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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.

Contributors

Agent

Created

Date Created
2016

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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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Mission and Motion Planning for Multi-robot Systems in Constrained Environments

Description

As robots become mechanically more capable, they are going to be more and more integrated into our daily lives. Over time, human’s expectation of what the robot capabilities are is getting higher. Therefore, it can be conjectured that often robots

As robots become mechanically more capable, they are going to be more and more integrated into our daily lives. Over time, human’s expectation of what the robot capabilities are is getting higher. Therefore, it can be conjectured that often robots will not act as human commanders intended them to do. That is, the users of the robots may have a different point of view from the one the robots do.

The first part of this dissertation covers methods that resolve some instances of this mismatch when the mission requirements are expressed in Linear Temporal Logic (LTL) for handling coverage, sequencing, conditions and avoidance. That is, the following general questions are addressed:

* What cause of the given mission is unrealizable?

* Is there any other feasible mission that is close to the given one?

In order to answer these questions, the LTL Revision Problem is applied and it is formulated as a graph search problem. It is shown that in general the problem is NP-Complete. Hence, it is proved that the heuristic algorihtm has 2-approximation bound in some cases. This problem, then, is extended to two different versions: one is for the weighted transition system and another is for the specification under quantitative preference. Next, a follow up question is addressed:

* How can an LTL specified mission be scaled up to multiple robots operating in confined environments?

The Cooperative Multi-agent Planning Problem is addressed by borrowing a technique from cooperative pathfinding problems in discrete grid environments. Since centralized planning for multi-robot systems is computationally challenging and easily results in state space explosion, a distributed planning approach is provided through agent coupling and de-coupling.

In addition, in order to make such robot missions work in the real world, robots should take actions in the continuous physical world. Hence, in the second part of this thesis, the resulting motion planning problems is addressed for non-holonomic robots.

That is, it is devoted to autonomous vehicles’ motion planning in challenging environments such as rural, semi-structured roads. This planning problem is solved with an on-the-fly hierarchical approach, using a pre-computed lattice planner. It is also proved that the proposed algorithm guarantees resolution-completeness in such demanding environments. Finally, possible extensions are discussed.

Contributors

Agent

Created

Date Created
2019

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Control and Estimation Theory in Ranging Applications

Description

For the last 50 years, oscillator modeling in ranging systems has received considerable

attention. Many components in a navigation system, such as the master oscillator

driving the receiver system, as well the master oscillator in the transmitting system

contribute significantly to timing errors.

For the last 50 years, oscillator modeling in ranging systems has received considerable

attention. Many components in a navigation system, such as the master oscillator

driving the receiver system, as well the master oscillator in the transmitting system

contribute significantly to timing errors. Algorithms in the navigation processor must

be able to predict and compensate such errors to achieve a specified accuracy. While

much work has been done on the fundamentals of these problems, the thinking on said

problems has not progressed. On the hardware end, the designers of local oscillators

focus on synthesized frequency and loop noise bandwidth. This does nothing to

mitigate, or reduce frequency stability degradation in band. Similarly, there are not

systematic methods to accommodate phase and frequency anomalies such as clock

jumps. Phase locked loops are fundamentally control systems, and while control

theory has had significant advancement over the last 30 years, the design of timekeeping

sources has not advanced beyond classical control. On the software end,

single or two state oscillator models are typically embedded in a Kalman Filter to

alleviate time errors between the transmitter and receiver clock. Such models are

appropriate for short term time accuracy, but insufficient for long term time accuracy.

Additionally, flicker frequency noise may be present in oscillators, and it presents

mathematical modeling complications. This work proposes novel H∞ control methods

to address the shortcomings in the standard design of time-keeping phase locked loops.

Such methods allow the designer to address frequency stability degradation as well

as high phase/frequency dynamics. Additionally, finite-dimensional approximants of

flicker frequency noise that are more representative of the truth system than the

tradition Gauss Markov approach are derived. Last, to maintain timing accuracy in

a wide variety of operating environments, novel Banks of Adaptive Extended Kalman

Filters are used to address both stochastic and dynamic uncertainty.

Contributors

Agent

Created

Date Created
2020

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Haptic perception, decision-making, and learning for manipulation with artificial hands

Description

Robotic systems are outmatched by the abilities of the human hand to perceive and manipulate the world. Human hands are able to physically interact with the world to perceive, learn, and act to accomplish tasks. Limitations of robotic systems to

