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Parallel optimization of polynomials for large-scale problems in stability and control

Description

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

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.

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Created

Date Created
2016

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Dexterous manipulation: sensorimotor learning and control

Description

Humans' ability to perform fine object and tool manipulation is a defining feature of their sensorimotor repertoire. How the central nervous system builds and maintains internal representations of such skilled hand-object interactions has attracted significant attention over the past three

Humans' ability to perform fine object and tool manipulation is a defining feature of their sensorimotor repertoire. How the central nervous system builds and maintains internal representations of such skilled hand-object interactions has attracted significant attention over the past three decades. Nevertheless, two major gaps exist: a) how digit positions and forces are coordinated during natural manipulation tasks, and b) what mechanisms underlie the formation and retention of internal representations of dexterous manipulation. This dissertation addresses these two questions through five experiments that are based on novel grip devices and experimental protocols. It was found that high-level representation of manipulation tasks can be learned in an effector-independent fashion. Specifically, when challenged by trial-to-trial variability in finger positions or using digits that were not previously engaged in learning the task, subjects could adjust finger forces to compensate for this variability, thus leading to consistent task performance. The results from a follow-up experiment conducted in a virtual reality environment indicate that haptic feedback is sufficient to implement the above coordination between digit position and forces. However, it was also found that the generalizability of a learned manipulation is limited across tasks. Specifically, when subjects learned to manipulate the same object across different contexts that require different motor output, interference was found at the time of switching contexts. Data from additional studies provide evidence for parallel learning processes, which are characterized by different rates of decay and learning. These experiments have provided important insight into the neural mechanisms underlying learning and control of object manipulation. The present findings have potential biomedical applications including brain-machine interfaces, rehabilitation of hand function, and prosthetics.

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Created

Date Created
2013

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On ehancing myoelectric interfaces by exploiting motor learning and flexible muscle synergies

Description

Myoelectric control is lled with potential to signicantly change human-robot interaction.

Humans desire compliant robots to safely interact in dynamic environments

associated with daily activities. As surface electromyography non-invasively measures

limb motion intent and correlates with joint stiness during co-contractions,

it has been identied

Myoelectric control is lled with potential to signicantly change human-robot interaction.

Humans desire compliant robots to safely interact in dynamic environments

associated with daily activities. As surface electromyography non-invasively measures

limb motion intent and correlates with joint stiness during co-contractions,

it has been identied as a candidate for naturally controlling such robots. However,

state-of-the-art myoelectric interfaces have struggled to achieve both enhanced

functionality and long-term reliability. As demands in myoelectric interfaces trend

toward simultaneous and proportional control of compliant robots, robust processing

of multi-muscle coordinations, or synergies, plays a larger role in the success of the

control scheme. This dissertation presents a framework enhancing the utility of myoelectric

interfaces by exploiting motor skill learning and

exible muscle synergies for

reliable long-term simultaneous and proportional control of multifunctional compliant

robots. The interface is learned as a new motor skill specic to the controller,

providing long-term performance enhancements without requiring any retraining or

recalibration of the system. Moreover, the framework oers control of both motion

and stiness simultaneously for intuitive and compliant human-robot interaction. The

framework is validated through a series of experiments characterizing motor learning

properties and demonstrating control capabilities not seen previously in the literature.

The results validate the approach as a viable option to remove the trade-o

between functionality and reliability that have hindered state-of-the-art myoelectric

interfaces. Thus, this research contributes to the expansion and enhancement of myoelectric

controlled applications beyond commonly perceived anthropomorphic and

\intuitive control" constraints and into more advanced robotic systems designed for

everyday tasks.

