We study the problem of sampling robot trajectories and introduce the notion of C-Uniformity. As opposed to the standard method of uniformly sampling control inputs (which lead to biased samples of the configuration space), C-Uniform trajectories are generated by control actions which lead to uniform sampling of the configuration space. After presenting an intuitive closed-form solution to generate C-Uniform trajectories for the 1D random-walker, we present a network-flow based optimization method to precompute action probabilities which lead to C-Uniform trajectories for general robot systems. We apply the notion of C-Uniformity to the design of Model Predictive Path Integral controllers. Through simulation experiments, we show that using C-Uniform trajectories significantly improvs the performance of MPPI-style controllers, achieving up to 40 % coverage performance gain compared to the best baseline. We demonstrate the practical applicability of our method with an implementation on a$1 / 10$th scale racer.

Sampling-based model predictive controllers generate trajectories by sampling control inputs from a fixed, simple distribution such as the normal or uniform distributions. This sampling method yields trajectory samples that are tightly clustered around a mean trajectory. This clustering behavior in turn, limits the exploration capability of the controller and reduces the likelihood of finding feasible solutions in complex environments. Recent work has attempted to address this problem by either reshaping the resulting trajectory distribution or increasing the sample entropy to enhance diversity and promote exploration. In our recent work, we introduced the concept of C-Uniform trajectory generation [1] which allows the computation of control input probabilities to generate trajectories that sample the configuration space uniformly. In this work, we first address the main limitation of this method: lack of scalability due to computational complexity. We introduce Neural C-Uniform, an unsupervised C-Uniform trajectory sampler that mitigates scalability issues by computing control input probabilities without relying on a discretized configuration space. Experiments show that Neural C-Uniform achieves a similar uniformity ratio to the original C-Uniform approach and generates trajectories over a longer time horizon while preserving uniformity. Next, we present CU-MPPI, which integrates Neural C-Uniform sampling into existing MPPI variants. We analyze the performance of CU-MPPI in simulation and real-world experiments. Our results indicate that in settings where the optimal solution has high curvature, CU-MPPI leads to drastic improvements in performance. Additionally, it performs as well as or better than baseline methods in dynamic environments. Additional results can be found at the project website.