Robotic systems are outmatched by the abilities of the human hand to perceive and manipulate the world. Human hands are able to physically interact with the world to perceive, learn, and act to accomplish tasks. Limitations of robotic systems to interact with and manipulate the world diminish their usefulness. In order to advance robot end effectors, specifically artificial hands, rich multimodal tactile sensing is needed. In this work, a multi-articulating, anthropomorphic robot testbed was developed for investigating tactile sensory stimuli during finger-object interactions. The artificial finger is controlled by a tendon-driven remote actuation system that allows for modular control of any tendon-driven end effector and capabilities for both speed and strength. The artificial proprioception system enables direct measurement of joint angles and tendon tensions while temperature, vibration, and skin deformation are provided by a multimodal tactile sensor. Next, attention was focused on real-time artificial perception for decision-making. A robotic system needs to perceive its environment in order to make decisions. Specific actions such as “exploratory procedures” can be employed to classify and characterize object features. Prior work on offline perception was extended to develop an anytime predictive model that returns the probability of having touched a specific feature of an object based on minimally processed sensor data. Developing models for anytime classification of features facilitates real-time action-perception loops. Finally, by combining real-time action-perception with reinforcement learning, a policy was learned to complete a functional contour-following task: closing a deformable ziplock bag. The approach relies only on proprioceptive and localized tactile data. A Contextual Multi-Armed Bandit (C-MAB) reinforcement learning algorithm was implemented to maximize cumulative rewards within a finite time period by balancing exploration versus exploitation of the action space. Performance of the C-MAB learner was compared to a benchmark Q-learner that eventually returns the optimal policy. To assess robustness and generalizability, the learned policy was tested on variations of the original contour-following task. The work presented contributes to the full range of tools necessary to advance the abilities of artificial hands with respect to dexterity, perception, decision-making, and learning.

Contributors

Agent

Created

Date Created
2016

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Robotic Swarm Control using Deep Reinforcement Learning Strategies based on Mean-Field Models

Description

As technological advancements in silicon, sensors, and actuation continue, the development of robotic swarms is shifting from the domain of science fiction to reality. Many swarm applications, such as environmental monitoring, precision agriculture, disaster response, and lunar prospecting, will require

As technological advancements in silicon, sensors, and actuation continue, the development of robotic swarms is shifting from the domain of science fiction to reality. Many swarm applications, such as environmental monitoring, precision agriculture, disaster response, and lunar prospecting, will require controlling numerous robots with limited capabilities and information to redistribute among multiple states, such as spatial locations or tasks. A scalable control approach is to program the robots with stochastic control policies such that the robot population in each state evolves according to a mean-field model, which is independent of the number and identities of the robots. Using this model, the control policies can be designed to stabilize the swarm to the target distribution. To avoid the need to reprogram the robots for different target distributions, the robot control policies can be defined to depend only on the presence of a “leader” agent, whose control policy is designed to guide the swarm to a particular distribution. This dissertation presents a novel deep reinforcement learning (deep RL) approach to designing control policies that redistribute a swarm as quickly as possible over a strongly connected graph, according to a mean-field model in the form of the discrete-time Kolmogorov forward equation. In the leader-based strategies, the leader determines its next action based on its observations of robot populations and shepherds the swarm over the graph by probabilistically repelling nearby robots. The scalability of this approach with the swarm size is demonstrated with leader control policies that are designed using two tabular Temporal-Difference learning algorithms, trained on a discretization of the swarm distribution. To improve the scalability of the approach with robot population and graph size, control policies for both leader-based and leaderless strategies are designed using an actor-critic deep RL method that is trained on the swarm distribution predicted by the mean-field model. In the leaderless strategy, the robots’ control policies depend only on their local measurements of nearby robot populations. The control approaches are validated for different graph and swarm sizes in numerical simulations, 3D robot simulations, and experiments on a multi-robot testbed.

Contributors

Agent

Created

Date Created
2021

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Magnetic Needle Steering for Medical Applications

Description

Many medical procedures, like surgeries, deal with the physical manipulation of sensitive internal tissues. Over time, new medical tools and techniques have been developed to improve the safety and efficacy of these procedures. Despite the leaps and bounds of progress

Many medical procedures, like surgeries, deal with the physical manipulation of sensitive internal tissues. Over time, new medical tools and techniques have been developed to improve the safety and efficacy of these procedures. Despite the leaps and bounds of progress made up to the present day, three major obstacles (among others) persist, bleeding, pain, and the risk of infection. Advances in minimally invasive treatments have transformed many formerly risky surgical procedures into very safe and highly successful routines. Minimally invasive surgeries are characterized by small incision profiles compared to the large incisions in open surgeries, minimizing the aforementioned issues. Minimally invasive procedures lead to several benefits, such as shorter recovery time, fewer complications, and less postoperative pain. In minimally invasive surgery, doctors use various techniques to operate with less damage to the body than open surgery. Today, these procedures have an established, successful history and promising future. Steerable needles are one of the tools proposed for minimally invasive operations. Needle steering is a method for guiding a long, flexible needle through curved paths to reach targets deep in the body, eliminating the need for large incisions. In this dissertation, we present a new needle steering technology: magnetic needle steering. This technology is proposed to address the limitations of conventional needle steering that hindered its clinical applications. Magnetic needle steering eliminates excessive tissue damage, restrictions of the minimum radius of curvature, and the need for a complex nonlinear model, to name a few. It also allows fabricating the needle shaft out of soft and tissue-compliant materials.
This is achieved by first developing an electromagnetic coil system capable of producing desired magnetic fields and gradients; then, a magnetically actuated needle is designed, and its effectiveness is experimentally evaluated. Afterward, the scalability of this technique was tested using permanent magnets controlled with a robotic arm.
Furthermore, different configurations of permanent magnets and their influence on the magnetic field are investigated, enabling the possibility of designing a desired magnetic field for a specific surgical procedure and operation on a particular organ. Finally, potential future directions towards animal studies and clinical trials are discussed.

