# Florian T. Pokorny

## Welcome

My current research focuses on two main directions: 1) explainable machine learning algorithms with a geometric or topological flavour and 2) machine learning methods that are tailored for robotic manipulation or motion planning and which incorporate available domain knowledge and information about physics and configuration space geometry in order to be data efficient.

## Positions & Professional Interests

• Assistant Professor, Machine Learning, RPL, EECS, KTH
• Responsible for WASP AI Graduate School at KTH

## Short Biography

I am currently an Assistant Professor in Machine Learning within the division of Robotics, Perception and Learning at KTH Royal Institute of Technology. In 2015-2016, I was a postdoctoral visiting scholar at the AMPlab and the Berkeley Automation Science Lab at the University of California, Berkeley where I worked with Ken Goldberg and his group. Previously, I was fortunate to be a researcher and postdoc working with Prof. Danica Kragic and her group. Before then, I was a pure mathematician and completed my PhD entitled "The Bergman Kernel on Toric Kähler Manifolds" under supervision of Prof. Michael Singer at the University of Edinburgh. Before that, I received my BSc mathematics from the University of Edinburgh and a Master of Advanced Study in Mathematics (Part III) from the University of Cambridge and also spent a year as an exchange student at the National University of Singapore.

## Contact

Room 713, Teknikringen 14 RPL, EECS, KTH, 114 28 Stockholm, Sweden, fpokorny (at) kth.se

# News

Co-organizing ICRA 2019 Workshop on Topological Methods
New course on Topological Data Analysis for WASP students in 2019

# Thesis Projects

## I currently offer master thesis projects in these topics

If you are interested in any of the topics below or would like to suggest your own topic, drop me an email with your CV and transcripts attached as well as a reason for why you are interested in this topic. Please note that I only have capacity to consider students that are already registered at KTH for thesis project work.
• Multiple topics in anomaly detection for financial transaction data, in collaboration with Salla Franzén, Chief Data Scientist, SEB.
• Topological Data Analysis on ImageNet. This project will investigate to what extent recently developed techniques in Topological Data Analysis can be used for the classification of images.
• Topological Data Analysis on ShapeNet. This project will investigate the use of recently developed techniques for the analysis and classification of 3D meshes.
• Determination of Statistical Patterns and Properties of Motion Planning Algorithms in the moduli space of configuration spaces. This project will investigate statistical properties of randomized motion planning algorithms.
• Approximation of Statistical Patterns and Properties of Motion Planning Algorithms using Deep Neural Networks.

# HarmonicRegression (C++/Python)

This C++ library with python bindings implements spherical harmonics and an associated least-squares regression to recover a smooth surface description from point-cloud data. These methods are described in our paper "Grasp Moduli Spaces and Spherical Harmonics", F. T. Pokorny, Y. Bekiroglu, D. Kragic, IEEE ICRA, 2014 This software is freely available for academic/research purposes, just drop me an email to get the code: fpokorny (at) kth.se

## Introduction

Consider the space $L^2(\mathbb{S}^2)$ of integrable functions on the sphere $\mathbb{S}^2\subset \mathbb{R}^3$. We choose a coordinate chart $p(\theta, \phi) = (\sin \theta \cos \phi, \sin \theta \sin \phi, \cos\theta)$ on the sphere, with $(\theta, \phi) \in [0, \pi]\times [0, 2\pi)$. For integers $l, m$, the real valued spherical harmonic function of degree $l$ and order $m$, $|m|\le l$, is defined by
$Y_{l,m}(\theta, \phi) = \begin{cases} c_{l,m}P_l^{|m|}(\cos \theta)\sin (|m|\phi) & -l\le m \le -1\\ \frac{c_{l,m}}{\sqrt{2}}P_l^0(\cos \theta) & m = 0\\ c_{l,m}P_l^{m}(\cos \theta)\cos(m\phi) & 1\le m \le l, \end{cases}$
where $c_{l,m} = \sqrt{\frac{2l+1}{2\pi}\frac{(l-|m|)!}{(l+|m|)!}}$ and $P_l^m$ denotes the associated Legendre polynomial of order $m$ and degree $l$. The functions $Y_{l,m}$ arise as eigen-functions of the Laplacian $\Delta=\frac{1}{\sin\theta}\frac{\partial}{\partial\theta}(\sin\theta \frac{\partial}{\partial\theta})+\frac{1}{\sin^2\theta}\frac{\partial^2}{\partial^2\phi}$ on $\mathbb{S}^2$ For fixed $l$, there are $2l+1$ eigenfunctions $\{Y_{l,m}: m\in\{-l, \ldots, l\}\}$ satisfying $\Delta Y_{l,m} = \lambda_l Y_{l,m},$ where $\lambda_l = l(l+1)$ denotes the corresponding eigen-value. These eigen-functions, for all $l, m$, form an infinite orthonormal basis for $L^2(\mathbb{S}^2)$ with respect to the standard inner product $\langle f, g\rangle = \int_{\mathbb{S}^2} fg \,dVol$, for $f, g\in L^2(\mathbb{S}^2)$ and where $dVol = \sin \theta d \theta d \phi$.

A visualization of the functions $Y_{l, m}$, where the degree changes from 0 to 4 along the horizontal axis and the order $m$ changes from $-l$ to $l$ along the vertical axis.

This library can be used to compute the functions $Y_{l, m}$ and their derivatives. Additionally, a least squares regression of point-cloud data which can be mapped onto a sphere can be performed easily with the provided code. The figure below illustrates an example reconstruction of a smooth surface from point-cloud data where all $Y_{l, m}$ up to degree $L$ are used.

Point cloud P with 25000 points and reconstructed surfaces, where all eigen-spaces up to degree $L$ are used.

# FastGrasp (C++/Python)

This C++ library with python bindings implements fast grasp quality evaluation methods outlined in our paper "Classical Grasp Quality Evaluation: New Theory and Algorithms", F. T. Pokorny, D. Kragic, IEEE/RSJ IROS, 2013. This software is freely available for academic/research purposes, just drop me an email to get the code: fpokorny (at) kth.se

## Introduction

This library is concerned with the evaluation of a classical $L^1$ grasp quality score $Q(g)$ for a grasp contact configuration $g$ which was originally defined by Ferrari and Canny. The value of $Q(g)$ is defined to be the radius of the largest ball around the origin completely contained in the grasp wrench space $W$, if such a ball exists and $0$ otherwise. This value cannot be computed precisely and a typical approach has hence been to approximate $W$ by a smaller convex hull spanned by finitely many points and which is obtained by approximating the friction cone $F$ at each contact by convex polyhedral cones $F_l$ with $l$ edges.

Polyhedral cone approximations of a friction cone

The resulting grasp quality approximation $Q_l^-(g)\le Q(g)$ has been popular in the grasping community for more than a decade. Our paper "Classical Grasp Quality Evaluation: New Theory and Algorithms", F. T. Pokorny, D. Kragic, IEEE/RSJ IROS, 2013 establishes for the first time error bounds on this approximation and provides a novel approach to also obtain an upper bound $Q^+(g)$ so that $$Q_l^-(g)\le Q(g) \le Q^+(g).$$ This library provides functions to compute $Q_l^-(g)$ and $Q^+(g)$. We use a subgradient-based method to compute $Q^+(g)$ as outlined in the above paper. Additionally, we provide a novel algorithm to speed-up the computation of $Q_l^-(g)$ by first filtering out unstable grasps using a convex optimization procedure. This results in a significant speedup compared to a standard evaluation of $Q_l^-(g)$.