Related papers: A Riemannian Metric for Geometry-Aware Singularity…
Shape analysis and compuational anatomy both make use of sophisticated tools from infinite-dimensional differential manifolds and Riemannian geometry on spaces of functions. While comprehensive references for the mathematical foundations…
We report on some advances made in the problem of singularities in general relativity. First is introduced the singular semi-Riemannian geometry for metrics which can change their signature (in particular be degenerate). The standard…
Limbless organisms of all sizes use undulating patterns of self-deformation to locomote. Geometric mechanics, which maps deformations to motions, provides a powerful framework to formalize and investigate the theoretical properties and…
We introduce the Riemannian Motion Policy (RMP), a new mathematical object for modular motion generation. An RMP is a second-order dynamical system (acceleration field or motion policy) coupled with a corresponding Riemannian metric. The…
Robots are moving towards applications in less structured environments, but their model-based controllers are challenged by the tasks' complexity and intrinsic environmental unpredictability. Studying biological motor control can provide…
The techniques and analysis presented in this thesis provide new methods to solve optimization problems posed on Riemannian manifolds. These methods are applied to the subspace tracking problem found in adaptive signal processing and…
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…
Two-dimensional multilinked structures can benefit aerial robots in both maneuvering and manipulation because of their deformation ability. However, certain types of singular forms must be avoided during deformation. Hence, an additional 1…
One of the most challenging issues in adaptive control of robot manipulators with kinematic uncertainties is requirement of the inverse of Jacobian matrix in regressor form. This requirement is inevitable in the case of the control of…
Assembly of large scale structural systems in space is understood as critical to serving applications that cannot be deployed from a single launch. Recent literature proposes the use of discrete modular structures for in-space assembly and…
Real-time control is an essential aspect of safe robot operation in the real world with dynamic objects. We present a framework for the analysis of object-aware controllers, methods for altering a robot's motion to anticipate and avoid…
In this paper, we introduce a novel approach to implicitly encode precise robot morphology using forward kinematics based on a configuration space signed distance function. Our proposed Robot Neural Distance Function (RNDF) optimizes the…
In this paper, we study Riemannian zeroth-order optimization in settings where the underlying Riemannian metric $g$ is geodesically incomplete, and the goal is to approximate stationary points with respect to this incomplete metric. To…
In many robotics applications, it is necessary to compute not only the distance between the robot and the environment, but also its derivative - for example, when using control barrier functions. However, since the traditional Euclidean…
When robot manipulators decide how to reach for an object, hand it over, or obey some task constraint, they implicitly assume a Euclidean distance metric in their configuration space. Their notion of what makes a configuration closer or…
In narrow spaces, motion planning based on the traditional hierarchical autonomous system could cause collisions due to mapping, localization, and control noises, especially for car-like Ackermann-steering robots which suffer from…
Robust and flexible leader-following is a critical capability for robots to integrate into human society. While existing methods struggle to generalize to leaders of arbitrary form and often fail when the leader temporarily leaves the…
The ability to deal with articulated objects is very important for robots assisting humans. In this work, a framework to robustly and adaptively operate common doors, using an autonomous mobile manipulator, is proposed. To push forward the…
In the future, extraterrestrial expeditions will not only be conducted by rovers but also by flying robots. The technical demonstration drone Ingenuity, that just landed on Mars, will mark the beginning of a new era of exploration…
In robotic navigation, maintaining precise pose estimation and navigation in complex and dynamic environments is crucial. However, environmental challenges such as smoke, tunnels, and adverse weather can significantly degrade the…