Contributors

Agent

Created

Date Created
2021

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Modeling Human Adaptation with Game-theoretic Intention Decoding in Human-Robot Interactions

Description

With the substantial development of intelligent robots, human-robot interaction (HRI) has become ubiquitous in applications such as collaborative manufacturing, surgical robotic operations, and autonomous driving. In all these applications, a human behavior model, which can provide predictions of human actions,

With the substantial development of intelligent robots, human-robot interaction (HRI) has become ubiquitous in applications such as collaborative manufacturing, surgical robotic operations, and autonomous driving. In all these applications, a human behavior model, which can provide predictions of human actions, is a helpful reference that helps robots to achieve intelligent interaction with humans. The requirement elicits an essential problem of how to properly model human behavior, especially when individuals are interacting or cooperating with each other. The major objective of this thesis is to utilize the human intention decoding method to help robots enhance their performance while interacting with humans. Preliminary work on integrating human intention estimation with an HRI scenario is shown to demonstrate the benefit. In order to achieve this goal, the research topic is divided into three phases. First, a novel method of an online measure of the human's reliance on the robot, which can be estimated through the intention decoding process from human actions,is described. An experiment that requires human participants to complete an object-moving task with a robot manipulator was conducted under different conditions of distractions. A relationship is discovered between human intention and trust while participants performed a familiar task with no distraction. This finding suggests a relationship between the psychological construct of trust and joint physical coordination, which bridges the human's action to its mental states. Then, a novel human collaborative dynamic model is introduced based on game theory and bounded rationality, which is a novel method to describe human dyadic behavior with the aforementioned theories. The mutual intention decoding process was also considered to inform this model. Through this model, the connection between the mental states of the individuals to their cooperative actions is indicated. A haptic interface is developed with a virtual environment and the experiments are conducted with 30 human subjects. The result suggests the existence of mutual intention decoding during the human dyadic cooperative behaviors. Last, the empirical results show that allowing agents to have empathy in inference, which lets the agents understand that others might have a false understanding of their intentions, can help to achieve correct intention inference. It has been verified that knowledge about vehicle dynamics was also important to correctly infer intentions. A new courteous policy is proposed that bounded the courteous motion using its inferred set of equilibrium motions. A simulation, which is set to reproduce an intersection passing case between an autonomous car and a human driving car, is conducted to demonstrate the benefit of the novel courteous control policy.

Contributors

Agent

Created

Date Created
2021

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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.

Contributors

Agent

Created

Date Created
2020

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Self-Organization of Multi-Agent Systems Using Markov Chain Models

Description

The problem of modeling and controlling the distribution of a multi-agent system has recently evolved into an interdisciplinary effort. When the agent population is very large, i.e., at least on the order of hundreds of agents, it is important that

The problem of modeling and controlling the distribution of a multi-agent system has recently evolved into an interdisciplinary effort. When the agent population is very large, i.e., at least on the order of hundreds of agents, it is important that techniques for analyzing and controlling the system scale well with the number of agents. One scalable approach to characterizing the behavior of a multi-agent system is possible when the agents' states evolve over time according to a Markov process. In this case, the density of agents over space and time is governed by a set of difference or differential equations known as a {\it mean-field model}, whose parameters determine the stochastic control policies of the individual agents. These models often have the advantage of being easier to analyze than the individual agent dynamics. Mean-field models have been used to describe the behavior of chemical reaction networks, biological collectives such as social insect colonies, and more recently, swarms of robots that, like natural swarms, consist of hundreds or thousands of agents that are individually limited in capability but can coordinate to achieve a particular collective goal.

This dissertation presents a control-theoretic analysis of mean-field models for which the agent dynamics are governed by either a continuous-time Markov chain on an arbitrary state space, or a discrete-time Markov chain on a continuous state space. Three main problems are investigated. First, the problem of stabilization is addressed, that is, the design of transition probabilities/rates of the Markov process (the agent control parameters) that make a target distribution, satisfying certain conditions, invariant. Such a control approach could be used to achieve desired multi-agent distributions for spatial coverage and task allocation. However, the convergence of the multi-agent distribution to the designed equilibrium does not imply the convergence of the individual agents to fixed states. To prevent the agents from continuing to transition between states once the target distribution is reached, and thus potentially waste energy, the second problem addressed within this dissertation is the construction of feedback control laws that prevent agents from transitioning once the equilibrium distribution is reached. The third problem addressed is the computation of optimized transition probabilities/rates that maximize the speed at which the system converges to the target distribution.

Contributors

Agent

Created

Date Created
2020