Robust and Efficient MuJoCo-based Model Predictive Control via Web of Affine Spaces Derivatives

2025-12-24

AI Summary

In MuJoCo Model Predictive Control (MJPC), finite-difference (FD)-based derivative computation becomes a critical bottleneck for real-time control of high-degree-of-freedom systems. To address this, we introduce the Web of Affine Spaces (WASP) into the MJPC framework as a drop-in replacement for FD, enabling efficient and robust gradient estimation by reusing affine space structures across time steps. Our method significantly reduces derivative computation overhead and improves numerical stability, thereby enabling real-time closed-loop MPC for high-dimensional robotic systems. Experiments demonstrate up to 2× speedup over FD on multi-robot tasks, while outperforming random-sampling planners in both computational efficiency and control reliability. The implementation is fully open-sourced and seamlessly integrated into the MJPC ecosystem.

Technology Category

• Multiagent Systems: Multiagent Planning
• Humans and AI: Human-Aware Planning and Behavior Prediction
• Planning, Routing, and Scheduling: Replanning and Plan Repair

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

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.

Problem

• Improving derivative computation efficiency in MuJoCo MPC
• Replacing finite differencing with WASP for faster derivatives
• Enhancing real-time control performance in high-DOF robotic systems

Innovation

• WASP derivatives replace finite differencing in MJPC
• WASP reuses prior derivative data for faster computation
• WASP enables robust MPC with up to 2x speedup