Motion Planning and Controls with Safety and Temporal Constraints

Motion planning, or trajectory planning, commonly refers to a process of converting high-level task specifications into low-level control commands that can be executed on the system of interest. For different applications, the system will be different. It can be an autonomous vehicle, an Unmanned Aerial Vehicle(UAV), a humanoid robot, or an industrial robotic arm. As human machine interaction is essential in many of these systems, safety is fundamental and crucial. Many of the applications also involve performing a task in an optimal manner within a given time constraint. Therefore, in this thesis, we focus on two aspects of the motion planning problem. One is the verification and synthesis of the safe controls for autonomous ground and air vehicles in collision avoidance scenarios. The other part focuses on the high-level planning for the autonomous vehicles with the timed temporal constraints. In the first aspect of our work, we first propose a verification method to prove the safety and robustness of a path planner and the path following controls based on reachable sets. We demonstrate the method on quadrotor and automobile applications. Secondly, we propose a reachable set based collision avoidance algorithm for UAVs. Instead of the traditional approaches of collision avoidance between trajectories, we propose a collision avoidance scheme based on reachable sets and tubes. We then formulate the problem as a convex optimization problem seeking control set design for the aircraft to avoid collision. We apply our approach to collision avoidance scenarios of quadrotors and fixed-wing aircraft. In the second aspect of our work, we address the high level planning problems with timed temporal logic constraints. Firstly, we present an optimization based method for path planning of a mobile robot subject to timed temporal constraints, in a dynamic environment. Temporal logic (TL) can address very complex task specifications such as safety, coverage, motion sequencing etc. We use metric temporal logic (MTL) to encode the task specifications with timing constraints. We then translate the MTL formulae into mixed integer linear constraints and solve the associated optimization problem using a mixed integer linear program solver. We have applied our approach on several case studies in complex dynamical environments subjected to timed temporal specifications. Secondly, we also present a timed automaton based method for planning under the given timed temporal logic specifications. We use metric interval temporal logic (MITL), a member of the MTL family, to represent the task specification, and provide a constructive way to generate a timed automaton and methods to look for accepting runs on the automaton to find an optimal motion (or path) sequence for the robot to complete the task.

Spectral graph theory with applications to quantum adiabatic optimization

In this dissertation I draw a connection between quantum adiabatic optimization, spectral graph theory, heat-diffusion, and sub-stochastic processes through the operators that govern these processes and their associated spectra. In particular, we study Hamiltonians which have recently become known as ``stoquastic'' or, equivalently, the generators of sub-stochastic processes. The operators corresponding to these Hamiltonians are of interest in all of the settings mentioned above. I predominantly explore the connection between the spectral gap of an operator, or the difference between the two lowest energies of that operator, and certain equilibrium behavior. In the context of adiabatic optimization, this corresponds to the likelihood of solving the optimization problem of interest. I will provide an instance of an optimization problem that is easy to solve classically, but leaves open the possibility to being difficult adiabatically. Aside from this concrete example, the work in this dissertation is predominantly mathematical and we focus on bounding the spectral gap. Our primary tool for doing this is spectral graph theory, which provides the most natural approach to this task by simply considering Dirichlet eigenvalues of subgraphs of host graphs. I will derive tight bounds for the gap of one-dimensional, hypercube, and general convex subgraphs. The techniques used will also adapt methods recently used by Andrews and Clutterbuck to prove the long-standing ``Fundamental Gap Conjecture''.

Dynamic Resource Allocation in Wireless Heterogeneous Networks

Deployment of low power basestations within cellular networks can potentially increase both capacity and coverage. However, such deployments require efficient resource allocation schemes for managing interference from the low power and macro basestations that are located within each other’s transmission range. In this dissertation, we propose novel and efficient dynamic resource allocation algorithms in the frequency, time and space domains. We show that the proposed algorithms perform better than the current state-of-art resource management algorithms. In the first part of the dissertation, we propose an interference management solution in the frequency domain. We introduce a distributed frequency allocation scheme that shares frequencies between macro and low power pico basestations, and guarantees a minimum average throughput to users. The scheme seeks to minimize the total number of frequencies needed to honor the minimum throughput requirements. We evaluate our scheme using detailed simulations and show that it performs on par with the centralized optimum allocation. Moreover, our proposed scheme outperforms a static frequency reuse scheme and the centralized optimal partitioning between the macro and picos. In the second part of the dissertation, we propose a time domain solution to the interference problem. We consider the problem of maximizing the alpha-fairness utility over heterogeneous wireless networks (HetNets) by jointly optimizing user association, wherein each user is associated to any one transmission point (TP) in the network, and activation fractions of all TPs. Activation fraction of a TP is the fraction of the frame duration for which it is active, and together these fractions influence the interference seen in the network. To address this joint optimization problem which we show is NP-hard, we propose an alternating optimization based approach wherein the activation fractions and the user association are optimized in an alternating manner. The subproblem of determining the optimal activation fractions is solved using a provably convergent auxiliary function method. On the other hand, the subproblem of determining the user association is solved via a simple combinatorial algorithm. Meaningful performance guarantees are derived in either case. Simulation results over a practical HetNet topology reveal the superior performance of the proposed algorithms and underscore the significant benefits of the joint optimization. In the final part of the dissertation, we propose a space domain solution to the interference problem. We consider the problem of maximizing system utility by optimizing over the set of user and TP pairs in each subframe, where each user can be served by multiple TPs. To address this optimization problem which is NP-hard, we propose a solution scheme based on difference of submodular function optimization approach. We evaluate our scheme using detailed simulations and show that it performs on par with a much more computationally demanding difference of convex function optimization scheme. Moreover, the proposed scheme performs within a reasonable percentage of the optimal solution. We further demonstrate the advantage of the proposed scheme by studying its performance with variation in different network topology parameters.

