Diffusion models have recently gained popularity for policy learning in robotics due to their ability to capture high-dimensional and multimodal distributions. However, diffusion policies are inherently stochastic and typically trained offline, limiting their ability to handle unseen and dynamic conditions where novel constraints not represented in the training data must be satisfied. To overcome this limitation, we propose diffusion predictive control with constraints (DPCC), an algorithm for diffusion-based control with explicit state and action constraints that can deviate from those in the training data. DPCC uses constraint tightening and incorporates model-based projections into the denoising process of a trained trajectory diffusion model. This allows us to generate constraint-satisfying, dynamically feasible, and goal-reaching trajectories for predictive control. We show through simulations of a robot manipulator that DPCC outperforms existing methods in satisfying novel test-time constraints while maintaining performance on the learned control task.

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