Abstracts

Andrea Cristofaro, Sapienza Università di Roma, Italy

Modeling and boundary control of flexible robots

Soft robotics has recently gained an increasing interest due to its versatility and advanced capabilities. In particular, flexible manipulators have promising advantages compared to conventional rigid systems, such as high speed of response, reduced energy consumption and enhanced mobility. Flexible manipulators, and flexible mechanical systems in general, are characterized by infinitely many degrees of freedom and their state depends simultaneously on time and location in space. For this reason, they are well suited to be modelled as dynamical systems governed by partial differential equations. The scope of this short course is to introduce the basic mathematical tools for the modelling of flexible manipulators, as well as to present some techniques for the design of boundary controllers and the relative stability analysis.

Matthias Gerdts, Bundeswehr University Munich, Germany

Online trajectory generation for mobile robots using model-predictive control

Automation and autonomy become more and more important in many robotics applications, especially for mobile robots, which move automatically in a production site, or for automated cars, which move in the traffic. These mobile robots typically do not just follow a precomputed reference path, but they need to be able to update their trajectories in real time in order to react on changing environments. This typically requires a feedback control strategy, which takes into account the current state of the robot and the environment. The course discusses model predictive control (MPC) techniques, which require solving optimal control problems online. In order to speed-up the computation times we exploit a parametric sensitivity analysis, which allows one to update optimal solutions in the presence of perturbations very quickly. Numerical experiments are included in the course to gain practical experience with MPC. In addition, case studies from industry and with our Vehicle-in the- loop platform are presented.

Luca Giuzzi, Università degli Studi di Brescia, Italy

Blockchains from bitcoin to robotics —distributed data security for industry 4.0

Blockchains and smart contracts are emerging technologies which promise increased resiliency and automated processing for distributed data, even in the presence of failures or in scenarios where a consensus cannot be guaranteed in general. Their integration with the paradigm of industry 4.0 might provide efficient and secure tools to monitor, certify and control the production of goods, as well as robustness in the presence of failure.

In these lectures, the basic theory involved in the construction of a blockchain, the security and usability goals required and the implementation choices to be made shall be discussed. Applications to distributed computation, manufacturing and robotics shall be considered.

Wolfgang Reichel, Karlsruhe Institute of Technology, Germany

Mathematical theory of Kerr frequency comb–solitons, bifurcations and numerics

Frequency combs are optical signals which consist of a superposition of modes with equally spaced frequencies. They occur in optical microresonators which are susceptible to the Kerr effect: a single-frequency strong laser pump is tuned to a resonance frequency of the microresonator and strongly enhances the optical intensity inside the resonator. The excited modes inside the resonator start to interact nonlinearly which eventually leads to a transfer of the power from the laser pump to spectral lines of the frequency combs. Chip-scale frequency combs have the potential to revolutionize future terabit/s telecommunication. Mathematically, frequency combs are stationary solutions of the Lugiato-Lefever equation: a nonlinear Schrödinger equation with a damping and a forcing term. It is crucial for applications to characterize those regions of the parameter space where soliton frequency combs exist which are stable under small perturbations. During my lecture series I will introduce the mathematical model for Kerr frequency combs and analyse the occurrence of frequency combs with techniques from nonlinear analysis. Numerical methods for their computation will be introduced as well as quality measures that allow to evaluate their usability.

Lev Truskinovsky, École Supérieure de Physique et de Chimie Industrielles de la Ville de Paris, France

Mechanics of active systems

In these lectures we discuss in some detail few instructive examples of how internal activity associated with the word life can enter the equations of mechanics and what are the most striking effects of such seemingly innocent modifications of the familiar equations.