Contributors

Agent

Created

Date Created
2015

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Techniques to Assess Balance and Mobility in Lower-Limb Prosthesis Users

Description

Lower-limb prosthesis users have commonly-recognized deficits in gait and posture control. However, existing methods in balance and mobility analysis fail to provide sufficient sensitivity to detect changes in prosthesis users' postural control and mobility in response to clinical intervention or

Lower-limb prosthesis users have commonly-recognized deficits in gait and posture control. However, existing methods in balance and mobility analysis fail to provide sufficient sensitivity to detect changes in prosthesis users' postural control and mobility in response to clinical intervention or experimental manipulations and often fail to detect differences between prosthesis users and non-amputee control subjects. This lack of sensitivity limits the ability of clinicians to make informed clinical decisions and presents challenges with insurance reimbursement for comprehensive clinical care and advanced prosthetic devices. These issues have directly impacted clinical care by restricting device options, increasing financial burden on clinics, and limiting support for research and development. This work aims to establish experimental methods and outcome measures that are more sensitive than traditional methods to balance and mobility changes in prosthesis users. Methods and analysis techniques were developed to probe aspects of balance and mobility control that may be specifically impacted by use of a prosthesis and present challenges similar to those experienced in daily life that could improve the detection of balance and mobility changes. Using the framework of cognitive resource allocation and dual-tasking, this work identified unique characteristics of prosthesis users’ postural control and developed sensitive measures of gait variability. The results also provide broader insight into dual-task analysis and the motor-cognitive response to demanding conditions. Specifically, this work identified altered motor behavior in prosthesis users and high cognitive demand of using a prosthesis. The residual standard deviation method was developed and demonstrated to be more effective than traditional gait variability measures at detecting the impact of dual-tasking. Additionally, spectral analysis of the center of pressure while standing identified altered somatosensory control in prosthesis users. These findings provide a new understanding of prosthetic use and new, highly sensitive techniques to assess balance and mobility in prosthesis users.

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Created

Date Created
2017

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Evaluating the Effects of Ankle-Foot-Orthoses, Functional Electrical Stimulators, and Trip-specific Training on Fall Outcomes in Individuals with Stroke

Description

This dissertation aimed to evaluate the effectiveness and drawbacks of promising fall prevention strategies in individuals with stroke by rigorously analyzing the biomechanics of laboratory falls and compensatory movements required to prevent a fall. Ankle-foot-orthoses (AFOs) and functional electrical stimulators

This dissertation aimed to evaluate the effectiveness and drawbacks of promising fall prevention strategies in individuals with stroke by rigorously analyzing the biomechanics of laboratory falls and compensatory movements required to prevent a fall. Ankle-foot-orthoses (AFOs) and functional electrical stimulators (FESs) are commonly prescribed to treat foot drop. Despite well-established positive impacts of AFOs and FES devices on balance and gait, AFO and FES users fall at a high rate. In chapter 2 (as a preliminary study), solely mechanical impacts of a semi-rigid AFO on the compensatory stepping response of young healthy individuals following trip-like treadmill perturbations were evaluated. It was found that a semi-rigid AFO on the stepping leg diminished the propulsive impulse of the compensatory step which led to decreased trunk movement control, shorter step length, and reduced center of mass (COM) stability. These results highlight the critical role of plantarflexors in generating an effective compensatory stepping response. In chapter 3, the underlying biomechanical mechanisms leading to high fall risk in long-term AFO and FES users with chronic stroke were studied. It was found that AFO and FES users fall more than Non-users because they have a more impaired lower limb that is not fully addressed by AFO/FES, therefore leading to a more impaired compensatory stepping response characterized by increased inability to generate a compensatory step with paretic leg and decreased trunk movement control. An ideal future AFO that provides dorsiflexion assistance during the swing phase and plantarflexion assistance during the push-off phase of gait is suggested to enhance the compensatory stepping response and reduce more falls. In chapter 4, the effects of a single-session trip-specific training on the compensatory stepping response of individuals with stroke were evaluated. Trunk movement control was improved after a single session of training suggesting that this type of training is a viable option to enhance compensatory stepping response and reduce falls in individuals with stroke. Finally, a future powered AFO with plantarflexion assistance complemented by a trip-specific training program is suggested to enhance the compensatory stepping response and decrease falls in individuals with stroke.

