Model Tensor Planning

2025-05-02

AI Summary

To address insufficient exploration in sampling-based Model Predictive Control (MPC) for nonlinear, contact-rich robotic tasks, this paper proposes the High-Entropy Tensor Sampling MPC framework. Methodologically, it introduces: (1) a novel structured tensorized multi-partite graph random sampling mechanism, coupled with B-spline/Akima interpolation to generate smooth, high-coverage trajectories; (2) a β-mixing strategy that jointly orchestrates local optimization and global exploration within the Cross-Entropy Method (CEM); and (3) theoretical guarantees of asymptotic path coverage and maximum entropy. Implemented entirely in JAX with full vectorization, the framework supports MuJoCo XLA acceleration, batched rollouts, and online domain randomization. Empirical evaluation on dexterous manipulation and humanoid locomotion demonstrates significant improvements in success rate and robustness over standard MPC and state-of-the-art evolutionary strategies.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Planning, Routing, and Scheduling: Mixed Discrete/Continuous Planning
• Machine Learning: Matrix & Tensor Methods

Application Category

• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions

Abstract

Sampling-based model predictive control (MPC) offers strong performance in nonlinear and contact-rich robotic tasks, yet often suffers from poor exploration due to locally greedy sampling schemes. We propose emph{Model Tensor Planning} (MTP), a novel sampling-based MPC framework that introduces high-entropy control trajectory generation through structured tensor sampling. By sampling over randomized multipartite graphs and interpolating control trajectories with B-splines and Akima splines, MTP ensures smooth and globally diverse control candidates. We further propose a simple $eta$-mixing strategy that blends local exploitative and global exploratory samples within the modified Cross-Entropy Method (CEM) update, balancing control refinement and exploration. Theoretically, we show that MTP achieves asymptotic path coverage and maximum entropy in the control trajectory space in the limit of infinite tensor depth and width. Our implementation is fully vectorized using JAX and compatible with MuJoCo XLA, supporting emph{Just-in-time} (JIT) compilation and batched rollouts for real-time control with online domain randomization. Through experiments on various challenging robotic tasks, ranging from dexterous in-hand manipulation to humanoid locomotion, we demonstrate that MTP outperforms standard MPC and evolutionary strategy baselines in task success and control robustness. Design and sensitivity ablations confirm the effectiveness of MTP tensor sampling structure, spline interpolation choices, and mixing strategy. Altogether, MTP offers a scalable framework for robust exploration in model-based planning and control.

Problem

• Improves exploration in sampling-based MPC for nonlinear robotic tasks
• Generates diverse control trajectories via tensor sampling and spline interpolation
• Balances local and global exploration using a β-mixing strategy in CEM

Innovation

• Structured tensor sampling for diverse control trajectories
• β-mixing strategy balancing exploration and exploitation
• Vectorized JAX implementation for real-time control