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Safe corridor-based Trajectory Optimization (TO) presents an appealing approach for collision-free path planning of autonomous robots, offering global optimality through its convex formulation. The safe corridor is constructed based on the…
We propose a variational formulation of an inverse problem in continuous-time stochastic control, aimed at identifying control costs consistent with a given distribution over trajectories. The formulation is based on minimizing the…
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…
The target stationary distribution problem (TSDP) is the following: given an irreducible stochastic matrix $G$ and a target stationary distribution $\hat \mu$, construct a minimum norm perturbation, $\Delta$, such that $\hat G = G+\Delta$…
Clustering mixtures of Gaussian distributions is a fundamental and challenging problem that is ubiquitous in various high-dimensional data processing tasks. While state-of-the-art work on learning Gaussian mixture models has focused…
We present a method for computing A-optimal sensor placements for infinite-dimensional Bayesian linear inverse problems governed by PDEs with irreducible model uncertainties. Here, irreducible uncertainties refers to uncertainties in the…
In this paper, we present a new control policy parametrization for the finite-horizon covariance steering problem for discrete-time Gaussian linear systems (DTGLS) which can reduce the latter stochastic optimal control problem to a…
In this work, we revisit the discrete-time Schr\"{o}dinger Bridge (SB) and Density Steering (DS) problems for Gaussian mixture model (GMM) boundary distributions. Building on the existing literature, we construct a set of feasible Markovian…
An adaptive direct collocation method is developed for solving optimal control problems constrained by parabolic partial differential equations. The partial differential equation is first reformulated in a variational setting, where the…
This work develops a stochastic model predictive controller~(SMPC) for uncertain linear systems with additive Gaussian noise subject to state and control constraints. The proposed approach is based on the recently developed finite-horizon…
While techniques have been developed for chance constrained stochastic optimal control using sample disturbance data that provide a probabilistic confidence bound for chance constraint satisfaction, far less is known about how to use sample…
This paper presents a stochastic model predictive control (SMPC) algorithm for linear systems subject to additive Gaussian mixture disturbances, with the goal of satisfying chance constraints. We focus on a special case where each Gaussian…
Optimal mass transport, also known as the earth mover's problem, is an optimization problem with important applications in various disciplines, including economics, probability theory, fluid dynamics, cosmology and geophysics to cite a few.…
Planning under process and measurement uncertainties is a challenging problem. In its most general form it can be modeled as a Partially Observed Markov Decision Process (POMDP) problem. However POMDPs are generally difficult to solve when…
Designing robust space trajectories in nonlinear dynamical environments, such as the Earth-Moon circular restricted three-body problem (CR3BP), poses significant challenges due to sensitivity to initial conditions and non-Gaussian…
We cast motion planning under uncertainty as a stochastic optimal control problem, where the optimal posterior distribution has an explicit form. To approximate this posterior, this work frames an optimization problem in the space of…
This work proposes an open-loop methodology to solve chance constrained stochastic optimal control problems for linear systems with a stochastic control matrix. We consider a joint chance constraint for polytopic time-varying target sets…
This paper investigates the problem of tracking solutions of stochastic optimization problems with time-varying costs that depend on random variables with decision-dependent distributions. In this context, we propose the use of an online…
Past research on pedestrian trajectory forecasting mainly focused on deterministic predictions which provide only point estimates of future states. These future estimates can help an autonomous vehicle plan its trajectory and avoid…
Tendon-driven continuum robot kinematic models are frequently computationally expensive, inaccurate due to unmodeled effects, or both. In particular, unmodeled effects produce uncertainties that arise during the robot's operation that lead…