Related papers: Accelerating Motion Planning via Optimal Transport
During the last decade, incremental sampling-based motion planning algorithms, such as the Rapidly-exploring Random Trees (RRTs) have been shown to work well in practice and to possess theoretical guarantees such as probabilistic…
Applications such as unbalanced and fully shuffled regression can be approached by optimizing regularized optimal transport (OT) distances, such as the entropic OT and Sinkhorn distances. A common approach for this optimization is to use a…
In general, optimal motion planning can be performed both locally and globally. In such a planning, the choice in favour of either local or global planning technique mainly depends on whether the environmental conditions are dynamic or…
This paper considers multi-goal motion planning in unstructured, obstacle-rich environments where a robot is required to reach multiple regions while avoiding collisions. The planned motions must also satisfy the differential constraints…
Optimal sampling based motion planning and trajectory optimization are two competing frameworks to generate optimal motion plans. Both frameworks have complementary properties: Sampling based planners are typically slow to converge, but…
This paper develops a computational framework for Multi-Period Martingale Optimal Transport (MMOT), addressing convergence rates, algorithmic efficiency, and financial calibration. Our contributions include: (1) Theoretical analysis: We…
We address the problem of reactive motion planning for quadrotors operating in unknown environments with dynamic obstacles. Our approach leverages a 4-dimensional spatio-temporal planner, integrated with vision-based Safe Flight Corridor…
Entropy regularized optimal transport and its multi-marginal generalization have attracted increasing attention in various applications, in particular due to efficient Sinkhorn-like algorithms for computing optimal transport plans. However,…
Optimal transport (OT) provides powerful tools for comparing probability measures in various types. The Wasserstein distance which arises naturally from the idea of OT is widely used in many machine learning applications. Unfortunately,…
In this paper, we study the Entropic Martingale Optimal Transport (EMOT) problem on \mathbb{R}. The investigation of the EMOT problem arises in the calibration problem of the Stochastic Volatility Models, where martingale constraints…
Real-world environments are inherently uncertain, and to operate safely in these environments robots must be able to plan around this uncertainty. In the context of motion planning, we desire systems that can maintain an acceptable level of…
While the optimal transport (OT) problem was originally formulated as a linear program, the addition of entropic regularization has proven beneficial both computationally and statistically, for many applications. The Sinkhorn fixed-point…
Motivated by robust dynamic resource allocation in operations research, we study the \textit{Online Learning to Transport} (OLT) problem where the decision variable is a probability measure, an infinite-dimensional object. We draw…
Most common Optimal Transport (OT) solvers are currently based on an approximation of underlying measures by discrete measures. However, it is sometimes relevant to work only with moments of measures instead of the measure itself, and many…
In this paper, we propose a novel methodology for path planning and scheduling for multi-robot navigation that is based on optimal transport theory and model predictive control. We consider a setup where $N$ robots are tasked to navigate to…
Over the last 20 years significant effort has been dedicated to the development of sampling-based motion planning algorithms such as the Rapidly-exploring Random Trees (RRT) and its asymptotically optimal version (e.g. RRT*). However,…
Mapping is essential in robotics and autonomous systems because it provides the spatial foundation for path planning. Efficient mapping enables planning algorithms to generate reliable paths while ensuring safety and adapting in real time…
High-level autonomy requires discrete and continuous reasoning to decide both what actions to take and how to execute them. Integrated Task and Motion Planning (TMP) algorithms solve these hybrid problems jointly to consider constraints…
Entropic regularization is quickly emerging as a new standard in optimal transport (OT). It enables to cast the OT computation as a differentiable and unconstrained convex optimization problem, which can be efficiently solved using the…
Sinkhorn algorithm has been used pervasively to approximate the solution to optimal transport (OT) and unbalanced optimal transport (UOT) problems. However, its practical application is limited due to the high computational complexity. To…