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We consider problems in which a mobile robot samples an unknown function defined over its operating space, so as to find a global optimum of this function. The path traveled by the robot matters, since it influences energy and time…
Optimal transport (OT) based data analysis is often faced with the issue that the underlying cost function is (partially) unknown. This paper is concerned with the derivation of distributional limits for the empirical OT value when the cost…
This paper presents a Nonlinear Model Predictive Control (NMPC) scheme targeted at motion planning for mechatronic motion systems, such as drones and mobile platforms. NMPC-based motion planning typically requires low computation times to…
Powder-bed-based additive manufacturing involves melting of a powder bed using a moving laser or electron beam as a heat source. In this paper, we formulate an optimization scheme that aims to control this type of melting. The goal consists…
During the last decade, sampling-based path planning algorithms, such as Probabilistic RoadMaps (PRM) and Rapidly-exploring Random Trees (RRT), have been shown to work well in practice and possess theoretical guarantees such as…
The current state-of-the-art gradient-based optimisation frameworks are able to produce impressive dynamic manoeuvres such as linear and rotational jumps. However, these methods, which optimise over the full rigid-body dynamics of the…
Recent research in robot exploration and mapping has focused on sampling environmental hotspot fields. This exploration task is formalized by Low, Dolan, and Khosla (2008) in a sequential decision-theoretic planning under uncertainty…
In this work, we present an efficient numerical implementation of the finite element method for modal analysis that leverages various symmetry operations, including spatial symmetry in point groups and space-time symmetry in…
An efficient method for computing solutions to the Optimal Transportation (OT) problem with a wide class of cost functions is presented. The standard linear programming (LP) discretization of the continuous problem becomes intractible for…
As a powerful technique in generative modeling, Flow Matching (FM) aims to learn velocity fields from noise to data, which is often explained and implemented as solving Optimal Transport (OT) problems. In this study, we bridge FM and the…
A new approach to solving two-point boundary value problems for a wave equation is developed. This new approach exploits the principle of stationary action to reformulate and solve such problems in the framework of optimal control. In…
We propose new methods to speed up convergence of the Alternating Direction Method of Multipliers (ADMM), a common optimization tool in the context of large scale and distributed learning. The proposed method accelerates the speed of…
The Orienteering Problem (OP) is a well-studied routing problem that has been extended to incorporate uncertainties, reflecting stochastic or dynamic travel costs, prize-collection costs, and prizes. Existing approaches may, however, be…
In this series of papers, we present a motion planning framework for planning comfortable and customizable motion of nonholonomic mobile robots such as intelligent wheelchairs and autonomous cars. In Part I, we presented the mathematical…
With the aim of bridging the gap between high quality reconstruction and mobile robot motion planning, we propose an efficient system that leverages the concept of adaptive-resolution volumetric mapping, which naturally integrates with the…
Within the field of optimal transport (OT), the choice of ground cost is crucial to ensuring that the optimality of a transport map corresponds to usefulness in real-world applications. It is therefore desirable to use known information to…
Driving vehicles in complex scenarios under harsh conditions is the biggest challenge for autonomous vehicles (AVs). To address this issue, we propose hierarchical motion planning and robust control strategy using the front-active steering…
In this paper we consider a broad class of infinite horizon discrete-time optimal control models that involve a nonnegative cost function and an affine mapping in their dynamic programming equation. They include as special cases classical…
Spatiotemporal dynamic medical imaging is critical in clinical applications, such as tomographic imaging of the heart or lung. To address such kind of spatiotemporal imaging problems, essentially, a time-dependent dynamic inverse problem,…
We study optimal transport for stationary stochastic processes taking values in finite spaces. In order to reflect the stationarity of the underlying processes, we restrict attention to stationary couplings, also known as joinings. The…