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Created

Date Created
2019

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Fractional Order PID Controller Tuning by Frequency Loop-Shaping: Analysis and Applications

Description

The purpose of this dissertation is to develop a design technique for fractional PID controllers to achieve a closed loop sensitivity bandwidth approximately equal to a desired bandwidth using frequency loop shaping techniques. This dissertation analyzes the effect of the

The purpose of this dissertation is to develop a design technique for fractional PID controllers to achieve a closed loop sensitivity bandwidth approximately equal to a desired bandwidth using frequency loop shaping techniques. This dissertation analyzes the effect of the order of a fractional integrator which is used as a target on loop shaping, on stability and performance robustness. A comparison between classical PID controllers and fractional PID controllers is presented. Case studies where fractional PID controllers have an advantage over classical PID controllers are discussed. A frequency-domain loop shaping algorithm is developed, extending past results from classical PID’s that have been successful in tuning controllers for a variety of practical systems.

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Created

Date Created
2017

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Assessing Performance, Role Sharing, and Control Mechanisms in Human-Human Physical Interaction for Object Manipulation

Description

Object manipulation is a common sensorimotor task that humans perform to interact with the physical world. The first aim of this dissertation was to characterize and identify the role of feedback and feedforward mechanisms for force control in object manipulation

Object manipulation is a common sensorimotor task that humans perform to interact with the physical world. The first aim of this dissertation was to characterize and identify the role of feedback and feedforward mechanisms for force control in object manipulation by introducing a new feature based on force trajectories to quantify the interaction between feedback- and feedforward control. This feature was applied on two grasp contexts: grasping the object at either (1) predetermined or (2) self-selected grasp locations (“constrained” and “unconstrained”, respectively), where unconstrained grasping is thought to involve feedback-driven force corrections to a greater extent than constrained grasping. This proposition was confirmed by force feature analysis. The second aim of this dissertation was to quantify whether force control mechanisms differ between dominant and non-dominant hands. The force feature analysis demonstrated that manipulation by the dominant hand relies on feedforward control more than the non-dominant hand. The third aim was to quantify coordination mechanisms underlying physical interaction by dyads in object manipulation. The results revealed that only individuals with worse solo performance benefit from interpersonal coordination through physical couplings, whereas the better individuals do not. This work showed that naturally emerging leader-follower roles, whereby the leader in dyadic manipulation exhibits significant greater force changes than the follower. Furthermore, brain activity measured through electroencephalography (EEG) could discriminate leader and follower roles as indicated power modulation in the alpha frequency band over centro-parietal areas. Lastly, this dissertation suggested that the relation between force and motion (arm impedance) could be an important means for communicating intended movement direction between biological agents.

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Created

Date Created
2017

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Scalable control strategies and a customizable swarm robotic platform for boundary coverage and collective transport tasks

Description

Swarms of low-cost, autonomous robots can potentially be used to collectively perform tasks over large domains and long time scales. The design of decentralized, scalable swarm control strategies will enable the development of robotic systems that can execute such tasks

Swarms of low-cost, autonomous robots can potentially be used to collectively perform tasks over large domains and long time scales. The design of decentralized, scalable swarm control strategies will enable the development of robotic systems that can execute such tasks with a high degree of parallelism and redundancy, enabling effective operation even in the presence of unknown environmental factors and individual robot failures. Social insect colonies provide a rich source of inspiration for these types of control approaches, since they can perform complex collective tasks under a range of conditions. To validate swarm robotic control strategies, experimental testbeds with large numbers of robots are required; however, existing low-cost robots are specialized and can lack the necessary sensing, navigation, control, and manipulation capabilities.

To address these challenges, this thesis presents a formal approach to designing biologically-inspired swarm control strategies for spatially-confined coverage and payload transport tasks, as well as a novel low-cost, customizable robotic platform for testing swarm control approaches. Stochastic control strategies are developed that provably allocate a swarm of robots around the boundaries of multiple regions of interest or payloads to be transported. These strategies account for spatially-dependent effects on the robots' physical distribution and are largely robust to environmental variations. In addition, a control approach based on reinforcement learning is presented for collective payload towing that accommodates robots with heterogeneous maximum speeds. For both types of collective transport tasks, rigorous approaches are developed to identify and translate observed group retrieval behaviors in Novomessor cockerelli ants to swarm robotic control strategies. These strategies can replicate features of ant transport and inherit its properties of robustness to different environments and to varying team compositions. The approaches incorporate dynamical models of the swarm that are amenable to analysis and control techniques, and therefore provide theoretical guarantees on the system's performance. Implementation of these strategies on robotic swarms offers a way for biologists to test hypotheses about the individual-level mechanisms that drive collective behaviors. Finally, this thesis describes Pheeno, a new swarm robotic platform with a three degree-of-freedom manipulator arm, and describes its use in validating a variety of swarm control strategies.

