Related papers: Lagrangian Reachtubes: The Next Generation

This paper presents a two-stage trajectory planning framework for a multi-UAV rigid-payload cascaded transportation system, aiming to address planning challenges in densely cluttered environments. In Stage I, an Enhanced Tube-RRT* algorithm…

Retrieval-Augmented Generation (RAG) has emerged as the predominant paradigm for grounding Large Language Model outputs in factual knowledge, effectively mitigating hallucinations. However, conventional RAG systems operate under a…

In this note, we propose a method to under-approximate finite-time reachable sets and tubes for a class of continuous-time linear uncertain systems. The class under consideration is the linear time-varying (LTV) class with integrable…

This work proposes a non-iterative, scalable, and statistically optimal way to triangulate called \texttt{LOSTU}. Unlike triangulation algorithms that minimize the reprojection ($L_2$) error, LOSTU will still provide the maximum likelihood…

Neural network (NN) dynamics models and control policies achieve strong performance in robotics, but providing sound guarantees under uncertainty remains difficult, especially for closed-loop NN systems. Existing reachability tools provide…

Motivated by robotic trajectory optimization problems we consider the Augmented Lagrangian approach to constrained optimization. We first propose an alternative augmentation of the Lagrangian to handle the inequality case (not based on…

Unlike short-form retrieval-augmented generation (RAG), such as factoid question answering, long-form RAG requires retrieval to provide documents covering a wide range of relevant information. Automated report generation exemplifies this…

This work presents a method of efficiently computing inner and outer approximations of forward reachable sets for nonlinear control systems with changed dynamics and diminished control authority, given an a priori computed reachable set for…

Probabilistic guarantees of safety and performance are important in constrained dynamical systems with stochastic uncertainty. We consider the stochastic reachability problem, which maximizes the probability that the state remains within…

We develop theory for nonlinear dimensionality reduction (NLDR). A number of NLDR methods have been developed, but there is limited understanding of how these methods work and the relationships between them. There is limited basis for using…

Recently, machine learning techniques, particularly deep learning, have demonstrated superior performance over traditional time series forecasting methods across various applications, including both single-variable and multi-variable…

This paper presents the development and application of a Large Language Model Retrieval-Augmented Generation (LLM-RAG) system tailored for nanotechnology research. The system leverages the capabilities of a sophisticated language model to…

Artificial neural networks with internal dynamics exhibit remarkable capability in processing information. Reservoir computing (RC) is a canonical example that features rich computing expressivity and compatibility with physical…

This paper addresses a class of general nonsmooth and nonconvex composite optimization problems subject to nonlinear equality constraints. We assume that a part of the objective function and the functional constraints exhibit local…

In trajectory design, fuel consumption and trajectory reachability are two key performance indicators for low-thrust missions. This paper proposes general-purpose pretrained neural networks to predict these metrics. The contributions of…

We develop a general framework for estimating the $L_\infty(\mathbb{T}^d)$ error for the approximation of multivariate periodic functions belonging to specific reproducing kernel Hilbert spaces (RHKS) using approximants that are…

We present Lower Bound Tree-RRT (LBT-RRT), a single-query sampling-based algorithm that is asymptotically near-optimal. Namely, the solution extracted from LBT-RRT converges to a solution that is within an approximation factor of 1+epsilon…

Reinforcement Learning (RL) algorithms have achieved remarkable performance in decision making and control tasks due to their ability to reason about long-term, cumulative reward using trial and error. However, during RL training, applying…

Robotic manipulation in contact-rich environments remains challenging, particularly when relying on conventional tactile sensors that suffer from limited sensing range, reliability, and cost-effectiveness. In this work, we present LVTG, a…

Backward reachability analysis computes the set of states that reach a target set under the competing influence of control input and disturbances. Depending on their interplay, the backward reachable set either represents all states that…