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.

Andrea
Baisero, Master 2012,Swedish AI Society's best master thesis award,
supervision with C. H. Ek and D. Kragic
Thesis: "Encoding
Sequential Structures using Kernels", next: PhD student University of Stuttgart and Northeastern University

Dex-Net 1.0: A Cloud-Based Network of 3D Objects and a
Multi-Armed Bandit Model with Correlated Rewards to Accelerate
Robust Grasp Planning

Jeffrey Mahler, Florian T. Pokorny, Brian Hou, Melrose
Roderick, Michael Laskey, Mathieu Aubry, Kai Kohlhoff, Torsten
Kroeger, James Kuffner, Ken Goldberg

IEEE ICRA, 2016, Finalist, Best Manipulation Paper Award, ICRA 2016

Let $(L,h)\to (X, \omega)$ be a compact toric polarized Kähler manifold of
complex dimension $n$. For each $k\in \mathbb{N}$, the fibre-wise Hermitian metric
$h^k$ on $L^k$ induces a natural inner product on the vector space $\mathcal{C}^{\infty}(X,
L^k)$ of smooth global sections of $L^k$ by integration with respect to the
volume form $\frac{\omega^n}{n!}$. The orthogonal projection
$P_k:\mathcal{C}^{\infty}(X, L^k)\to H^0(X, L^k)$ onto the space $H^0(X, L^k)$ of global
holomorphic sections of $L^k$ is represented by an integral kernel $B_k$ which
is called the Bergman kernel (with parameter $k\in \mathbb{N}$). The restriction $\rho_k:X\to
\mathbb{R}$ of the norm of $B_k$ to the diagonal in $X\times X$ is called the density
function of $B_k$.
On a dense subset of $X$, we describe a method for computing the coefficients of
the asymptotic expansion of $\rho_k$ as $k\to \infty$ in this toric
setting. We also provide a direct proof of a result which illuminates the
off-diagonal decay behaviour of toric Bergman kernels.
We fix a parameter $l\in \mathbb{N}$ and consider the projection $P_{l,k}$ from
$\mathcal{C}^{\infty}(X, L^k)$ onto those global holomorphic sections of $L^k$ that
vanish to order at least $lk$ along some toric submanifold of $X$. There exists an
associated toric partial Bergman kernel $B_{l, k}$ giving rise to a toric partial density function
$\rho_{l, k}:X\to \mathbb{R}$.
For such toric partial density functions,
we determine new asymptotic expansions over
certain subsets of $X$ as $k\to \infty$. Euler-Maclaurin sums and Laplace's method are utilized as important
tools for this. We discuss the case of a polarization of $\mathbb{CP}^n$ in detail
and also investigate the non-compact Bargmann-Fock model with imposed vanishing
at the origin.
We then discuss the relationship between the slope inequality and the asymptotics
of Bergman kernels with vanishing and study how a version of Song and Zelditch's
toric localization of sums result generalizes to arbitrary polarized Kähler
manifolds.
Finally, we construct families of induced metrics on blow-ups of
polarized Kähler manifolds. We relate those metrics to partial density
functions and study their properties for a specific blow-up of $\mathbb{C}^n$ and $\mathbb{CP}^n$
in more detail.

@phdthesis{pokorny2011a,
title = {The Bergman Kernel on Toric K{\"a}hler Manifolds},
author = {Pokorny, Florian T.},
year = {2011},
school = {The University of Edinburgh},
doi = {1842/5301},
url = {http://www.csc.kth.se/~fpokorny/static/publications/FTPokornyPhD.pdf},
}

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.

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 $Q_l^-(g)$.