Search

This paper presents a geometric control system for a quadrotor unmanned aerial vehicle with decoupled attitude controls. In particular, the attitude control system on the special orthogonal group is decomposed into the reduced attitude controls for the total thrust direction evolving on the two-dimensional unit sphere, and for the remaining one-dimensional rotations about the thrust vector corresponding to the yawing motion. Consequently, the yaw dynamics are controlled separately from the roll and pitch dynamics that are critical for the stability of the translational dynamics of the quadrotor. As such, the proposed controller exhibits improved position tracking capabilities especially for large-angle yawing motions. These are constructed directly on the two-sphere and the one-sphere to avoid complexities and singularities associated with local coordinates. Furthermore, the control systems are augmented with integral terms to deal with fixed disturbances. The efficacy of the proposed method is illustrated by numerical simulation.

Two variations of the joint probabilistic data association filter (JPDAF) are derived and simulated in various cases in this paper. First, an analytic solution for an optimal gain that minimizes posterior estimate uncertainty is derived, referred to as the minimum uncertainty JPDAF (M-JPDAF). Second, the coalescence-avoiding JPDAF (C-JPDAF) is derived, which removes coalescence by minimizing a weighted sum of the posterior uncertainty and a measure of similarity between estimated probability densities. Both novel algorithms are tested in much further depth than any prior work to show how the algorithms perform in various scenarios. In particular, the M-JPDAF more accurately tracks objects than the conventional JPDAF in all simulated cases. When coalescence degrades the estimates at too great of a level, and the C-JPDAF is often superior at removing coalescence when its parameters are properly tuned.

This paper presents nonlinear observability criteria for the relative orbital dynamics represented by the solutions of the two-body problem. It is assumed that a chief is on a circular orbit with a prescribed orbital radius, and it measures lines-of-sight toward a deputy only. A differential geometric method, based on the Lie derivatives, is used to derive sufficient conditions for observability of the orbital properties of the deputy. It is shown that under certain geometric conditions on the relative configuration between the chief and the deputy, the nonlinear relative motion is observable from angles-only measurements. The second part of this paper presents a quantitative measure of observability for the relative orbits, and it is formulated by generalizing the observability Gramian of linear dynamic systems. An extended Kalman filter is also developed to numerically illustrate the observability of nonlinear relative orbits with angles-only measurements and to show correspondence between the proposed observability measure and filtered solution accuracy.

This paper deals with the aerial exploration for an unknown three-dimensional environment, where Bayesian probabilistic mapping is integrated with a stochastic motion planning scheme to minimize the map uncertainties in an optimal fashion. We utilize the popular occupancy grid mapping representation, with the goal of determining occupancy probabilities of evenly-spaced grid cells in 3D with sensor fusion from multiple depth sensors with realistic sensor capabilities. The 3D exploration problem is decomposed into 3D mapping and 2D motion planning for efficient real-time implementation. This is achieved by projecting important aspects of the 3D map onto 2D maps, where a predicted level of map uncertainty, known as Shannon's entropy, provides an exploration policy that governs robotic motion. Both mapping and exploration algorithms are demonstrated with both numerical simulations and quadrotor flight experiments.

Occupancy grid maps are spatial representations of environments, where the space of interest is decomposed into a number of cells that are considered either occupied or free. This paper focuses on occupancy grid mapping, which is to estimate the probability of occupancy for each cell based on range measurements from a known location. For a given probabilistic model of a range sensor, we propose a computationally efficient method to obtain an exact inverse sensor model, and it is utilized to construct a probabilistic mapping algorithm according to the Bayesian framework. Compared with the existing occupancy grid mapping techniques that rely on approximate, heuristic inverse sensor models, the proposed approach yields substantially more accurate maps for the same set of measurements. These are illustrated by numerical examples and experiments.

This paper presents a deterministic hybrid observer for the attitude dynamics of a rigid body that guarantees global asymptotical stability. Any smooth attitude observer suffers from the inherent topological restriction that it is impossible to achieve global attractivity. It is illustrated that such attitude observers may yield very slow initial convergence rates, and motivated by this, we propose a hybrid attitude observer that guarantees global asymptotic stability on the special orthogonal group. This is shown to exhibit substantially improved convergence rate uniformly via numerical examples.

This paper presents design and development of an experimental testbed for nonlinear geometric controls of a rigid body. We develop a fully actuated hexrotor UAV that uses six variable pitch propellers to control six degrees of freedom maneuvers, namely three position and three attitude variables, independently. In contrast to the popular quadrotor UAVs that can hover at a single attitude, the hexrotor presented in this paper is capable of hovering at any attitude provided that thrust is sufficiently large. A geometric controller is also developed on the special Euclidean group to track given desired position and attitude trajectories under the effects of unknown disturbances. These are particularly useful for ground tests for large angle rotational dynamics of spacecraft that are combined with arbitrary translational motions. A numerical example that involves a nontrivial maneuver and preliminary experimental tests are also presented.

This paper makes three innovative contributions to the field of human resource management. First, an HRM frequency distribution is presented that depicts the key empirical facts that form the center of research in the field; second, a new microeconomics-based model is presented that develops a new theoretical and empirical tool - the HRM demand function - and uses this tool to predict the performance maximizing level of HRM expenditure; and third, a unique data set is used to estimate the parameters of the HRM input demand function for several American hundred companies. A variety of new insights and implications emerge.