Related papers: Optimal Scheduling of Dynamic Transport
We study the estimation of optimal transport (OT) maps between an arbitrary source probability measure and a log-concave target probability measure. Our contributions are twofold. First, we propose a new evolution equation in the set of…
This work presents an efficient method to solve a class of continuous-time, continuous-space stochastic optimal control problems of robot motion in a cluttered environment. The method builds upon a path integral representation of the…
High-dimensional generative modeling is fundamentally a manifold-learning problem: real data concentrate near a low-dimensional structure embedded in the ambient space. Effective generators must therefore balance support fidelity -- placing…
This article details a novel numerical scheme to approximate gradient flows for optimal transport (i.e. Wasserstein) metrics. These flows have proved useful to tackle theoretically and numerically non-linear diffusion equations that model…
To perform autonomous driving maneuvers, such as parallel or perpendicular parking, a vehicle requires continual speed and steering adjustments to follow a generated path. In consequence, the path's quality is a limiting factor of the…
We propose a deterministic sampling framework using Score-Based Transport Modeling for sampling an unnormalized target density $\pi$ given only its score $\nabla \log \pi$. Our method approximates the Wasserstein gradient flow on…
We present a flow-based approach to the optimal transport (OT) problem between two continuous distributions $\pi_0,\pi_1$ on $\mathbb{R}^d$, of minimizing a transport cost $\mathbb{E}[c(X_1-X_0)]$ in the set of couplings $(X_0,X_1)$ whose…
Automated driving in urban scenarios requires efficient planning algorithms able to handle complex situations in real-time. A popular approach is to use graph-based planning methods in order to obtain a rough trajectory which is…
Understanding the complex patterns in space-time exhibited by active systems has been the subject of much interest in recent times. Complementing this forward problem is the inverse problem of controlling active matter. Here we use optimal…
Time-dependent fixed-time control is a cost-effective control method that is widely employed at signalized intersections in numerous countries. Existing optimization models rely on traditional delay models with specific assumptions…
We propose a new model of one-dimensional traffic flow using a coupled map lattice. In the model, each vehicle is assigned a map and changes its velocity according to it. A single map is designed so as to represent the motion of a vehicle…
Sampling from high-dimensional distributions is a fundamental problem in statistical research and practice. However, great challenges emerge when the target density function is unnormalized and contains isolated modes. We tackle this…
We study an optimal transportation approach for recovering parameters in dynamical systems with a single smoothly varying attractor. We assume that the data is not sufficient for estimating time derivatives of state variables but enough to…
We propose a simple subsampling scheme for fast randomized approximate computation of optimal transport distances. This scheme operates on a random subset of the full data and can use any exact algorithm as a black-box back-end, including…
Motion planning is a fundamental problem in autonomous robotics that requires finding a path to a specified goal that avoids obstacles and takes into account a robot's limitations and constraints. It is often desirable for this path to also…
By building upon the recent theory that established the connection between implicit generative modeling (IGM) and optimal transport, in this study, we propose a novel parameter-free algorithm for learning the underlying distributions of…
Efficient trajectory generation is crucial for autonomous systems; however, current numerical methods often struggle to handle periodic behaviors effectively, particularly when the onboard sensors require equidistant temporal sampling. This…
Planning a safe and feasible trajectory for autonomous vehicles in real-time by fully utilizing perceptual information in complex urban environments is challenging. In this paper, we propose a spatio-temporal trajectory planning method…
This paper studies a stochastic model that describes the evolution of vehicle densities in a road network. It is consistent with the class of (deterministic) kinematic wave models, which describe traffic flows on the basis of conservation…
In machine learning and computer vision, optimal transport has had significant success in learning generative models and defining metric distances between structured and stochastic data objects, that can be cast as probability measures. The…