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Date Created
2017

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Development of a Novel Low Inertia Exoskeleton Device for Characterizing the Neuromuscular Properties of the Human Shoulder

Description

The human shoulder plays an integral role in upper limb motor function. As the basis of arm motion, its performance is vital to the accomplishment of daily tasks. Impaired motor control, as a result of stroke or other disease, can

The human shoulder plays an integral role in upper limb motor function. As the basis of arm motion, its performance is vital to the accomplishment of daily tasks. Impaired motor control, as a result of stroke or other disease, can cause errors in shoulder position to accumulate and propagate to the entire arm. This is why it is a highlight of concern for clinicians and why it is an important point of study. One of the primary causes of impaired shoulder motor control is abnormal mechanical joint impedance, which can be modeled as a 2nd order system consisting of mass, spring and damper. Quantifying shoulder stiffness and damping between healthy and impaired subjects could help improve our collective understanding of how many different neuromuscular diseases impact arm performance. This improved understanding could even lead to better rehabilitation protocols for conditions such as stroke through better identification and targeting of damping dependent spasticity and stiffness dependent hypertonicity. Despite its importance, there is a fundamental knowledge gap in the understanding of shoulder impedance, mainly due to a lack of appropriate characterization tools. Therefore, in order to better quantify shoulder stiffness and damping, a novel low-inertia shoulder exoskeleton is introduced in this work. The device was developed using a newly pioneered parallel actuated robot architecture specifically designed to interface with complex biological joints like the shoulder, hip, wrist and ankle. In addition to presenting the kinematics and dynamics of the shoulder exoskeleton, a series of validation experiments are performed on a human shoulder mock-up to quantify its ability to estimate known impedance properties. Finally, some preliminary data from human experiments is provided to demonstrate the device’s ability to collect the measurements needed to estimate shoulder stiffness and damping while worn by a subject.

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Created

Date Created
2020

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Decentralized Control of Collective Transport by Multi-Robot Systems with Minimal Information

Description

One potential application of multi-robot systems is collective transport, a task in which multiple mobile robots collaboratively transport a payload that is too large or heavy to be carried by a single robot. Numerous control schemes have been proposed for

One potential application of multi-robot systems is collective transport, a task in which multiple mobile robots collaboratively transport a payload that is too large or heavy to be carried by a single robot. Numerous control schemes have been proposed for collective transport in environments where robots can localize themselves (e.g., using GPS) and communicate with one another, have information about the payload's geometric and dynamical properties, and follow predefined robot and/or payload trajectories. However, these approaches cannot be applied in uncertain environments where robots do not have reliable communication and GPS and lack information about the payload. These conditions characterize a variety of applications, including construction, mining, assembly in space and underwater, search-and-rescue, and disaster response.
Toward this end, this thesis presents decentralized control strategies for collective transport by robots that regulate their actions using only their local sensor measurements and minimal prior information. These strategies can be implemented on robots that have limited or absent localization capabilities, do not explicitly exchange information, and are not assigned predefined trajectories. The controllers are developed for collective transport over planar surfaces, but can be extended to three-dimensional environments.

This thesis addresses the above problem for two control objectives. First, decentralized controllers are proposed for velocity control of collective transport, in which the robots must transport a payload at a constant velocity through an unbounded domain that may contain strictly convex obstacles. The robots are provided only with the target transport velocity, and they do not have global localization or prior information about any obstacles in the environment. Second, decentralized controllers are proposed for position control of collective transport, in which the robots must transport a payload to a target position through a bounded or unbounded domain that may contain convex obstacles. The robots are subject to the same constraints as in the velocity control scenario, except that they are assumed to have global localization. Theoretical guarantees for successful execution of the task are derived using techniques from nonlinear control theory, and it is shown through simulations and physical robot experiments that the transport objectives are achieved with the proposed controllers.

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Agent

Created

Date Created
2020