Related papers: Ten Problems in Geobotics
While robots are increasingly integrated into the built environment, little is known how their qualities can meaningfully influence our spaces to facilitate enjoyable and agreeable interaction, rather than robotic settings that are driven…
Autonomous robots are currently one of the most popular Artificial Intelligence problems, having experienced significant advances in the last decade, from Self-driving cars and humanoids to delivery robots and drones. Part of the problem is…
We study a generalized motion planning problem involving multiple autonomous robots navigating in a $d$-dimensional Euclidean space in the presence of a set of obstacles whose positions are unknown a priori. Each robot is required to visit…
We consider the problem of searching for an intruder in a geometric domain by utilizing multiple search robots. The domain is a simply connected orthogonal polygon with edges parallel to the cartesian coordinate axes. Each robot has a…
In this chapter, we identify fundamental geometric structures that underlie the problems of sampling, optimisation, inference and adaptive decision-making. Based on this identification, we derive algorithms that exploit these geometric…
Assembling parts into an object is a combinatorial problem that arises in a variety of contexts in the real world and involves numerous applications in science and engineering. Previous related work tackles limited cases with identical unit…
This survey article deals with applications of optimal control to aerospace problems with a focus on modern geometric optimal control tools and numerical continuation techniques. Geometric optimal control is a theory combining optimal…
Most conventional wheeled robots can only move in flat environments and simply divide their planar workspaces into free spaces and obstacles. Deeming obstacles as non-traversable significantly limits wheeled robots' mobility in real-world,…
Geodesic problems involve computing trajectories between prescribed initial and final states to minimize a user-defined measure of distance, cost, or energy. They arise throughout physics and engineering -- for instance, in determining…
As robots and other intelligent agents move from simple environments and problems to more complex, unstructured settings, manually programming their behavior has become increasingly challenging and expensive. Often, it is easier for a…
Identifying and categorizing specific robot tasks, behaviors, and resources is an essential precursor to reproducing and evaluating robotics experiments across laboratories and platforms. Without some means of capturing how one environment,…
The task-specific optimization of robotic systems has long been divided into the optimization of the robot and the optimization of the environment. In this letter, we argue that these two problems are interdependent and should be treated as…
After decades of uninterrupted progress and growth, information technology has so evolved that it can be said we are entering the age of autonomous machines, but there exist many roadblocks in the way of making this a reality. In this…
We study an elementary problem of topological robotics: rotation of a line, which is fixed by a revolving joint at a base point: one wants to bring the line from its initial position to a final position by a continuous motion in the space.…
We discuss issues of problem formulation for algorithms in real algebraic geometry, focussing on quantifier elimination by cylindrical algebraic decomposition. We recall how the variable ordering used can have a profound effect on both…
Humans excel in grasping and manipulating objects because of their life-long experience and knowledge about the 3D shape and weight distribution of objects. However, the lack of such intuition in robots makes robotic grasping an…
In this paper we introduce and study a new concept of parametrised topological complexity, a topological invariant motivated by the motion planning problem of robotics. In the parametrised setting, a motion planning algorithm has high…
Algorithms for continuous optimization problems have a rich history of design and innovation over the past several decades, in which mathematical analysis of their convergence and complexity properties plays a central role. Besides their…
Robots are increasingly tested in public spaces, towards a future where urban environments are not only for humans but for autonomous systems. While robots are promising, for convenience and efficiency, there are challenges associated with…
We review some recent applications of machine learning to algebraic geometry and physics. Since problems in algebraic geometry can typically be reformulated as mappings between tensors, this makes them particularly amenable to supervised…