In this thesis, we focus on some of the NP-hard problems in control theory. Thanks to the converse Lyapunov theory, these problems can often be modeled as optimization over polynomials. To avoid the problem of intractability, we establish a trade off between accuracy and complexity. In particular, we develop a sequence of tractable optimization problems - in the form of Linear Programs (LPs) and/or Semi-Definite Programs (SDPs) - whose solutions converge to the exact solution of the NP-hard problem. However, the computational and memory complexity of these LPs and SDPs grow exponentially with the progress of the sequence - meaning that improving the accuracy of the solutions requires solving SDPs with tens of thousands of decision variables and constraints. Setting up and solving such problems is a significant challenge. The existing optimization algorithms and software are only designed to use desktop computers or small cluster computers - machines which do not have sufficient memory for solving such large SDPs. Moreover, the speed-up of these algorithms does not scale beyond dozens of processors. This in fact is the reason we seek parallel algorithms for setting-up and solving large SDPs on large cluster- and/or super-computers.

We propose parallel algorithms for stability analysis of two classes of systems: 1) Linear systems with a large number of uncertain parameters; 2) Nonlinear systems defined by polynomial vector fields. First, we develop a distributed parallel algorithm which applies Polya's and/or Handelman's theorems to some variants of parameter-dependent Lyapunov inequalities with parameters defined over the standard simplex. The result is a sequence of SDPs which possess a block-diagonal structure. We then develop a parallel SDP solver which exploits this structure in order to map the computation, memory and communication to a distributed parallel environment. Numerical tests on a supercomputer demonstrate the ability of the algorithm to efficiently utilize hundreds and potentially thousands of processors, and analyze systems with 100+ dimensional state-space. Furthermore, we extend our algorithms to analyze robust stability over more complicated geometries such as hypercubes and arbitrary convex polytopes. Our algorithms can be readily extended to address a wide variety of problems in control such as Hinfinity synthesis for systems with parametric uncertainty and computing control Lyapunov functions.

The environmental impact of the fossil fuels has increased tremendously in the last decade. This impact is one of the most contributing factors of global warming. This research aims to reduce the amount of fuel consumed by vehicles through optimizing the control scheme for the future route information. Taking advantage of more degrees of freedom available within PHEV, HEV, and FCHEV “energy management” allows more margin to maximize efficiency in the propulsion systems. The application focuses on reducing the energy consumption in vehicles by acquiring information about the road grade. Road elevations are obtained by use of Geographic Information System (GIS) maps to optimize the controller. The optimization is then reflected on the powertrain of the vehicle.The approach uses a Model Predictive Control (MPC) algorithm that allows the energy management strategy to leverage road grade to prepare the vehicle for minimizing energy consumption during an uphill and potential energy harvesting during a downhill. The control algorithm will predict future energy/power requirements of the vehicle and optimize the performance by instructing the power split between the internal combustion engine (ICE) and the electric-drive system. Allowing for more efficient operation and higher performance of the PHEV, and HEV. Implementation of different strategies, such as MPC and Dynamic Programming (DP), is considered for optimizing energy management systems. These strategies are utilized to have a low processing time. This approach allows the optimization to be integrated with ADAS applications, using current technology for implementable real time applications.

The Thesis presents multiple control strategies designed, implemented, and tested using real-world road elevation data from three different routes. Initial simulation based results show significant energy savings. The savings range between 11.84% and 25.5% for both Rule Based (RB) and DP strategies on the real world tested routes. Future work will take advantage of vehicle connectivity and ADAS systems to utilize Vehicle to Vehicle (V2V), Vehicle to Infrastructure (V2I), traffic information, and sensor fusion to further optimize the PHEV and HEV toward more energy efficient operation.

Wearable robotics is a growing sector in the robotics industry, they can increase the productivity of workers and soldiers and can restore some of the lost function to people with disabilities. Wearable robots should be comfortable, easy to use, and intuitive. Robust control methods are needed for wearable robots that assist periodic motion.

This dissertation studies a phase based oscillator constructed with a second order dynamic system and a forcing function based on the phase angle of the system. This produces a bounded control signal that can alter the damping and stiffens properties of the dynamic system. It is shown analytically and experimentally that it is stable and robust. It can handle perturbations remarkably well. The forcing function uses the states of the system to produces stable oscillations. Also, this work shows the use of the phase based oscillator in wearable robots to assist periodic human motion focusing on assisting the hip motion. One of the main problems to assist periodic motion properly is to determine the frequency of the signal. The phase oscillator eliminates this problem because the signal always has the correct frequency. The input requires the position and velocity of the system. Additionally, the simplicity of the controller allows for simple implementation.

