Approximate C-Uniform Sampling: An Information-Theoretic and Bayesian Inference Perspective

Sampling control trajectories from standard distributions—a foundation for Model Predictive Control (MPC) and Model Predictive Path Integral (MPPI) methods—although probabilistically complete, in practice leads to poor exploration of the configuration space, resulting in catastrophic outcomes in the robot’s operation. Recent works have proposed a family of approaches for sampling in control space that lead to uniform coverage of the configuration space, introducing the notion of C-Uniformity. However, those methods suffer from the need for state and action space discretization and level-sets, pre-computation. In this work, we introduce a proof-of-concept training strategy for deep generative models to achieve diverse and near C-Uniform sampling capabilities. Two variational inference approaches—information maximization algorithm and Stein variational gradient descent—are used as a foundation for training normalizing flow and flow matching models to sample control sequences that lead to a wider coverage of the configuration space, compared to the standard distributions, without state/action space discretization. Qualitative and quantitative evaluations support the advantage of the methods in terms of state space coverage and success rate in downstream social navigation tasks.