Trajectory Generation, Control, and Safety with Denoising Diffusion Probabilistic Models

The Control barrier functions (CBFs) (Ames et al., 2017; 2019) technology of control barrier functions (CBFs), represent a formal framework aiming to achieve safety as encoding desired safety constraints, is used in a hard constraint in an optimization problem in which the combination with DDPMs to plan actions by iteratively cost function encodes information on the nominal task to denoising trajectories through a CBFbased be executed. In particular CBF-based safety constraints are guided sampling procedure. At the same represented by forward invariance of so-called safe sets, i.e. time, the generated trajectories are also guided to subsets of the state space which the controlled system should maximize a future cumulative reward representing not leave during the task execution. We stress that within a specific task to be optimally executed. The this context, safety becomes a mathematically rigorous system proposed scheme can be seen as an offline and theoretic property and, even if unable to represent any model-based reinforcement learning algorithm resembling possible safety hazard, it is very useful to design safety constraints, in its functionalities a model-predictive e.g.