Related papers: Bring the Heat: Rapid Trajectory Optimization with…
A new and effective computational approach is presented for analyzing transient heat conduction problems. The approach consists of a meshless Fragile Points Method (FPM) being utilized for spatial discretization, and a Local Variational…
Joint space trajectory optimization under end-effector task constraints leads to a challenging non-convex problem. Thus, a real-time adaptation of prior computed trajectories to perturbation in task constraints often becomes intractable.…
The ability to understand spatial-temporal patterns for crowds of people is crucial for achieving long-term autonomy of mobile robots deployed in human environments. However, traditional historical data-driven memory models are inadequate…
Over the past decade, Finite Element Method (FEM) has served as a foundational numerical framework for approximating the terms of Time Series Expansion (TSE) as solutions to transient Partial Differential Equation (PDE). However, the…
One of the oldest and most studied subject in scientific computing is algorithms for solving partial differential equations (PDEs). A long list of numerical methods have been proposed and successfully used for various applications. In…
The quasi-harmonic Debye approximation has been implemented within the AFLOW and Materials Project frameworks for high-throughput computational science (Automatic Gibbs Library, AGL), in order to calculate thermal properties such as the…
An efficient, reliable, and interpretable global solution method, the Deep learning-based algorithm for Heterogeneous Agent Models (DeepHAM), is proposed for solving high dimensional heterogeneous agent models with aggregate shocks. The…
We present a semi-real-time algorithm for minimal-time optimal path planning based on optimal control theory, dynamic programming, and Hamilton-Jacobi (HJ) equations. Partial differential equation (PDE) based optimal path planning methods…
In this study, we present a novel swarm-based approach for generating optimized stress-aligned trajectories for 3D printing applications. The method utilizes swarming dynamics to simulate the motion of virtual agents along the stress…
As robotic systems continue to address emerging issues in areas such as logistics, mobility, manufacturing, and disaster response, it is increasingly important to rapidly generate safe and energy-efficient trajectories. In this article, we…
Moving Horizon Estimation~(MHE) is essentially an optimization-based approach designed to estimate the states of dynamic systems within a moving time horizon. Traditional MHE solutions become computationally prohibitive due to the…
This paper presents a novel method of global adaptive dynamic programming (ADP) for the adaptive optimal control of nonlinear polynomial systems. The strategy consists of relaxing the problem of solving the Hamilton-Jacobi-Bellman (HJB)…
Several challenging problem in clustering, partitioning and imaging have traditionally been solved using the "spectral technique". These problems include the normalized cut problem, the graph expander ratio problem, the Cheeger constant…
Pose graph optimization (PGO) is a well-known technique for solving the pose-based simultaneous localization and mapping (SLAM) problem. In this paper, we represent the rotation and translation by a unit quaternion and a three-dimensional…
The inverse one-phase Stefan problem in one dimension, aimed at identifying the unknown time-dependent heat flux P(t) with a known moving boundary position s(t), is investigated. A previous study [16] attempted to reconstruct the unknown…
We consider the geometric optics problem of finding a system of two reflectors that transform a spherical wavefront into a beam of parallel rays with prescribed intensity distribution. Using techniques from optimal transportation theory, it…
Profile hidden Markov models (pHMMs) are widely employed in various bioinformatics applications to identify similarities between biological sequences, such as DNA or protein sequences. In pHMMs, sequences are represented as graph…
The linear primal-dual hybrid gradient (PDHG) method is a first-order method that splits convex optimization problems with saddle-point structure into smaller subproblems. Unlike those obtained in most splitting methods, these subproblems…
In the Material Point Method (MPM), accurately imposing Neumann-type thermal boundary conditions, particularly convective heat flux boundaries, remains a significant challenge due to the inherent nonconformity between complex evolving…
In this paper, we propose GOHOME, a method leveraging graph representations of the High Definition Map and sparse projections to generate a heatmap output representing the future position probability distribution for a given agent in a…