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For plane frameworks with reflection or rotational symmetries, where the group action is not necessarily free on the vertex set, we introduce a phase-symmetric orbit rigidity matrix for each irreducible representation of the group. We then…
Rigidity of the interaction graph is a fundamental condition for achieving the desired formation which can be defined in terms of distance or bearing constraints between agents. In this paper, for reaching a unique formation with the same…
In this article, we analyse a stabilised equal-order finite element approximation for the Stokes equations on anisotropic meshes. In particular, we allow arbitrary anisotropies in a sub-domain, for example along the boundary of the domain,…
This paper studies 3-D distributed network localization using mixed types of local relative measurements. Each node holds a local coordinate frame without a common orientation and can only measure one type of information (relative position,…
We introduce a notion of algorithmic stability of learning algorithms---that we term \emph{argument stability}---that captures stability of the hypothesis output by the learning algorithm in the normed space of functions from which…
Algorithmic stability is a key characteristic to ensure the generalization ability of a learning algorithm. Among different notions of stability, \emph{uniform stability} is arguably the most popular one, which yields exponential…
We introduce a weak asymptotic version of nonlinear contraction, termed \emph{asymptotic pointwise contraction}. For a mapping on a metric space, this notion requires the existence of a sequence of functions that dominate the distances…
Robots often have to deal with the challenges of operating in dynamic and sometimes unpredictable environments. Although an occupancy map of the environment is sufficient for navigation of a mobile robot or manipulation tasks with a robotic…
This paper proposes a unified approach for dynamic modeling and simulations of general tensegrity structures with rigid bars and rigid bodies of arbitrary shapes. The natural coordinates are adopted as a non-minimal description in terms of…
Extrinsic manipulation, a technique that enables robots to leverage extrinsic resources for object manipulation, presents practical yet challenging scenarios. Particularly in the context of extrinsic manipulation on a supporting plane,…
Rigid body localization refers to a problem of estimating the position of a rigid body along with its orientation using anchors. We consider a setup in which a few sensors are mounted on a rigid body. The absolute position of the rigid body…
A linearly constrained framework in $\mathbb{R}^d$ is a point configuration together with a system of constraints which fixes the distances between some pairs of points and additionally restricts some of the points to lie in given affine…
Real-world object manipulation has been commonly challenged by physical uncertainties and perception limitations. Being an effective strategy, while caging configuration-based manipulation frameworks have successfully provided robust…
Global mobile robot localization is the problem of determining a robot's pose in an environment, using sensor data, when the starting position is unknown. A family of probabilistic algorithms known as Monte Carlo Localization (MCL) is…
This paper addresses the problem of bearing-based network localization, which aims to localize all the nodes in a static network given the locations of a subset of nodes termed anchors and inter-node bearings measured in a common reference…
Consider a set of autonomous computational entities, called \emph{robots}, operating inside a polygonal enclosure (possibly with holes), that have to perform some collaborative tasks. The boundary of the polygon obstructs both visibility…
We propose new symmetry-adapted rigidity matrices to analyze the infinitesimal rigidity of arbitrary-dimensional bar-joint frameworks with Abelian point group symmetries. These matrices define new symmetry-adapted rigidity matroids on…
We consider finite element approximations of ill-posed elliptic problems with conditional stability. The notion of {\emph{optimal error estimates}} is defined including both convergence with respect to mesh parameter and perturbations in…
We introduce a planner designed to guide robot manipulators in stably placing objects within intricate scenes. Our proposed method reverses the traditional approach to object placement: our planner selects contact points first and then…
In this paper, we develop new methods for the analysis of decentralized control systems and we apply them to formation control problems. The basic set-up consists of a system with multiple agents corresponding to the nodes of a graph whose…