Related papers: Certifiable Alignment of GNSS and Local Frames via…
To provide backup and augmentation to global navigation satellite system (GNSS), Doppler shift from Low Earth Orbit (LEO) satellites can be employed as signals of opportunity (SOP) for position, navigation and timing (PNT). Since the…
In this paper we present the first fast optimality certifier for the non-minimal version of the Relative Pose problem for calibrated cameras from epipolar constraints. The proposed certifier is based on Lagrangian duality and relies on a…
We present a certifiably globally optimal algorithm for determining the extrinsic calibration between two sensors that are capable of producing independent egomotion estimates. This problem has been previously solved using a variety of…
Sensor calibration is crucial for autonomous driving, providing the basis for accurate localization and consistent data fusion. Enabling the use of high-accuracy GNSS sensors, this work focuses on the antenna lever arm calibration. We…
State-of-the-art techniques for simultaneous localization and mapping (SLAM) employ iterative nonlinear optimization methods to compute an estimate for robot poses. While these techniques often work well in practice, they do not provide…
Mutual localization is essential for coordination and cooperation in multi-robot systems. Previous works have tackled this problem by assuming available correspondences between measurements and received odometry estimations, which are…
A common approach to localize a mobile robot is by measuring distances to points of known positions, called anchors. Locating a device from distance measurements is typically posed as a non-convex optimization problem, stemming from the…
This work contributes an efficient algorithm to compute the Relative Pose problem (RPp) between calibrated cameras and certify the optimality of the solution, given a set of pair-wise feature correspondences affected by noise and probably…
We present novel, convex relaxations for rotation and pose estimation problems that can a posteriori guarantee global optimality for practical measurement noise levels. Some such relaxations exist in the literature for specific problem…
We introduce a novel approach addressing global analysis of a difficult class of nonconvex-nonsmooth optimization problems within the important framework of Lagrangian-based methods. This genuine nonlinear class captures many problems in…
A recent set of techniques in the robotics community, known as certifiably correct methods, frames robotics problems as polynomial optimization problems (POPs) and applies convex, semidefinite programming (SDP) relaxations to either find or…
Global navigation satellite system (GNSS) positioning is widely used for urban navigation, but the covariance reported by the GNSS solver is often unreliable in urban canyons. Existing differentiable factor graph optimization (DFGO) methods…
In this paper, the trajectory planning problem for autonomous rendezvous and docking between a controlled spacecraft and a tumbling target is addressed. The use of a variable planning horizon is proposed in order to construct an appropriate…
In this paper we explore the role of duality principles within the problem of rotation averaging, a fundamental task in a wide range of computer vision applications. In its conventional form, rotation averaging is stated as a minimization…
We propose the first general and practical framework to design certifiable algorithms for robust geometric perception in the presence of a large amount of outliers. We investigate the use of a truncated least squares (TLS) cost function,…
This paper investigates the problem of certifying optimality for sparse generalized linear models (GLMs), where sparsity is enforced through an $\ell_0$ cardinality constraint. While branch-and-bound (BnB) frameworks can certify optimality…
This paper proposes a new algorithm that solves non-convex optimal control problems with a theoretical guarantee for global convergence to a feasible local solution of the original problem. The proposed algorithm extends the recently…
For reliable operation on urban roads, navigation using the Global Navigation Satellite System (GNSS) requires both accurately estimating the positioning detail from GNSS pseudorange measurements and determining when the estimated position…
We investigate the problem of certifying optimality for sparse generalized linear models (GLMs), where sparsity is enforced through a cardinality constraint. While Branch-and-Bound (BnB) frameworks can certify optimality using perspective…
The Knapsack Problem is a classic problem in combinatorial optimisation. Solving these problems may be computationally expensive. Recent years have seen a growing interest in the use of deep learning methods to approximate the solutions to…