Nina Mahmoudian

Approximate Analytical Turning Conditions for Underwater Gliders: Implications for Motion Control and Path Planning

This paper describes analysis of steady motions for underwater gliders, a type of highly efficient underwater vehicle which uses gravity for propulsion. Underwater gliders are winged underwater vehicles which locomote by modulating their buoyancy and their attitude. Several underwater gliders have been developed and have proven their worth as efficient long-distance, long-duration ocean sampling platforms. Underwater gliders are so efficient because they spend much of their flight time in stable, steady motion. Wings-level gliding flight for underwater gliders has been well studied, but analysis of steady turning flight is more subtle. This paper presents an approximate analytical expression for steady turning motion for a realistic underwater glider model. The problem is formulated in terms of regular perturbation theory, with the vehicle turn rate as the perturbation parameter. The resulting solution exhibits a special structure that suggests an efficient approach to motion control as well as a planning strategy for energy efficient paths.

Underwater glider motion control

This paper describes an underwater glider motion control system intended to enhance locomotive efficiency by reducing the energy expended by vehicle guidance. In previous work, the authors derived an approximate analytical expression for steady turning motion by applying regular perturbation theory to a realistic vehicle model. The analysis results suggested the use of a well-known time-optimal path planning procedure developed for the Dubins car, an often-used model of a wheeled mobile robot. For underwater gliders operating at their most efficient flight condition, time-optimal glide paths correspond to energy-optimal glide paths. Thus, an analytically informed strategy for energy-efficient locomotion is to generate sequences of steady wings-level and turning motions according to the Dubins path planning procedure. Because the turning motion results are only approximate, however, and to compensate for model and environmental uncertainty, one must incorporate feedback to ensure convergent path following. This paper describes the dynamic modelling of the complete multi-body control system and the development and numerical implementation of a motion control system. The control system can be combined with a higher level guidance strategy involving Dubins-like paths to achieve energy-efficient locomotion.

Ankle Angles During Step Turn and Straight Walk: Implications for the Design of a Steerable Ankle-Foot Prosthetic Robot

This article compares the three-dimensional angles of the ankle during step turn and straight walking. We used an infrared camera system (Qualisys Oqus ®) to track the trajectories and angles of the foot and leg at different stages of the gait. The range of motion (ROM) of the ankle during stance periods was estimated for both straight step and step turn. The duration of combined phases of heel strike and loading response, mid stance, and terminal stance and pre-swing were determined and used to measure the average angles at each combined phase. The ROM in Inversion/Eversion (IE) increased during turning while Medial/Lateral (ML) rotation decreased and Dorsiflexion/Plantarflexion (DP) changed the least. During the turning step, ankle displacement in DP started with similar angles to straight walk (−9.68° of dorsiflexion) and progressively showed less plantarflexion (1.37° at toe off). In IE, the ankle showed increased inversion leaning the body toward the inside of the turn (angles from 5.90° to 13.61°). ML rotation initiated with an increased medial rotation of 5.68° relative to the straight walk transitioning to 12.06° of increased lateral rotation at the toe off. A novel tendon driven transtibial ankle-foot prosthetic robot with active controls in DP and IE directions was fabricated. It is shown that the robot was capable of mimicking the recorded angles of the human ankle in both straight walk and step turn.Copyright

Low cost underwater gliders for littoral marine research

Current off-the-shelf underwater gliders (UGs) are large, heavy, expensive, and difficult to modify, both in hardware and software, which limits their use for multivehicle coordination experiments and deployment in high risk environments. To address these challenges, the Nonlinear and Autonomous Systems Laboratory (NAS Lab) at Michigan Tech has designed two types of UGs for concept development, testing, and problem solving, and additionally, for scaffolding advanced interest and education in engineering. The first, a Glider for Underwater Presentation and Promoting Interest in Engineering (GUPPIE), nationally targets high school students and undergraduates to provide these students a UG platform for hands-on experience in concept development, testing, and problem solving. The second platform is a Glider for Autonomous Littoral Underwater Research (GALUR). At 10% of the cost of current models, the GALUR was designed to serve as a low cost multivehicle control testbed for disparate research groups who need to test and validate control algorithms. Still a highly-maneuverable UG, the GALUR allows researchers to address underwater communication issues by implementing control strategies for individual and multiple vehicle underwater data collection and mapping. Through the process of developing and testing these two UGs, the research team is ultimately working toward their long term goal of developing a fleet of low cost highly maneuverable underwater gliders. This paper details the challenges and milestones of the development process, and outlines the future research trajectory and goals.

