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. Our code repository is available at www.github.com/darshangm/dynamics-aware-diffusion.

翻译：本文研究了利用扩散模型生成满足动力学约束的轨迹以解决控制任务的问题，特别是在环境复杂且系统动力学对实际应用至关重要的场景中。我们提出了一种新颖的框架，通过序列预测与投影机制，将系统动力学直接整合到扩散模型的去噪过程中。该机制与扩散模型的加噪调度相协调，确保生成的轨迹既符合专家演示，又遵循底层的物理约束。值得注意的是，即使在没有显式动力学知识的情况下，我们的方法仍能生成最大似然轨迹，并精确复现由线性反馈控制器生成的轨迹。我们通过在标准控制任务以及涉及航点跟踪与避障的复杂非凸最优控制问题上的实验，验证了所提方法的有效性，展示了其在实际应用中高效生成轨迹的潜力。我们的代码仓库公开于 www.github.com/darshangm/dynamics-aware-diffusion。