Dynamics-aware Diffusion Models for Planning and Control

2025-03-31

AI Summary

This work addresses the challenge of generating dynamically feasible control trajectories in complex environments. We propose a novel framework that implicitly embeds system dynamics into the denoising process of diffusion models. Methodologically, we design a temporal-aware physical projection mechanism that aligns denoising steps with the noise schedule and enforces kinematic or dynamic constraints at each iteration—without requiring explicit dynamical priors—enabling recovery of linear feedback controller trajectories directly from expert demonstrations. Our key contributions are: (i) the first diffusion-based trajectory generation method ensuring dynamical consistency under maximum-likelihood estimation; and (ii) the integration of implicit dynamics learning with projection-based constraint optimization. Evaluated on standard control benchmarks and non-convex optimal control tasks involving obstacle avoidance and path tracking, our approach significantly improves trajectory feasibility and task success rates, demonstrating strong potential for real-world deployment.

Technology Category

• Computer Vision: Diffusion Models for Vision
• Search and Optimization: Sampling/Simulation-based Search
• Humans and AI: Human-Aware Planning and Behavior Prediction

Application Category

• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

Abstract

This paper addresses the problem of generating dynamically admissible trajectories for control tasks using diffusion models, particularly in scenarios where the environment is complex and system dynamics are crucial for practical application. We propose a novel framework that integrates system dynamics directly into the diffusion model's denoising process through a sequential prediction and projection mechanism. This mechanism, aligned with the diffusion model's noising schedule, ensures generated trajectories are both consistent with expert demonstrations and adhere to underlying physical constraints. Notably, our approach can generate maximum likelihood trajectories and accurately recover trajectories generated by linear feedback controllers, even when explicit dynamics knowledge is unavailable. We validate the effectiveness of our method through experiments on standard control tasks and a complex non-convex optimal control problem involving waypoint tracking and collision avoidance, demonstrating its potential for efficient trajectory generation in practical applications.

Problem

• Generating dynamically admissible trajectories for control tasks
• Integrating system dynamics into diffusion models for planning
• Ensuring trajectories adhere to physical constraints and expert demonstrations

Innovation

• Integrates system dynamics into diffusion models
• Ensures trajectories adhere to physical constraints
• Generates maximum likelihood trajectories efficiently