Related papers: Geometric Algebra for Optimal Control with Applica…
The use of geometric and symmetry techniques in quantum and classical information processing has a long tradition across the physical sciences as a means of theoretical discovery and applied problem solving. In the modern era, the emergent…
A key challenge in intelligent robotics is creating robots that are capable of directly interacting with the world around them to achieve their goals. The last decade has seen substantial growth in research on the problem of robot…
Continuum robots with floating bases demonstrate exceptional operational capabilities in confined spaces, such as those encountered in medical surgeries and equipment maintenance. However, developing low-cost solutions for their motion and…
Motion planning for articulated robots has traditionally been governed by algorithms that operate within manufacturer-defined payload limits. Our empirical analysis of the Franka Emika Panda robot demonstrates that this approach…
A common task in robotics is unloading identical goods from a tray with rectangular grid structure. This naturally leads to the idea of programming the process at one grid position only and translating the motion to the other grid points,…
The paper presents a novel modular hybrid parallel robot for pancreatic surgery and its higher-order kinematics derived based on various formalisms. The classical vector, homogeneous transformation matrices and dual quaternion approaches…
In this paper a new method for geometric robot calibration is introduced, which uses a calibration plate with precisely known distances between its measuring points. The relative measurement between two points on the calibration plate is…
We study the role of symmetries in control systems through the geometric algebra approach. We discuss two specific control problems on Carnot groups of step $2$ invariant with respect to the action of $SO(3)$. We understand the geodesics as…
We present a general and modular algorithmic framework for path planning of robots. Our framework combines geometric methods for exact and complete analysis of low-dimensional configuration spaces, together with practical, considerably…
This paper concerns models and convergence principles for dealing with stochasticity in a wide range of algorithms arising in nonlinear analysis and optimization in Hilbert spaces. It proposes a flexible geometric framework within which…
In this paper, we evaluate a semi-autonomous brain-computer interface (BCI) for manipulation tasks. In such system, the user controls a robotic arm through motor imagery commands. In traditional process-control BCI systems, the user has to…
The art of quantum algorithm design is highly nontrivial. Grover's search algorithm constitutes a masterpiece of quantum computational software. In this article, we use methods of geometric algebra (GA) and information geometry (IG) to…
The applications of geometric control theory methods on Lie groups and homogeneous spaces to the theory of quantum computations are investigated. These methods are shown to be very useful for the problem of constructing an universal set of…
Complex manipulation tasks can contain various execution branches of primitive skills in sequence or in parallel under different scenarios. Manual specifications of such branching conditions and associated skill parameters are not only…
This survey explores the geometric perspective on policy optimization within the realm of feedback control systems, emphasizing the intrinsic relationship between control design and optimization. By adopting a geometric viewpoint, we aim to…
In this paper we present a framework to learn skills from human demonstrations in the form of geometric nullspaces, which can be executed using a robot. We collect data of human demonstrations, fit geometric nullspaces to them, and also…
Ergodic control synthesizes optimal coverage behaviors over spatial distributions for nonlinear systems. However, existing formulations model the robot as a non-volumetric point, whereas in practice a robot interacts with the environment…
Efficient motion planning algorithms are of central importance for deploying robots in the real world. Unfortunately, these algorithms often drastically reduce the dimensionality of the problem for the sake of feasibility, thereby foregoing…
The Geometric Algebra Transformer (GATr) is a versatile architecture for geometric deep learning based on projective geometric algebra. We generalize this architecture into a blueprint that allows one to construct a scalable transformer…
Optimal control in general, and flatness-based control in particular, of robotic arms necessitate to compute the first and second time derivatives of the joint torques/forces required to achieve a desired motion. In view of the required…