly across tasks, delivers consistently robust performance, and achieves up to a 2$\mathsf{x}$ speedup compared to an FD backend when used with derivative-based planners, such as iLQG. In addition, WASP-based MPC outperforms MJPC's stochastic sampling-based planners on our evaluation tasks, offering both greater efficiency and reliability. To support adoption and future research, we release an open-source implementation of MJPC with WASP derivatives fully integrated.