Related papers: Geometry-Aware Sampling-Based Motion Planning on R…
The length of the geodesic between two data points along a Riemannian manifold, induced by a deep generative model, yields a principled measure of similarity. Current approaches are limited to low-dimensional latent spaces, due to the…
We describe a general probabilistic framework to address a variety of Frechet-distance optimization problems. Specifically, we are interested in finding minimal bottleneck-paths in $d$-dimensional Euclidean space between given start and…
Riemannian optimization is concerned with problems, where the independent variable lies on a smooth manifold. There is a number of problems from numerical linear algebra that fall into this category, where the manifold is usually specified…
We determine explicit formulas for geodesics (in the Euclidean metric) in the configuration space of ordered pairs (x,x') of points in R^n which satisfy d(x,x')>=epsilon. We interpret this as two or three (depending on the parity of n)…
Autonomous exploration of unknown environments using a team of mobile robots demands distributed perception and planning strategies to enable efficient and scalable performance. Ideally, each robot should update its map and plan its motion…
This paper develops a Bayesian optimal experimental design for robot kinematic calibration on ${\mathbb{S}^3 \!\times\! \mathbb{R}^3}$. Our method builds upon a Gaussian process approach that incorporates a geometry-aware kernel based on…
Motion planning under differential constraints, kinodynamic motion planning, is one of the canonical problems in robotics. Currently, state-of-the-art methods evolve around kinodynamic variants of popular sampling-based algorithms, such as…
We propose a theoretically justified and practically applicable slice sampling based Markov chain Monte Carlo (MCMC) method for approximate sampling from probability measures on Riemannian manifolds. The latter naturally arise as posterior…
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…
Random geometric graphs are random graph models defined on metric measure spaces. A random geometric graph is generated by first sampling points from a metric space and then connecting each pair of sampled points independently with a…
Industrial robots are widely used in various manufacturing environments due to their efficiency in doing repetitive tasks such as assembly or welding. A common problem for these applications is to reach a destination without colliding with…
Several important algorithms for machine learning and data analysis use pairwise distances as input. On Riemannian manifolds these distances may be prohibitively costly to compute, in particular for large datasets. To tackle this problem,…
The paper surveys topological problems relevant to the motion planning problem of robotics and includes some new results and constructions. First we analyse the notion of topological complexity of configuration spaces which is responsible…
Sampling-based algorithms are viewed as practical solutions for high-dimensional motion planning. Recent progress has taken advantage of random geometric graph theory to show how asymptotic optimality can also be achieved with these…
Path planning for robotic coverage is the task of determining a collision-free robot trajectory that observes all points of interest in an environment. Robots employed for such tasks are often capable of exercising active control over…
In recent years, manifold learning has become increasingly popular as a tool for performing non-linear dimensionality reduction. This has led to the development of numerous algorithms of varying degrees of complexity that aim to recover man…
Motion planning is a key tool that allows robots to navigate through an environment without collisions. The problem of robot motion planning has been studied in great detail over the last several decades, with researchers initially focusing…
Fitting an unknown number of hyperplanes to data is a fundamental yet challenging problem in machine learning, characterized by its non-convexity, non-differentiability, and unknown model order. Existing approaches often struggle with local…
Kinodynamic motion planning for non-holomonic mobile robots is a challenging problem that is lacking a universal solution. One of the computationally efficient ways to solve it is to build a geometric path first and then transform this path…
Shape optimization is commonly applied in engineering to optimize shapes with respect to an objective functional relying on PDE solutions. In this paper, we view shape optimization as optimization on Riemannian shape manifolds. We consider…