State Space Models as Foundation Models: A Control Theoretic Overview

In recent years, there has been a growing interest in integrating linear state-space models (SSM) in deep neural network architectures of foundation models. This is exemplified by the recent success of Mamba, showing better performance than the state-of-the-art Transformer architectures in language tasks. Foundation models, like e.g. GPT-4, aim to encode sequential data into a latent space in order to learn a compressed representation of the data. The same goal has been pursued by control theorists using SSMs to efficiently model dynamical systems. Therefore, SSMs can be naturally connected to deep sequence modeling, offering the opportunity to create synergies between the corresponding research areas. This paper is intended as a gentle introduction to SSM-based architectures for control theorists and summarizes the latest research developments. It provides a systematic review of the most successful SSM proposals and highlights their main features from a control theoretic perspective. Additionally, we present a comparative analysis of these models, evaluating their performance on a standardized benchmark designed for assessing a model's efficiency at learning long sequences.

Chronos and CRS: Design of a miniature car-like robot and a software framework for single and multi-agent robotics and control

From both an educational and research point of view, experiments on hardware are a key aspect of robotics and control. In the last decade, many open-source hardware and software frameworks for wheeled robots have been presented, mainly in the form of unicycles and car-like robots, with the goal of making robotics accessible to a wider audience and to support control systems development. Unicycles are usually small and inexpensive, and therefore facilitate experiments in a larger fleet, but they are not suited for high-speed motion. Car-like robots are more agile, but they are usually larger and more expensive, thus requiring more resources in terms of space and money. In order to bridge this gap, we present Chronos, a new car-like 1/28th scale robot with customized open-source electronics, and CRS, an open-source software framework for control and robotics. The CRS software framework includes the implementation of various state-of-the-art algorithms for control, estimation, and multi-agent coordination. With this work, we aim to provide easier access to hardware and reduce the engineering time needed to start new educational and research projects.

Design, Optimal Guidance and Control of a Low-cost Re-usable Electric Model Rocket

In the last decade, autonomous vertical take-off and landing (VTOL) vehicles have become increasingly important as they lower mission costs thanks to their re-usability. However, their development is complex, rendering even the basic experimental validation of the required advanced guidance and control (G & C) algorithms prohibitively time-consuming and costly. In this paper, we present the design of an inexpensive small-scale VTOL platform that can be built from off-the-shelf components for less than 1000 USD. The vehicle design mimics the first stage of a reusable launcher, making it a perfect test-bed for G & C algorithms. To control the vehicle during ascent and descent, we propose a real-time optimization-based G & C algorithm. The key features are a real-time minimum fuel and free-final-time optimal guidance combined with an offset-free tracking model predictive position controller. The vehicle hardware design and the G & C algorithm are experimentally validated both indoors and outdoor, showing reliable operation in a fully autonomous fashion with all computations done on-board and in real-time.