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We study projection-free methods for constrained Riemannian optimization. In particular, we propose the Riemannian Frank-Wolfe (RFW) method. We analyze non-asymptotic convergence rates of RFW to an optimum for (geodesically) convex…
An adaptation of Response Surface Methodology (RSM) when the covariate is of high or infinite dimensional is proposed, providing a tool for black-box optimization in this context. We combine dimension reduction techniques with classical…
Modular Self-Reconfigurable Robot (MSRR) systems are a class of robots capable of forming higher-level robotic systems by altering the topological relationships between modules, offering enhanced adaptability and robustness in various…
In this paper, we address the problem of real-time motion planning for multiple robotic manipulators that operate in close proximity. We build upon the concept of dynamic fabrics and extend them to multi-robot systems, referred to as…
In this paper, we investigate decentralized non-convex optimization with orthogonal constraints. Conventional algorithms for this setting require either manifold retractions or other types of projection to ensure feasibility, both of which…
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…
In this work, the problem of 4 degree-of-freedom (3D position and heading) robot-to-robot relative frame transformation estimation using onboard odometry and inter-robot distance measurements is studied. Firstly, we present a theoretical…
We study two fundamental problems in computational geometry: finding the maximum inscribed ball (MaxIB) inside a bounded polyhedron defined by $m$ hyperplanes, and the minimum enclosing ball (MinEB) of a set of $n$ points, both in…
This paper addresses an interval analysis based study that is applied to the design and the comparison of 3-DOF parallel kinematic machines. Two design criteria are used, (i) a regular workspace shape and, (ii) a kinetostatic performance…
Understanding atomic structures is crucial, yet amorphous materials remain challenging due to their irregular and non-periodic nature. The Wavelet Transform Radial Distribution Function (WT-RDF) offers a physics-based framework for…
In Redirected Walking (RDW), resets are an overt method that explicitly interrupts users, and they should be avoided to provide a quality user experience. The number of resets depends on the configuration of the physical environment; thus,…
Compacting orthogonal drawings is a challenging task. Usually algorithms try to compute drawings with small area or edge length while preserving the underlying orthogonal shape. We present a one-dimensional compaction algorithm that alters…
The subject of this paper is the optimal design of a parallel mechanism intended for three-axis machining applications. Parallel mechanisms are interesting alternative designs in this context but most of them are designed for three- or…
Real time calculation of inverse kinematics (IK) with dynamically stable configuration is of high necessity in humanoid robots as they are highly susceptible to lose balance. This paper proposes a methodology to generate joint-space…
The polyhedral model allows a structured way of defining semantics-preserving transformations to improve the performance of a large class of loops. Finding profitable points in this space is a hard problem which is usually approached by…
As the pace of AI technology continues to accelerate, more tools have become available to researchers to solve longstanding problems, Hybrid approaches available today continue to push the computational limits of efficiency and precision.…
We consider discretized two-dimensional PDE-constrained shape optimization problems, in which shapes are represented by triangular meshes. Given the connectivity, the space of admissible vertex positions was recently identified to be a…
Intelligent robots must be able to perform safe and efficient motion planning in their environments. Central to modern motion planning is the configuration space. Configuration spaces define the set of configurations of a robot that result…
The paper addresses a problem of constrained spacecraft attitude stabilization with simultaneous reaction wheel (RW) desaturation. The spacecraft has a reaction wheel array (RWA) consisting of four RWs in a pyramidal configuration. The…
Optimization with orthogonality constraints frequently arises in various fields such as machine learning. Riemannian optimization offers a powerful framework for solving these problems by equipping the constraint set with a Riemannian…