Related papers: Globally Asymptotically Stable Trajectory Tracking…
Self-consistent chaotic transport is studied in a Hamiltonian mean-field model. The model provides a simplified description of transport in marginally stable systems including vorticity mixing in strong shear flows and electron dynamics in…
This paper explores the application of geometric algebra to Galilean spacetime and its physical implications. We introduce the Galilean Spacetime Algebra (GSTA), a five-dimensional conformal geometric algebra (CGA) generated by a specific…
All practical systems often pose a problem of finite control capability, which can notably degrade the performance if not properly addressed. Since actuator input bounds are typically known, integrating actuator saturation considerations…
In this paper we address the control problem of aerial cable suspended load transportation, using multiple Unmanned Aerial Vehicles (UAVs). First, the dynamical model of the coupled system is obtained using the Newton-Euler formalism, for…
This paper addresses the motion control problem for underactuated mechanical systems with full attitude control and one translational force input to manage the six degrees of freedom involved in the three-dimensional Euclidean space. These…
These lectures demonstrate the development of a PID control framework for mechanical systems. Based on the observation that mechanical systems are essentially double integrator systems, we generalize the linear PID controller to mechanical…
Unmanned aerial vehicle (UAV) use continues to increase, including operating beyond line of sight in unknown environments where the vehicle must autonomously generate a trajectory to safely navigate. In this article, we develop a trajectory…
Problems involving geometric data arise in physics, chemistry, robotics, computer vision, and many other fields. Such data can take numerous forms, for instance points, direction vectors, translations, or rotations, but to date there is no…
We present a closed-loop control strategy for a delta-wing unmanned aerial aquatic-vehicle (UAAV) that enables autonomous swim, fly, and water-to-air transition. Our control system consists of a hybrid state estimator and a closed-loop…
Motion control of underwater robotic vehicles is a demanding task with great challenges imposed by external disturbances, model uncertainties and constraints of the operating workspace. Thus, robust motion control is still an open issue for…
We design a reduced attitude controller for reorienting the spin axis of a gyroscope in a geometric control framework. The proposed controller preserves the inherent gyroscopic stability associated with a spinning axis-symmetric rigid body.…
In this paper, we present a series of techniques to describe General Relativity using Geometric Algebra (GA). We emphasize the physical interpretation of quantities and provide a step-by-step guide for performing calculations. In doing so,…
In this paper, we consider a geometric formalism for optimal control of underactuated mechanical systems. Our techniques are an adaptation of the classical Skinner and Rusk approach for the case of Lagrangian dynamics with higher-order…
This paper presents an approach to trajectory-centric learning control based on contraction metrics and disturbance estimation for nonlinear systems subject to matched uncertainties. The approach uses deep neural networks to learn uncertain…
This work employs an unmanned aerial vehicle (UAV) as a jammer to aid a covert communication from a transmitter Alice to a receiver Bob, where the UAV transmits artificial noise (AN) with random power to deliberately create interference to…
Systems like aircraft and spacecraft are expensive to operate in the real world. The design, validation, and testing for such systems therefore relies on a combination of mathematical modeling, abundant numerical simulations, and a…
The gentlest ascent dynamics (GAD) (Nonlinearity, vol. 24, no. 6, p1831, 2011) is a continuous time dynamics coupling both the position and the direction variables to efficiently locate the saddle point with a given index. These saddle…
In this paper, we consider the problem of using a robot to explore an environment with an unknown, state-dependent disturbance function while avoiding some forbidden areas. The goal of the robot is to safely collect observations of the…
This paper presents the development of a real time tracking algorithm that runs on a 1.2 GHz PC/104 computer on-board a small UAV. The algorithm uses zero mean normalized cross correlation to detect and locate an object in the image. A…
Geometric integration of non-autonomous classical engineering problems, such as rotor dynamics, is investigated. It is shown, both numerically and by backward error analysis, that geometric (structure preserving) integration algorithms are…