Motion generation in cluttered, dense, and dynamic environments is a central topic in robotics, rendered as a multi-objective decision-making problem. Current approaches trade-off between safety and performance. On the one hand, reactive policies guarantee fast response to environmental changes at the risk of suboptimal behavior. On the other hand, planning-based motion generation provides feasible trajectories, but the high computational cost may limit the control frequency and thus safety. To combine the benefits of reactive policies and planning, we propose a hierarchical motion generation method. Moreover, we adopt probabilistic inference methods to formalize the hierarchical model and stochastic optimization. We realize this approach as a weighted product of stochastic, reactive expert policies, where planning is used to adaptively compute the optimal weights over the task horizon. This stochastic optimization avoids local optima and proposes feasible reactive plans that find paths in cluttered and dense environments. Our extensive experimental study in planar navigation and 6DoF manipulation shows that our proposed hierarchical motion generation method outperforms both myopic reactive controllers and online re-planning methods.

We present hierarchical policy blending as optimal transport (HiPBOT). HiPBOT hierarchically adjusts the weights of low-level reactive expert policies of different agents by adding a look-ahead planning layer on the parameter space. The high-level planner renders policy blending as unbalanced optimal transport consolidating the scaling of the underlying Riemannian motion policies. As a result, HiPBOT effectively decides the priorities between expert policies and agents, ensuring the task's success and guaranteeing safety. Experimental results in several application scenarios, from low-dimensional navigation to high-dimensional whole-body control, show the efficacy and efficiency of HiPBOT. Our method outperforms state-of-the-art baselines -- either adopting probabilistic inference or defining a tree structure of experts -- paving the way for new applications of optimal transport to robot control. More material at https://sites.google.com/view/hipobot