### EPFL Student Project Proposals

The descriptions below are available for either semester projects or master projects (the content will be adjusted accordingly). Suggestions of other projects (or variants of existing projects) are also welcome, as long as they fit within the group's research interests.

#### SMARTPHONE INTERFACE USING AUGMENTED REALITY

We have developed an augmented reality interface running on Android smartphones to display a virtual robot (left image). The app relies on ARCore, Google's toolkit for building augmented reality applications on Android and iOS devices. This toolkit is used to estimate the location of the phone and to render 3D graphics on top of the camera's image displayed on the screen.

The aim of the project is to extend this interface to let the user move the virtual robot to a desired configuration (see right images as an illustration). Several options can be considered, such as clicking on the robot articulations and dragging them to their desired positions, or drawing a stick figure on top of the image, which is then interpreted to set the desired pose of the robot.

The Android smartphone will be programmed in Java (knowledge of either Java or C++ is required for the project).

The developed interface will be tested to change the pose of a real 7-axis Panda robot (Franka Emika), by first setting and visualizing the motion of the virtual robot on the smartphone, and then running the motion on the real robot. A basic interface between the mobile phone and the robot is already available for the project (by using the ROS middleware). The proposed approach will finally be evaluated with inexperienced user to determine if it is accurate and easy-to-use.

Keywords: augmented reality, smartphone interfaces, robotics, inverse kinematics, machine learning

#### TENSOR-VARIATE REGRESSION IN ROBOTICS APPLICATIONS

Many regression problems in robotics can be formulated as that of collecting data in the form of input x and output y, which are then used to estimate a new output y', given a new input x'. This project proposes to extend regression to the more general case in which x and y are multidimensional arrays (also called tensors).

Tensors are generalization of matrices to arrays of higher dimensions, where vectors and matrices correspond to 1st and 2nd-order tensors. When data are organized in matrices or arrays of higher dimensions (tensors), classical regression methods first transform these data into vectors, therefore ignoring the underlying structure of the data and increasing the dimensionality of the problem. This flattening operation typically leads to overfitting when only few training data are available.

Tensor methods are well established in several machine learning fields such as image/video processing and recommendation systems, but this area of research is still at its infancy in robotics.

The project proposes to test and evaluate different generalizations of the pseudoinverse for tensor-variate data (see references below), which will be exploited in the context of linear regression for robotics applications.

Keywords: tensor methods, regression

References:

#### TENSOR-VARIATE DICTIONARY LEARNING OF MOVEMENT PRIMITIVES

In robotics, it is useful to represent movements as a superposition of basis functions. Often, the set of basis functions is predefined. The corresponding learning problem consists of estimating how to combine the set of basis functions to form a desired movement. The set of basis functions (dictionary of movement primitives) can be learned together with their combination. To do this, a sparse coding approach for dictionary learning will be exploited, as presented in the video and paper below. The approach will be evaluated on robot motion data.

The standard dictionary learning problem is formulated with data in the form of input x and output y, which are then used to estimate a new output y_new, given a new input x_new. The project proposes to extend this approach to the more general case in which x and y are multidimensional arrays (also called tensors, see slides below). The approach will be evaluated on robot motion data.

Keywords: tensor methods, movement primitives, sparse coding

#### SUBSPACE LEARNING FOR ROBOT CONTROL APPLICATIONS

In robotics, movements can be represented as a dynamical system describing the evolution in time of the robot. Most often, the system is nonlinear, and the standard approach is to linearize the system so that locally, a linear system can be considered. Another approach, originally proposed by Koopman, is to augment the original set of variables composing the state space so that the nonlinear system can be expressed as a linear system in this augmented state space.

To do this, several approaches have been proposed, such as forming this augmented state space with polynomial or Fourier expansions of the original signal, or learning this augmented state space with autoencoders. Often, these approaches consider systems that estimate the next state based on the current state.

A promising approach recently proposed in the reference below is to consider a history of the previous states. This approach suggests to go beyond standard polynomial basis functions or Fourier basis functions by exploiting delay coordinates as basis functions, in the form of a factorization of a Hankel matrix. The resulting algorithm is surprisingly short and simple to implement. This project proposes to explore this approach in a robot control task with the 7-axis Panda robot (Franka Emika).

Keywords: dynamical systems, robot control, subspace learning, delay embedding, time series analysis

References:

Steven L. Brunton, Bingni W. Brunton, Joshua L. Proctor, Eurika Kaiser, and J. Nathan Kutz, "Chaos as an Intermittently Forced Linear System", Nature Communications, 2017

Hankel Alternative View of Koopman (HAVOK) Analysis (video)

#### LEARNING TO SEARCH: AN ERGODIC CONTROL APPROACH

In ergodic control, the aim is to find a sequence of control commands u(t) so that the retrieved trajectory x(t) covers a bounded space X in proportion of a given spatial distribution phi(x). The objective is formulated as a tracking problem in the frequency domain, in which the goal is to match the frequency patterns by putting more importance on low frequency components than high frequency components.

The resulting controller produces a natural movement to explore the regions of interest. Interestingly, this search pattern does not rely on random moves, but is instead well defined mathematically as a tracking problem in the frequency domain (i.e., matching Fourier series coefficients).

The aim of this project is to combine learning from demonstration with ergodic control, by extracting from the demonstration the regions that we need to explore, and then letting ergodic control explores these regions. The approach will be tested in an insertion task with a 7-axis Panda robot (Franka Emika). The implementation will be in C++ or Matlab (example codes for ergodic control in C++ and Matlab will be provided).

Keywords: robot control, learning from demonstration, Fourier series

Reference:

Calinon, S., "Mixture Models for the Analysis, Edition, and Synthesis of Continuous Time Series", Bouguila, N. and Fan, W. (eds), Mixture Models and Applications, Springer, 2019

#### CIGAR BOX JUGGLING WITH ROBOTS

"Cigar box juggling" consists of manipulating three boxes, by holding two boxes while one box is free. It involves the juggler to skillfully move two of the boxes to change their configurations (see above sequence). For beginners, the movement is typically executed by moving the boxes up-and-down when changing the configuration, so that there is more time to change the orientation of the box being held (since the other hand will accompany'' the falling box). If the up-and-down motion has high amplitude, the movement to change the configuration is relatively slow.

This project proposes to explore whether such motion could be planned and executed on two 7-axis Panda robots (Franka Emika). The dynamical model will first be built to determine the motion to execute. Model predictive control will then be employed to control the robot with anticipation capability.

Keywords: robot control, robot planning, skills learning and adaptation, model predictive control