Related papers: A robot that unknots knots
Round-based models are very common message-passing models; combinatorial topology applied to distributed computing provides sweeping results like general lower bounds. We combine both to study the computability of k-set agreement. Among all…
A {\it stuck knot} is a knot diagram containing designated crossings, called {\it stuck crossings}, whose incident strands are required to remain locally non-separable. These rigidity constraints restrict the allowable ambient isotopies and…
The majority of inverse kinematics (IK) algorithms search for solutions in a configuration space defined by joint angles. However, the kinematics of many robots can also be described in terms of distances between rigidly-attached points,…
A classical knot is described by a one-stroke trajectory with entanglements of a string. The replica method appears as a powerful tool in statistical mechanics for a polymer or self-avoiding walk. We consider this replica N to 0 limit in…
Fast and precise motion control is important for industrial robots in manufacturing applications. However, some collaborative robots sacrifice precision for safety, particular for high motion speed. The performance degradation is caused by…
We present a novel motion generation approach for robot arms, with high degrees of freedom, in complex settings that can adapt online to obstacles or new via points. Learning from Demonstration facilitates rapid adaptation to new tasks and…
We consider the following variant of the two dimensional gathering problem for swarms of robots: Given a swarm of $n$ indistinguishable, point shaped robots on a two dimensional grid. Initially, the robots form a closed chain on the grid…
Legged robot locomotion requires the planning of stable reference trajectories, especially while traversing uneven terrain. The proposed trajectory optimization framework is capable of generating dynamically stable base and footstep…
Learning from demonstration (LfD) provides a convenient means to equip robots with dexterous skills when demonstration can be obtained in robot intrinsic coordinates. However, the problem of compounding errors in long and complex skills…
This paper introduces a new systematic algorithm for constructing periodic Euclidean weaving diagrams with combinatorial arguments. It is shown that such a weaving diagram can be considered as a specific type of four-regular periodic planar…
We use the rational Witt class of a knot in the 3-sphere as a tool for addressing questions about its unknotting number. We apply these tools to several low crossing knots (151 knots with 11 crossing and 100 knots with 12 crossings) and to…
To ensure that a robot is able to accomplish an extensive range of tasks, it is necessary to achieve a flexible combination of multiple behaviors. This is because the design of task motions suited to each situation would become increasingly…
We study the rendezvous problem for two robots moving in the plane (or on a line). Robots are autonomous, anonymous, oblivious, and carry colored lights that are visible to both. We consider deterministic distributed algorithms in which…
Unknot recognition is one of the fundamental questions in low dimensional topology. In this work, we show that this problem can be encoded as a validity problem in the existential fragment of the first-order theory of real closed fields.…
Robots interacting with humans must not only generate learned movements in real-time, but also infer the intent behind observed behaviors and estimate the confidence of their own inferences. This paper proposes a unified model that achieves…
We have been developing a paradigm, which we refer to as Learning-from-observation, for a robot to automatically acquire what-to-do through observation of human performance. Since a simple mimicking method to repeat exact joint angles does…
We prove that any arc-presentation of the unknot admits a monotonic simplification by elementary moves; this yields a simple algorithm for recognizing the unknot. We obtain similar results for split links and composite links.
Bipedal locomotion is a key challenge in robotics, particularly for robots like Bolt, which have a point-foot design. This study explores the control of such underactuated robots using constrained reinforcement learning, addressing their…
We propose a learning framework to find the representation of a robot's kinematic structure and motion embedding spaces using graph neural networks (GNN). Finding a compact and low-dimensional embedding space for complex phenomena is a key…
This paper presents an algorithm to geometrically characterize inertial parameter identifiability for an articulated robot. The geometric approach tests identifiability across the infinite space of configurations using only a finite set of…