The interaction between humans and robots has become an important area of research as the diversity of robotic applications has grown. The cooperation of a human and robot to achieve a goal is an important area within the physical human-robot interaction (pHRI) field. The expansion of this field is toward moving robotics into applications in unstructured environments. When humans cooperate with each other, often there are leader and follower roles. These roles may change during the task. This creates a need for the robotic system to be able to exchange roles with the human during a cooperative task. The unstructured nature of the new applications in the field creates a need for robotic systems to be able to interact in six degrees of freedom (DOF). Moreover, in these unstructured environments, the robotic system will have incomplete information. This means that it will sometimes perform an incorrect action and control methods need to be able to correct for this. However, the most compelling applications for robotics are where they have capabilities that the human does not, which also creates the need for robotic systems to be able to correct human action when it detects an error. Activity in the brain precedes human action. Utilizing this activity in the brain can classify the type of interaction desired by the human. For this dissertation, the cooperation between humans and robots is improved in two main areas. First, the ability for electroencephalogram (EEG) to determine the desired cooperation role with a human is demonstrated with a correct classification rate of 65%. Second, a robotic controller is developed to allow the human and robot to cooperate in six DOF with asymmetric role exchange. This system allowed human-robot cooperation to perform a cooperative task at 100% correct rate. High, medium, and low levels of robotic automation are shown to affect performance, with the human making the greatest numbers of errors when the robotic system has a medium level of automation.

The presented work in this report is about Real time Estimation of wind and analyzing current wind correction algorithm in commercial off the shelf Autopilot board. The open source ArduPilot Mega 2.5 (APM 2.5) board manufactured by 3D Robotics is used. Currently there is lot of development being done in the field of Unmanned Aerial Systems (UAVs), various aerial platforms and corresponding; autonomous systems for them. This technology has advanced to such a stage that UAVs can be used for specific designed missions and deployed with reliability. But in some areas like missions requiring high maneuverability with greater efficiency is still under research area. This would help in increasing reliability and augmenting range of UAVs significantly. One of the problems addressed through this thesis work is, current autopilot systems have algorithm that handles wind by attitude correction with appropriate Crab angle. But the real time wind vector (direction) and its calculated velocity is based on geometrical and algebraic transformation between ground speed and air speed vectors. This method of wind estimation and prediction, many a times leads to inaccuracy in attitude correction. The same has been proved in the following report with simulation and actual field testing. In later part, new ways to tackle while flying windy conditions have been proposed.

Humans have an inherent capability of performing highly dexterous and skillful tasks with their arms, involving maintaining posture, movement and interacting with the environment. The latter requires for them to control the dynamic characteristics of the upper limb musculoskeletal system. Inertia, damping and stiffness, a measure of mechanical impedance, gives a strong representation of these characteristics. Many previous studies have shown that the arm posture is a dominant factor for determining the end point impedance in a horizontal plane (transverse plane). The objective of this thesis is to characterize end point impedance of the human arm in the three dimensional (3D) space. Moreover, it investigates and models the control of the arm impedance due to increasing levels of muscle co-contraction. The characterization is done through experimental trials where human subjects maintained arm posture, while perturbed by a robot arm. Moreover, the subjects were asked to control the level of their arm muscles' co-contraction, using visual feedback of their muscles' activation, in order to investigate the effect of the muscle co-contraction on the arm impedance. The results of this study showed a very interesting, anisotropic increase of the arm stiffness due to muscle co-contraction. This can lead to very useful conclusions about the arm biomechanics as well as many implications for human motor control and more specifically the control of arm impedance through muscle co-contraction. The study finds implications for the EMG-based control of robots that physically interact with humans.

A computational framework based on convex optimization is presented for stability analysis of systems described by Partial Differential Equations (PDEs). Specifically, two forms of linear PDEs with spatially distributed polynomial coefficients are considered.

The first class includes linear coupled PDEs with one spatial variable. Parabolic, elliptic or hyperbolic PDEs with Dirichlet, Neumann, Robin or mixed boundary conditions can be reformulated in order to be used by the framework. As an example, the reformulation is presented for systems governed by Schr¨odinger equation, parabolic type, relativistic heat conduction PDE and acoustic wave equation, hyperbolic types. The second form of PDEs of interest are scalar-valued with two spatial variables. An extra spatial variable allows consideration of problems such as local stability of fluid flows in channels and dynamics of population over two dimensional domains.

The approach does not involve discretization and is based on using Sum-of-Squares (SOS) polynomials and positive semi-definite matrices to parameterize operators which are positive on function spaces. Applying the parameterization to construct Lyapunov functionals with negative derivatives allows to express stability conditions as a set of LinearMatrix Inequalities (LMIs). The MATLAB package SOSTOOLS was used to construct the LMIs. The resultant LMIs then can be solved using existent Semi-Definite Programming (SDP) solvers such as SeDuMi or MOSEK. Moreover, the proposed approach allows to calculate bounds on the rate of decay of the solution norm.

