Minh‐Khai Nguyen

Ishaan Mahajan, Khai Nguyen, Sam Schoedel et al. · cmu

Model-predictive control (MPC) is a state-of-the-art control method for constrained robotic systems, yet deployment on resource-limited hardware remains difficult. This challenge is magnified by expressive conic constraints, which offer greater modeling power but require significantly more computation than linear alternatives. To address this challenge, we extend recent work developing fast, structure-exploiting, cached solvers for embedded applications based on the Alternating Direction Method of Multipliers (ADMM) to provide support for second-order cones, as well as C++ code generation from Python, MATLAB, and Julia. Microcontroller benchmarks show that our solver provides up to a two-order-of-magnitude speedup, ranging from 10.6x to 142.7x, over state-of-the-art embedded solvers on QP and SOCP problems, and enables us to fit order-of-magnitude larger problems in memory. We validate our solver's deployed performance through simulation and hardware experiments, including trajectory tracking with conic constraints on a 27g Crazyflie quadrotor. Our open-source code is available at https://tinympc.org.

Khai Nguyen, Shujian Zhang, Tam Le et al.

Slicing distribution selection has been used as an effective technique to improve the performance of parameter estimators based on minimizing sliced Wasserstein distance in applications. Previous works either utilize expensive optimization to select the slicing distribution or use slicing distributions that require expensive sampling methods. In this work, we propose an optimization-free slicing distribution that provides a fast sampling for the Monte Carlo estimation of expectation. In particular, we introduce the random-path projecting direction (RPD) which is constructed by leveraging the normalized difference between two random vectors following the two input measures. From the RPD, we derive the random-path slicing distribution (RPSD) and two variants of sliced Wasserstein, i.e., the Random-Path Projection Sliced Wasserstein (RPSW) and the Importance Weighted Random-Path Projection Sliced Wasserstein (IWRPSW). We then discuss the topological, statistical, and computational properties of RPSW and IWRPSW. Finally, we showcase the favorable performance of RPSW and IWRPSW in gradient flow and the training of denoising diffusion generative models on images.