# Model Tensor Planning

arXiv: https://arxiv.org/abs/2505.01059 · HTML: https://mlsanity.com/paper/2505.01059/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 30 of its 47 references that are in the map.
- First posted on arXiv 2 May 2025.

## Builds on (most cited first, 30 of 30)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Diffusion Policy: Visuomotor Policy Learning via Action Diffusion](https://mlsanity.com/paper/2303.04137/) (2023)
- [Isaac Gym: High Performance GPU-Based Physics Simulation For Robot Learning](https://mlsanity.com/paper/2108.10470/) (2021)
- [Evolution Strategies as a Scalable Alternative to Reinforcement Learning](https://mlsanity.com/paper/1703.03864/) (2017)
- [The CMA Evolution Strategy: A Tutorial](https://mlsanity.com/paper/1604.00772/) (2016)
- [Motion Planning Diffusion: Learning and Planning of Robot Motions with Diffusion Models](https://mlsanity.com/paper/2308.01557/) (2023)
- [Sample-efficient Cross-Entropy Method for Real-time Planning](https://mlsanity.com/paper/2008.06389/) (2020)
- [STORM: An Integrated Framework for Fast Joint-Space Model-Predictive Control for Reactive Manipulation](https://mlsanity.com/paper/2104.13542/) (2021)
- [Predictive Sampling: Real-time Behaviour Synthesis with MuJoCo](https://mlsanity.com/paper/2212.00541/) (2022)
- [evosax: JAX-based Evolution Strategies](https://mlsanity.com/paper/2212.04180/) (2022)
- [Motion Planning Diffusion: Learning and Adapting Robot Motion Planning with Diffusion Models](https://mlsanity.com/paper/2412.19948/) (2024)
- [Full-Order Sampling-Based MPC for Torque-Level Locomotion Control via Diffusion-Style Annealing](https://mlsanity.com/paper/2409.15610/) (2024)
- [Learning Implicit Priors for Motion Optimization](https://mlsanity.com/paper/2204.05369/) (2022)
- [DiffusionSeeder: Seeding Motion Optimization with Diffusion for Rapid Motion Planning](https://mlsanity.com/paper/2410.16727/) (2024)
- [Motions in Microseconds via Vectorized Sampling-Based Planning](https://mlsanity.com/paper/2309.14545/) (2023)
- [Diffusion Models are Evolutionary Algorithms](https://mlsanity.com/paper/2410.02543/) (2024)
- [FlowMP: Learning Motion Fields for Robot Planning with Conditional Flow Matching](https://mlsanity.com/paper/2503.06135/) (2025)
- [DROP: Dexterous Reorientation via Online Planning](https://mlsanity.com/paper/2409.14562/) (2024)
- [Accelerating Motion Planning via Optimal Transport](https://mlsanity.com/paper/2309.15970/) (2023)
- [Inferring Smooth Control: Monte Carlo Posterior Policy Iteration with Gaussian Processes](https://mlsanity.com/paper/2210.03512/) (2022)
- [VP-STO: Via-point-based Stochastic Trajectory Optimization for Reactive Robot Behavior](https://mlsanity.com/paper/2210.04067/) (2022)
- [A Simple Decentralized Cross-Entropy Method](https://mlsanity.com/paper/2212.08235/) (2022)
- [Stochastic MPC with Offline Uncertainty Sampling](https://mlsanity.com/paper/1606.06056/) (2016)
- [CoVO-MPC: Theoretical Analysis of Sampling-based MPC and Optimal Covariance Design](https://mlsanity.com/paper/2401.07369/) (2024)
- [Real-Time Whole-Body Control of Legged Robots with Model-Predictive Path Integral Control](https://mlsanity.com/paper/2409.10469/) (2024)
- [pRRTC: GPU-Parallel RRT-Connect for Fast, Consistent, and Low-Cost Motion Planning](https://mlsanity.com/paper/2503.06757/) (2025)
- [Global Tensor Motion Planning](https://mlsanity.com/paper/2411.19393/) (2024)
- [GPU Parallelization of Policy Iteration RRT#](https://mlsanity.com/paper/2003.04920/) (2020)
- [Kino-PAX: Highly Parallel Kinodynamic Sampling-based Planner](https://mlsanity.com/paper/2409.06807/) (2024)

## Abstract (arXiv)

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 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 β-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 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.