The methodology is tested using several numerical examples and compared with the results obtained from simulation using standard methods of numerical discretization and analytic solutions.

Unmanned aerial vehicles have received increased attention in the last decade due to their versatility, as well as the availability of inexpensive sensors (e.g. GPS, IMU) for their navigation and control. Multirotor vehicles, specifically quadrotors, have formed a fast growing field in robotics, with the range of applications spanning from surveil- lance and reconnaissance to agriculture and large area mapping. Although in most applications single quadrotors are used, there is an increasing interest in architectures controlling multiple quadrotors executing a collaborative task. This thesis introduces a new concept of control involving more than one quadrotors, according to which two quadrotors can be physically coupled in mid-flight. This concept equips the quadro- tors with new capabilities, e.g. increased payload or pursuit and capturing of other quadrotors. A comprehensive simulation of the approach is built to simulate coupled quadrotors. The dynamics and modeling of the coupled system is presented together with a discussion regarding the coupling mechanism, impact modeling and additional considerations that have been investigated. Simulation results are presented for cases of static coupling as well as enemy quadrotor pursuit and capture, together with an analysis of control methodology and gain tuning. Practical implementations are introduced as results show the feasibility of this design.

In-situ exploration of planetary bodies such as Mars or the Moon have provided geologists and planetary scientists a detailed understanding of how these bodies formed and evolved. In-situ exploration has aided in the quest for water and life-supporting chemicals. In-situ exploration of Mars carried out by large SUV-sized rovers that travel long distance, carry sophisticated onboard laboratories to perform soil analysis and sample collection. But their large size and mobility method prevents them from accessing or exploring extreme environments, particularly caves, canyons, cliffs and craters.

This work presents sub- 2 kg ball robots that can roll and hop in low gravity environments. These robots are low-cost enabling for one or more to be deployed in the field. These small robots can be deployed from a larger rover or lander and complement their capabilities by performing scouting and identifying potential targets of interest. Their small size and ball shape allow them to tumble freely, preventing them from getting stuck. Hopping enables the robot to overcome obstacles larger than the size of the robot.

The proposed ball-robot design consists of a spherical core with two hemispherical shells with grouser which act as wheels for small movements. These robots have two cameras for stereovision which can be used for localization. Inertial Measurement Unit (IMU) and wheel encoder are used for dead reckoning. Communication is performed using Zigbee radio. This enables communication between a robot and a lander/rover or for inter-robot communication. The robots have been designed to have a payload with a 300 gram capacity. These may include chemical analysis sensors, spectrometers and other small sensors.

The performance of the robot has been evaluated in a laboratory environment using Low-gravity Offset and Motion Assistance Simulation System (LOMASS). An evaluation was done to understand the effect of grouser height and grouser separation angle on the performance of the robot in different terrains. The experiments show with higher grouser height and optimal separation angle the power requirement increases but an increase in average robot speed and traction is also observed. The robot was observed to perform hops of approximately 20 cm in simulated lunar condition. Based on theoretical calculations, the robot would be able to perform 208 hops with single charge and will operate for 35 minutes. The study will be extended to operate multiple robots in a network to perform exploration. Their small size and cost makes it possible to deploy dozens in a region of interest. Multiple ball robots can cooperatively perform unique in-situ science measurements and analyze a larger surface area than a single robot alone on a planet surface.

The advancements in the technology of MEMS fabrication has been phenomenal in recent years. In no mean measure this has been the result of continued demand from the consumer electronics market to make devices smaller and better. MEMS inertial measuring units (IMUs) have found revolutionary applications in a wide array of fields like medical instrumentation, navigation, attitude stabilization and virtual reality. It has to be noted though that for advanced applications of motion tracking, navigation and guidance the cost of the IMUs is still pretty high. This is mainly because the process of calibration and signal processing used to get highly stable results from MEMS IMU is an expensive and time-consuming process. Also to be noted is the inevitability of using external sensors like GPS or camera for aiding the IMU data due to the error propagation in IMU measurements adds to the complexity of the system.

First an efficient technique is proposed to acquire clean and stable data from unaided IMU measurements and then proceed to use that system for tracking human motion. First part of this report details the design and development of the low-cost inertial measuring system ‘yIMU’. This thesis intends to bring together seemingly independent techniques that were highly application specific into one monolithic algorithm that is computationally efficient for generating reliable orientation estimates. Second part, systematically deals with development of a tracking routine for human limb movements. The validity of the system has then been verified.

The central idea is that in most cases the use of expensive MEMS IMUs is not warranted if robust smart algorithms can be deployed to gather data at a fraction of the cost. A low-cost prototype has been developed comparable to tactical grade performance for under $15 hardware. In order to further the practicability of this device we have applied it to human motion tracking with excellent results. The commerciality of device has hence been thoroughly established.