Later chapters consider the algorithms and representations that make these capabilities possible, while this chapter concentrates on the underlying hardware, with special emphasis on locomotion for wheeled robots.

In this chapter we draw motivation from real-world networks and formulate random graph models for them. We focus on some of the models that have received the most attention in the literature, namely, Erdos–Rényi random graphs, inhomogeneous random graphs, configuration models, and preferential attachment models. We follow Volume 1, both for the motivation as well as for the introduction of the random graph models involved. Furthermore, we add some convenient additional results, such as degree-truncation for configuration models and switching techniques for uniform random graphs with prescribed degrees. We also discuss preliminaries used in the book, for example concerning power-law distributions.

For autonomous robots it may seem like we can avoid needing the ability to make maps automatically. That is, it is sometimes assumed that a robot should be able to take for granted the a priori availability of a map. Unfortunately, this is rarely the case. Not only do architectural blueprints or related types of maps fail to be consistently reliable (since even during construction they are not always updated to reflect necessary alternations), but, furthermore, numerous aspects of an environment are not likely to appear on a map, such as tables, chairs, and transitory objects.

In this chapter, we implement a machine translation application as an example of an encoder-decoder task. In particular, we build on pretrained encoder-decoder transformer models, which exist in the Hugging Face library for a wide variety of language pairs. We first show how to use one of these models out-of-the-box to perform translation for one of the language pairs it has been exposed to during pretraining: English to Romanian. Afterward, we fine-tune the model to a new language combination that is has not seen before: Romanian to English. In both use cases, we use the T5 encoder-decoder model, which has been pretrained for several tasks, including machine translation.

In this chapter we investigate the small-world structure in rank-1 and general inhomogeneous random graphs. For this, we develop path-counting techniques that are interesting in their own right.

Although the vast majority of mobile robotic systems involve a single robot operating alone in its environment, a growing number of researchers are considering the challenges and potential advantages of having a group of robots cooperate in order to complete some required task. For some specific robotic tasks, such as exploring an unknown planet [374], search and rescue [812], pushing objects [608], [513], [687], [821], or cleaning up toxic waste [609], it has been suggested that rather than send one very complex robot to perform the task it would more effective to send a number of smaller, simpler robots.