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Efficient computation of the optimal transport distance between two distributions serves as an algorithm subroutine that empowers various applications. This paper develops a scalable first-order optimization-based method that computes…
This paper studies motion planning of a mobile robot under uncertainty. The control objective is to synthesize a {finite-memory} control policy, such that a high-level task specified as a Linear Temporal Logic (LTL) formula is satisfied…
We propose an adaptive smoothing algorithm based on Nesterov's smoothing technique in \cite{Nesterov2005c} for solving "fully" nonsmooth composite convex optimization problems. Our method combines both Nesterov's accelerated proximal…
We propose three novel mathematical optimization formulations that solve the same two-type heterogeneous multiprocessor scheduling problem for a real-time taskset with hard constraints. Our formulations are based on a global scheduling…
This paper proposes a new indirect solution method for solving state-constrained optimal control problems by revisiting the well-established optimal control theory and addressing the long-standing issue of discontinuous control and costate…
Computational guidance is an emerging and accelerating trend in aerospace guidance and control. Combining machine learning and convex optimization, this paper presents a real-time computational guidance method for the 6-degrees-of-freedom…
This paper studies energy-efficient unmanned aerial vehicle (UAV)-enabled wireless communications, where the UAV acts as a flying base station (BS) to serve the ground users (GUs) within some predetermined latency constraints, e.g.,…
We introduce a new algorithm to solve constrained nonlinear optimal control problem, with an emphasis on low-thrust trajectory in highly nonlinear dynamics. The algorithm, dubbed Pontryagin-Bellman Differential Dynamic Programming (PDDP),…
This paper considers the problem of planning trajectories for a team of sensor-equipped robots to reduce uncertainty about a dynamical process. Optimizing the trade-off between information gain and energy cost (e.g., control effort,…
Most of the optimal guidance problems can be formulated as nonconvex optimization problems, which can be solved indirectly by relaxation, convexification, or linearization. Although these methods are guaranteed to converge to the global…
In this series of papers, we present a motion planning framework for planning comfortable and customizable motion of nonholonomic mobile robots such as intelligent wheelchairs and autonomous cars. In Part I, we presented the mathematical…
The main goal of this paper is developing the method of discrete approximations to derive necessary optimality conditions for a class of constrained sweeping processes with nonsmooth perturbations. Optimal control problems for sweeping…
Machine learning techniques have demonstrated their effectiveness in achieving autonomy and optimality for nonlinear and high-dimensional dynamical systems. However, traditional black-box machine learning methods often lack formal stability…
As a core part of autonomous driving systems, motion planning has received extensive attention from academia and industry. However, real-time trajectory planning capable of spatial-temporal joint optimization is challenged by nonholonomic…
One of the keys to flying quadrotors is to optimize their trajectories within the set of collision-free corridors. These corridors impose nonconvex constraints on the trajectories, making real-time trajectory optimization challenging. We…
We introduce an efficient and scalable method for density-based multi-material topology optimization, integrating classical mirror descent techniques with point-wise polytopal design constraints. Such constraints arise naturally in this…
This paper studies optimal time-bounded control in multi-mode systems with discrete costs. Multi-mode systems are an important subclass of linear hybrid systems, in which there are no guards on transitions and all invariants are global.…
Obstacle avoidance between polytopes is a challenging topic for optimal control and optimization-based trajectory planning problems. Existing work either solves this problem through mixed-integer optimization, relying on simplification of…
Trajectory planning for mobile robots in cluttered environments remains a major challenge due to narrow passages, where conventional methods often fail or generate suboptimal paths. To address this issue, we propose the adaptive trajectory…
We propose a homotopy method for solving mathematical programs with complementarity constraints (CCs). The indicator function of the CCs is relaxed by a Lasry-Lions double envelope, an extension of the Moreau envelope that enjoys an…