Related papers: Accelerating Motion Planning via Optimal Transport
This paper presents an efficient algorithm, naming Centralized Searching and Decentralized Optimization (CSDO), to find feasible solution for large-scale Multi-Vehicle Trajectory Planning (MVTP) problem. Due to the intractable growth of…
The Sinkhorn algorithm is a numerical method for the solution of optimal transport problems. Here, I give a brief survey of this algorithm, with a strong emphasis on its geometric origin: it is natural to view it as a discretization, by…
We present an optimization-based motion planning algorithm to compute a smooth, collision-free trajectory for a manipulator used to transfer a liquid from a source to a target container. We take into account fluid dynamics constraints as…
MPC (Model predictive control)-based motion planning and trajectory generation are essential in applications such as unmanned aerial vehicles, robotic manipulators, and rocket control. However, the real-time implementation of such…
Sliced Optimal Transport (SOT) is a rapidly developing branch of optimal transport (OT) that exploits the tractability of one-dimensional OT problems. By combining tools from OT, integral geometry, and computational statistics, SOT enables…
Cross-modal matching, a fundamental task in bridging vision and language, has recently garnered substantial research interest. Despite the development of numerous methods aimed at quantifying the semantic relatedness between image-text…
Simultaneous Localization and Planning (SLAP) under process and measurement uncertainties is a challenge. It involves solving a stochastic control problem modeled as a Partially Observed Markov Decision Process (POMDP) in a general…
In machine learning, Optimal Transport (OT) theory is extensively utilized to compare probability distributions across various applications, such as graph data represented by node distributions and image data represented by pixel…
Cooperative path planning, a crucial aspect of multi-agent systems research, serves a variety of sectors, including military, agriculture, and industry. Many existing algorithms, however, come with certain limitations, such as simplified…
To achieve optimal robot behavior in dynamic scenarios we need to consider complex dynamics in a predictive manner. In the vehicle dynamics community, it is well know that to achieve time-optimal driving on low surface, the vehicle should…
We consider the problem of unconstrained minimization of a smooth objective function in $\mathbb{R}^d$ in setting where only function evaluations are possible. We propose and analyze stochastic zeroth-order method with heavy ball momentum.…
Trajectory optimization offers mature tools for motion planning in high-dimensional spaces under dynamic constraints. However, when facing complex configuration spaces, cluttered with obstacles, roboticists typically fall back to…
Optimal transport (OT) is a powerful tool for measuring the distance between two defined probability distributions. In this paper, we develop a new manifold named the coupling matrix manifold (CMM), where each point on CMM can be regarded…
We present a unified probabilistic framework for simultaneous trajectory estimation and planning (STEAP). Estimation and planning problems are usually considered separately, however, within our framework we show that solving them…
Path Planning and target searching in a three-dimensional environment is a challenging task in the field of robotics. It is an optimization problem as the path from source to destination has to be optimal. This paper aims to generate a…
We present a general and modular algorithmic framework for path planning of robots. Our framework combines geometric methods for exact and complete analysis of low-dimensional configuration spaces, together with practical, considerably…
Monotone gradient functions play a central role in solving the Monge formulation of the optimal transport (OT) problem, which arises in modern applications ranging from fluid dynamics to robot swarm control. When the transport cost is the…
A new path planning method for Mobile Robots (MR) has been developed and implemented. On the one hand, based on the shortest path from the start point to the goal point, this path planner can choose the best moving directions of the MR,…
In this paper, we propose a new framework named Communication Optimal Transport (CommOT) for computing the rate distortion (RD) function. This work is motivated by observing the fact that the transition law and the relative entropy in…
We introduce a functional gradient descent trajectory optimization algorithm for robot motion planning in Reproducing Kernel Hilbert Spaces (RKHSs). Functional gradient algorithms are a popular choice for motion planning in complex…