Manifold-Constrained MPPI: Real-Time Sampling-Based Control Under Hard Constraints

2026-05-23

AI Summary

Standard Model Predictive Path Integral (MPPI) control struggles to enforce hard constraints, limiting its applicability in highly constrained tasks such as closed-chain manipulation. This work proposes the Manifold-Constrained MPPI (MC-MPPI) framework, which, for the first time, embeds manifold equality constraints directly into MPPI. The approach leverages a variational autoencoder (VAE) to learn a low-dimensional latent representation of the constraint manifold and decouples constraint satisfaction from trajectory generation by introducing a single-step quadratic programming (QP) correction at the execution layer. While preserving MPPI’s computational efficiency, MC-MPPI rigorously enforces hard constraints, achieving stable 100 Hz operation on a 14-degree-of-freedom dual-arm closed-chain system. Both simulation and real-world experiments demonstrate significant improvements over baseline methods, reliably maintaining constraints and enhancing trajectory tracking accuracy.

Abstract

Sampling-based model predictive control methods, such as Model Predictive Path Integral (MPPI), offer derivative-free optimization and robustness in complex robotic systems. However, standard MPPI relies on cost-based soft penalties that cannot guarantee hard-constraint satisfaction, severely limiting its applicability to highly constrained tasks such as closed-chain manipulation. To address this, we propose Manifold-Constrained MPPI (MC-MPPI), a real-time sampling-based control framework that enforces manifold-based equality constraints while preserving the computational advantages of MPPI. The key idea is to decouple the constrained optimal control problem into latent-space planning and execution-level correction. At the planning stage, a Variational Autoencoder (VAE) learns a low-dimensional latent representation of the constraint manifold, enabling MPPI to efficiently generate near-feasible candidate trajectories without per-sample modification. Since this reference enables accurate linearization of the equality constraints, an execution-level Quadratic Programming (QP) controller resolves the residual manifold mismatch in a single solve rather than through iterative projection. Experiments on a 14-DoF closed-chain dual-arm system in both simulation and real-world settings demonstrate that MC-MPPI operates stably at 100 Hz, reliably navigates dynamic environments while effectively maintaining hard equality constraints, and significantly outperforms baseline methods in tracking accuracy. Supplementary videos and implementation details are available at https://rcilab.github.io/mcmppi.

Problem

• hard constraints
• equality constraints
• manifold constraints
• sampling-based control
• closed-chain manipulation

Innovation

• Manifold-Constrained MPPI
• Variational Autoencoder
• Hard Constraints
• Sampling-Based Control
• Quadratic Programming