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We present a novel, automatic eye gaze tracking scheme inspired by smooth pursuit eye motion while playing mobile games or watching virtual reality contents. Our algorithm continuously calibrates an eye tracking system for a head mounted…

This paper presents an algorithmic framework for the minimization of strictly convex quadratic functions. The framework is flexible and generic. At every iteration the search direction is a linear combination of the negative gradient, as…

The realization space of geometric constraint systems is given by the vanishing locus of polynomials corresponding to natural geometric constraints. Such geometric constraint systems arise in many real-world scenarios such as structural…

In motion planning problems for autonomous robots, such as self-driving cars, the robot must ensure that its planned path is not in close proximity to obstacles in the environment. However, the problem of evaluating the proximity is…

In this paper, we address the problem of stabilizing a system around a desired manifold determined by virtual nonlinear nonholonomic constraints. Virtual constraints are relationships imposed on a control system that are rendered invariant…

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 addition to the theoretical value of challenging optimal control problmes, recent progress in autonomous vehicles mandates further research in optimal motion planning for wheeled vehicles. Since current numerical optimal control…

Augmented reality (AR) games, particularly those designed for head-mounted displays, have grown increasingly prevalent. However, most existing systems depend on pre-scanned, static environments and rely heavily on continuous tracking or…

We consider the optimal control problem for null curves in de Sitter 3-space defined by a functional which is linear in the curvature of the trajectory. We show how techniques based on the method of moving frames and exterior differential…

Nonlinear PID control systems for a quadrotor UAV are proposed to follow an attitude tracking command and a position tracking command. The control systems are developed directly on the special Euclidean group to avoid singularities of…

Higher-order gravity models have been recently the subject of much attention in the context of cosmic acceleration. These models are derived by adding various curvature invariants to the Einstein-Hilbert action. Several studies showed that…

We propose a goal-oriented mesh-adaptive algorithm for a finite element method stabilized via residual minimization on dual discontinuous-Galerkin norms. By solving a saddle-point problem, this residual minimization delivers a stable…

In this paper we study the problem of driving an agent to an unknown source whose location is estimated in real-time by a recursive optimization algorithm. The optimization criterion is subject to a least-square cost function constructed…

Suppose that there is a ground set which consists of a large number of vectors in a Hilbert space. Consider the problem of selecting a subset of the ground set such that the projection of a vector of interest onto the subspace spanned by…

In the application of computer-vision based displacement measurement, an optical target is usually required to prove the reference. In the case that the optical target cannot be attached to the measuring objective, edge detection, feature…

This paper presents a unified Least-Squares framework for solving nonlinear partial differential equations by recasting the governing system as a residual minimisation problem. A Least-Squares functional is formulated and the corresponding…

We consider a swarm of $n$ robots in \mathbb{R}^d. The robots are oblivious, disoriented (no common coordinate system/compass), and have limited visibility (observe other robots up to a constant distance). The basic formation task gathering…

A safety-critical measure of legged locomotion performance is a robot's ability to track its desired time-varying position trajectory in an environment, which is herein termed as "global-position tracking". This paper introduces a nonlinear…

In this paper, we introduce a novel method to capture visual trajectories for navigating an indoor robot in dynamic settings using streaming image data. First, an image processing pipeline is proposed to accurately segment trajectories from…

Collaborative robots should ideally use low torque actuators for passive safety reasons. However, some applications require these collaborative robots to reach deep into confined spaces while assisting a human operator in physically…