Minchan Jung

Yuichiro Aoyama, Minchan Jung, Akash Ratheesh et al.

This paper investigates the optimization mechanisms of non-convex Model Predictive Control (MPC) using the Maximum Entropy Differential Dynamic Programming (ME-DDP) framework. Navigating non-convex cost landscapes induced by nonlinear dynamics, multiple obstacles, etc. remains a fundamental challenge in robotics, where gradient-based methods frequently converge to suboptimal local minima. We demonstrate a dual-step optimization mechanism designed to overcome these traps. (1) an initial phase of using DDP to exploit the gradient of the cost landscape, followed by (2) disruption of the optimization via sampling from policies characterized by the inverse Hessian of the action-value function. We provide a rigorous analysis of this sampling mechanism of three ME-DDP variants: Unimodal Gaussian ME-DDP, Multimodal Gaussian ME-DDP, and Stein Variational DDP. Furthermore, with navigation tasks of four robotic systems under cluttered environments, we conduct extensive benchmarking of three variants of the ME-DDP, against deterministic DDP, and one of the most successful sampling-based schemes, Model Predictive Path Integral (MPPI) control with three policy parameterizations and update laws that correspond to those of ME-DDPs. The results show that in low-dimensional systems where the cost landscapes are relatively simple and local information is sufficiently representative, our framework consistently outperforms MPPIs. In high-dimensional systems, MPPI can occasionally discover aggressive maneuvers that enable it to steer the systems faster than DDP-based methods, whereas our method maintains a higher, more stable success rate. Finally, we validate the practical efficacy of the framework through hardware experiments with a quadrotor navigating a dense, non-convex obstacle field, confirming the robustness of the proposed framework for real-world deployment.

Hunter Kuperman, Minchan Jung, Rahul V. Ghosh et al.

Distributed optimization is a highly scalable and structurally transparent technique to solve multi-agent robotics problems; however, such methods often suffer from the need for highly-specialized, problem-specific hyperparameter tunings. In this work, we propose Deep Coordinator, a deep-unfolding framework that learns to dynamically adjust the hyperparameters of ADMM-DDP, a popular distributed solver for robotics tasks, at solve-time in response to optimizer performance. Our architecture consists of unrolling a fixed number of ADMM-DDP iterations into a neural network with learnable functions between layers mapping the optimizer state to the next hyperparameters. To the best of our knowledge, Deep Coordinator is the first deep-unfolding framework to adapt the penalty parameters of a non-convex optimizer at solve-time; we show that the mainstream supervised approach can yield degenerate solutions when training such models, and propose an unsupervised learning scheme. On simulations with fleets of cars and quadrotors, Deep Coordinator produces trajectories of comparable quality 6.18-9.44x faster than conventional solvers. Furthermore, Deep Coordinator retains its performance benefits when deployed to systems up to 8x larger than trained on.