相关论文: Hilbert Space Embedding-based Trajectory Optimizat…

In this paper, we present an efficient algorithm for solving a class of chance constrained optimization under non-parametric uncertainty. Our algorithm is built on the possibility of representing arbitrary distributions as functions in…

We present a distributionally robust approach for collision avoidance by incorporating contextual information. Specifically, we embed the conditional distribution of future trajectory of the obstacle conditioned on the motion of the ego…

This paper proposes a method for constructing one-step prediction tubes for nonlinear systems using reproducing kernel Hilbert spaces. We approximate a bounded reproducing kernel Hilbert space (RKHS) hypothesis set by a finite-dimensional…

We propose a new, nonparametric approach to learning and representing transition dynamics in Markov decision processes (MDPs), which can be combined easily with dynamic programming methods for policy optimisation and value estimation. This…

Data-driven decision-making under uncertainty typically presumes the collection of historical data from an unknown target probability distribution. However, one may have no access to any data from the target distribution prior to…

We present algorithms for performing data-driven stochastic reachability as an addition to SReachTools, an open-source stochastic reachability toolbox. Our method leverages a class of machine learning techniques known as kernel embeddings…

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…

The probabilistic velocity obstacle (PVO) extends the concept of velocity obstacle (VO) to work in uncertain dynamic environments. In this paper, we show how a robust model predictive control (MPC) with PVO constraints under non-parametric…

Reduced modeling of a computationally demanding dynamical system aims at approximating its trajectories, while optimizing the trade-off between accuracy and computational complexity. In this work, we propose to achieve such an approximation…

A Hilbert space embedding of a distribution---in short, a kernel mean embedding---has recently emerged as a powerful tool for machine learning and inference. The basic idea behind this framework is to map distributions into a reproducing…

We propose MMD-OPT: a sample-efficient approach for minimizing the risk of collision under arbitrary prediction distribution of the dynamic obstacles. MMD-OPT is based on embedding distribution in Reproducing Kernel Hilbert Space (RKHS) and…

We develop a new framework for estimating joint probability distributions using tensor product reproducing kernel Hilbert spaces (RKHS). Our framework accommodates a low-dimensional, normalized and positive model of a Radon--Nikodym…

We present a data-driven algorithm for efficiently computing stochastic control policies for general joint chance constrained optimal control problems. Our approach leverages the theory of kernel distribution embeddings, which allows…

We present an embedding of stochastic optimal control problems, of the so called path integral form, into reproducing kernel Hilbert spaces. Using consistent, sample based estimates of the embedding leads to a model free, non-parametric…

Autonomous systems, like vehicles or robots, require reliable, accurate, fast, resource-efficient, scalable, and low-latency trajectory predictions to get initial knowledge about future locations and movements of surrounding objects for…

This paper addresses sampling-based trajectory optimization for risk-aware navigation under stochastic dynamics. Typically such approaches operate by computing $\tilde{N}$ perturbed rollouts around the nominal dynamics to estimate the…

Recently, some works have suggested methods to combine variational probabilistic inference with Monte Carlo sampling. One promising approach is via local optimal transport. In this approach, a gradient steepest descent method based on local…

The reproducing kernel Hilbert space (RKHS) embedding method is a recently introduced estimation approach that seeks to identify the unknown or uncertain function in the governing equations of a nonlinear set of ordinary differential…

Autonomous highway driving involves high-speed safety risks due to limited reaction time, where rare but dangerous events may lead to severe consequences. This places stringent requirements on trajectory planning in terms of both…

We present several generative and predictive algorithms based on the RKHS (reproducing kernel Hilbert spaces) methodology, which, most importantly, are scale up efficiently with large datasets or high-dimensional data. It is well recognized…