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 20152016, 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
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 leastsquares regression to
recover a smooth surface description from pointcloud 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 $c_{l,m} = \sqrt{\frac{2l+1}{2\pi}\frac{(lm)!}{(l+m)!}}$ and
$P_l^m$ denotes the associated Legendre polynomial of order $m$ and degree $l$.
The functions $Y_{l,m}$ arise as eigenfunctions 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 eigenvalue. These eigenfunctions, 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 pointcloud 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 pointcloud data where all $Y_{l, m}$ up to degree $L$
are used.
Point cloud P with 25000 points and reconstructed surfaces, where all eigenspaces 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 subgradientbased method to compute $Q^+(g)$
as outlined in the above
paper.
Additionally, we provide a novel algorithm to speedup 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 $Q_l^(g)$.
This is a personal homepage. Opinions expressed here or implied by links provided do not
represent the official views of KTH Royal Institute of Technology.
© Florian T. Pokorny, all rights reserved.