Related papers: Singularity Distance Computations for 3-RPR Manipu…

Continuum parallel robots (CPR) combine rigid actuation mechanisms with multiple elastic rods in a closed-loop topology, making forward statics challenging when rigid--continuum junctions are enforced by explicit kinematic constraints. Such…

The radius of regularity sometimes spelled as the radius of nonsingularity is a measure providing the distance of a given matrix to the nearest singular one. Despite its possible application strength this measure is still far from being…

This paper proposes a redundancy resolution algorithm for a redundant manipulator based on dynamic programming. This algorithm can compute the desired joint angles at each point on a pre-planned discrete path in Cartesian space, while…

Generically, a fully measured elasticity tensor has no material symmetry. For single crystals with a cubic lattice, or for the aeronautics turbine blades superalloys such as Nickelbased CMSX-4, cubic symmetry is nevertheless expected. It is…

Realizing relative localization by leveraging inter-robot local measurements is a challenging problem, especially in the presence of measurement noise. Motivated by this challenge, in this paper we propose a novel and systematic 3-D…

This paper presents a new distance geometry algorithm for calculating atomic coordinates from estimates of the interatomic distances, which maintains the positions of the atoms in a known rigid substructure. Given an $M \times 3$ matrix of…

Cutting plane methods, particularly outer approximation, are a well-established approach for solving nonlinear discrete optimization problems without relaxing the integrality of decision variables. While powerful in theory, their…

This paper investigates the singular curves in two-dimensional slices of the joint space of a family of planar parallel manipulators. It focuses on special points, referred to as cusp points, which may appear on these curves. Cusp points…

This paper addresses the real structured controllability, stabilizability, and stability radii (RSCR, RSSZR, and RSSR, respectively) of linear systems, which involve determining the distance (in terms of matrix norms) between a (possibly…

We consider a class of (possibly strongly) geodesically convex optimization problems on Hadamard manifolds, where the objective function splits into the sum of a smooth and a possibly nonsmooth function. We introduce an intrinsic convex…

Parallel robots (PRs) are closed-chain manipulators with diverse applications due to their accuracy and high payload. However, there are configurations within the workspace named Type II singularities where the PRs lose control of the…

This paper develops a robust angles-only IROD method based on polynomial optimization for arbitrary nonlinear dynamics. First, the relative motion is approximated by high-order Taylor polynomials within the differential algebra framework,…

An isogeometric boundary element method for problems in elasticity is presented, which is based on an independent approximation for the geometry, traction and displacement field. This enables a flexible choice of refinement strategies,…

Optimal Morse matchings reveal essential structures of cell complexes which lead to powerful tools to study discrete geometrical objects, in particular discrete 3-manifolds. However, such matchings are known to be NP-hard to compute on…

Parallel robots (PRs) have singular configurations where the robot gains at least one degree of freedom and loses control. Theoretically, such singularity occurs when the Forward Jacobian-matrix determinant becomes zero (Type II). However,…

We develop theory for nonlinear dimensionality reduction (NLDR). A number of NLDR methods have been developed, but there is limited understanding of how these methods work and the relationships between them. There is limited basis for using…

This paper proposes a novel geometric method for analytically determining the base inertial parameters of robotic systems. The rigid body dynamics is reformulated using projective geometric algebra, leading to a new identification model…

Minimum distance constraints (minDCs) appear in many geometric optimization problems. They pose major challenges for mixed-integer nonlinear programming (MINLP) due to their reverse-convexity. We develop new algorithms for tightening…

As we move to increasingly complex cyber-physical systems (CPS), new approaches are needed to plan efficient state trajectories in real-time. In this paper, we propose an approach to significantly reduce the complexity of solving optimal…

Data-sensitive metrics adapt distances locally based the density of data points with the goal of aligning distances and some notion of similarity. In this paper, we give the first exact algorithm for computing a data-sensitive metric called…