Effects of Nonlinearities on the Steady State Dynamic Behavior of Electric Actuated Microcantilever-based Resonators

This paper presents the dynamic behavior of microcantilever-based microresonators and compares their steady state behavior for polarized and nonpolarized systems at different levels of nonlinearities. A microcantilever, equipped with a time-varying capacitor, makes the microresonator system. The capacitor is activated by a constant polarization voltage, and an alternative actuating voltage. The partial differential equation of motion of the vibrating electrode can be reduced to a highly nonlinear parametric second order ordinary differential equation. The steady state behavior of the microresonator has been analyzed with and without polarization voltage. The main characteristic of the non-polarized model is explained by the stability of the system in parameter plane. A set of stability chart is provided to predict the boundary between the stable and unstable domains. Furthermore, the main characteristic of the polarized model is determination by the period-amplitude relationship of the system. Applying perturbation methods, analytical equations are derived to describe the frequency response of the system, which are suitable to be utilized in parameter study and design.

Steady Turns and Optimal Paths for Underwater Gliders

This paper describes analysis of steady turning motions for a new type of highly efficient underwater vehicle which uses gravity for propulsio n. Underwater gliders are winged underwater vehicles which locomote by modulating their buoyancy and their attitude. Several such vehicles have been developed and have already proven their worth as long-endurance ocean sampling platforms. The ultimate aim of our research is to develop optimal motion control strategies which further enhance the natural efficiency of these vehicles by minimizing the energy expended by the control system. First and foremost, the predominant vehicle motions should be stable, steady motions requiring little or no additional control effort. Moreover, these motions should be blended in a way that minimizes control effort. The primary contribution of this paper is an approximate analytical expression for steady turning motion obtained via regular perturbation analysis of a general and realistic vehicle model. The solution suggests a well-known time-optimal path planning procedure developed for a general type of nonholonomic mobile robot known as Dubins car. Assuming quasi-steady glider motions, time-optimality of Dubins paths corresponds to energy-optimality of underwater glider paths.

MATHEMATICAL MODELING OF THERMAL EFFECTS IN STEADY STATE DYNAMICS OF MICRORESONATORS USING LORENTZIAN FUNCTION: PART 2 - TEMPERATURE RELAXATION

Thermal phenomena have two distinct effects, which are called, in this report, “thermal damping” and “temperature relaxation”. In this second part of a two-part report we (only) model and investigate the temperature relaxation and its effects on microresonator dynamics. A reduced order mathematical model of the system is introduced as a mass-spring-damper system actuated by a linearized electrostatic force. Temperature relaxation is the thermal stiffness softening and is modeled as a decrease in stiffness rate, utilizing a Lorentzian function of excitation frequency. The steady state frequency-amplitude dependency of the system will be derived utilizing averaging perturbation method. Analytic equation describing the frequency response of the system near resonance which can be utilized to explain the dynamics of the system, as well as design of involved dynamic parameters is developed.Copyright

Highly Maneuverable Low-Cost Underwater Glider: Design and Development

This letter presents the design and potential impact of the developed Research Oriented Underwater Glider for Hands-on Investigative Engineering (ROUGHIE). The ROUGHIE is an open-source, highly maneuverable, and low-cost vehicle that enables rapid development and testing of new hardware and software. ROUGHIE is an internally actuated glider capable of performing steady sawtooth glides in shallow water down to 3 m, tight turns with a minimum radius of 3 m, and a minimum endurance of 60 h. The novelty of this study is twofold: 1) a rail-based design to facilitate modularity and ease of assembly and 2) an effective internal rotary mass mechanism to increase maneuverability and perform tight turns. The ROUGHIE design strategically uses 3D printed plastic parts in low stress situations, which allows extreme design flexibility and enables tightly packed modules that can be easily customized.

A multi-level motion controller for low-cost Underwater Gliders

An underwater glider named ROUGHIE (Research Oriented Underwater Glider for Hands-on Investigative Engineering) is designed and manufactured to provide a test platform and framework for experimental underwater automation. This paper presents an efficient multi-level motion controller that can be used to enhance underwater glider control systems or easily modified for additional sensing, computing, or other requirements for advanced automation design testing. The ultimate goal is to have a fleet of modular and inexpensive test platforms for addressing the issues that currently limit the use of autonomous underwater vehicles (AUVs). Producing a low-cost vehicle with maneuvering capabilities and a straightforward expansion path will permit easy experimentation and testing of different approaches to improve underwater automation.

GUPPIE, underwater 3D printed robot a game changer in control design education

This paper presents innovative strategies to teach control and robotic concepts. These strategies include: 1) a real world focus on social/environmental contexts that are meaningful and “make a difference”; 2) continuous design potential and engagement through use of a platform that integrates design with engineering; 3) mission-based versus application-based approaches, where meaningful application justifies the process; and 4) hands-on, inquiry-based problem-solving. For this purpose a Glider for Underwater Problem-solving and Promotion of Interest in Engineering or “GUPPIE” platform and its simulator were utilized. GUPPIE is easy and inexpensive to manufacture, with readily available lightweight and durable components. It is also modular to accommodate a variety of learning activities. This paper describes how GUPPIE and its interdisciplinary nature was used as a pedagogical platform for teaching core control concepts for different age groups. The activities are designed to attract the interest of students as early as middle school and sustain their interest through college. The game changing aspect of this approach is scaffolded learning and the fact that the students will work with the same platform while progressing through the concepts.