ADVERTISEMENT ALLOCATION AND TRUST MECHANISMS DESIGN IN SOCIAL NETWORKS

Social network sites (SNS), such as Facebook, Google+ and Twitter, have attracted hundreds of millions of users daily since their appearance. Within SNS, users connect to each other, express their identity, disseminate information and form cooperation by interacting with their connected peers. The increasing popularity and ubiquity of SNS usage and the invaluable user behaviors and connections give birth to many applications and business models. We look into several important problems within the social network ecosystem. The first one is the SNS advertisement allocation problem. The other two are related to trust mechanisms design in social network setting, including local trust inference and global trust evaluation. In SNS advertising, we study the problem of advertisement allocation from the ad platform's angle, and discuss its differences with the advertising model in the search engine setting. By leveraging the connection between social networks and hyperbolic geometry, we propose to solve the problem via approximation using hyperbolic embedding and convex optimization. A hyperbolic embedding method, \hcm, is designed for the SNS ad allocation problem, and several components are introduced to realize the optimization formulation. We show the advantages of our new approach in solving the problem compared to the baseline integer programming (IP) formulation. In studying the problem of trust mechanisms in social networks, we consider the existence of distrust (i.e. negative trust) relationships, and differentiate between the concept of local trust and global trust in social network setting. In the problem of local trust inference, we propose a 2-D trust model. Based on the model, we develop a semiring-based trust inference framework. In global trust evaluation, we consider a general setting with conflicting opinions, and propose a consensus-based approach to solve the complex problem in signed trust networks.

JOINT ENERGY BEAMFORMING AND TIME ASSIGNMENT FOR COOPERATIVE WIRELESS POWERED NETWORKS

Wireless power transfer (WPT) and radio frequency (RF)-based energy har- vesting arouses a new wireless network paradigm termed as wireless powered com- munication network (WPCN), where some energy-constrained nodes are enabled to harvest energy from the RF signals transferred by other energy-sufficient nodes to support the communication operations in the network, which brings a promising approach for future energy-constrained wireless network design. In this paper, we focus on the optimal WPCN design. We consider a net- work composed of two communication groups, where the first group has sufficient power supply but no available bandwidth, and the second group has licensed band- width but very limited power to perform required information transmission. For such a system, we introduce the power and bandwidth cooperation between the two groups so that both group can accomplish their expected information delivering tasks. Multiple antennas are employed at the hybrid access point (H-AP) to en- hance both energy and information transfer efficiency and the cooperative relaying is employed to help the power-limited group to enhance its information transmission throughput. Compared with existing works, cooperative relaying, time assignment, power allocation, and energy beamforming are jointly designed in a single system. Firstly, we propose a cooperative transmission protocol for the considered system, where group 1 transmits some power to group 2 to help group 2 with information transmission and then group 2 gives some bandwidth to group 1 in return. Sec- ondly, to explore the information transmission performance limit of the system, we formulate two optimization problems to maximize the system weighted sum rate by jointly optimizing the time assignment, power allocation, and energy beamforming under two different power constraints, i.e., the fixed power constraint and the aver- age power constraint, respectively. In order to make the cooperation between the two groups meaningful and guarantee the quality of service (QoS) requirements of both groups, the minimal required data rates of the two groups are considered as constraints for the optimal system design. As both problems are non-convex and have no known solutions, we solve it by using proper variable substitutions and the semi-definite relaxation (SDR). We theoretically prove that our proposed solution method can guarantee to find the global optimal solution. Thirdly, consider that the WPCN has promising application potentials in future energy-constrained net- works, e.g., wireless sensor network (WSN), wireless body area network (WBAN) and Internet of Things (IoT), where the power consumption is very critical. We investigate the minimal power consumption optimal design for the considered co- operation WPCN. For this, we formulate an optimization problem to minimize the total consumed power by jointly optimizing the time assignment, power allocation, and energy beamforming under required data rate constraints. As the problem is also non-convex and has no known solutions, we solve it by using some variable substitutions and the SDR method. We also theoretically prove that our proposed solution method for the minimal power consumption design guarantees the global optimal solution. Extensive experimental results are provided to discuss the system performance behaviors, which provide some useful insights for future WPCN design. It shows that the average power constrained system achieves higher weighted sum rate than the fixed power constrained system. Besides, it also shows that in such a WPCN, relay should be placed closer to the multi-antenna H-AP to achieve higher weighted sum rate and consume lower total power.

Energy Management of a Battery-Ultracapacitor Hybrid Energy Storage System in Electric Vehicles

Electric vehicle (EV) batteries tend to have accelerated degradation due to high peak power and harsh charging/discharging cycles during acceleration and deceleration periods, particularly in urban driving conditions. An oversized energy storage system (ESS) can meet the high power demands; however, it suffers from increased size, volume and cost. In order to reduce the overall ESS size and extend battery cycle life, a battery-ultracapacitor (UC) hybrid energy storage system (HESS) has been considered as an alternative solution. In this work, we investigate the optimized configuration, design, and energy management of a battery-UC HESS. One of the major challenges in a HESS is to design an energy management controller for real-time implementation that can yield good power split performance. We present the methodologies and solutions to this problem in a battery-UC HESS with a DC-DC converter interfacing with the UC and the battery. In particular, a multi-objective optimization problem is formulated to optimize the power split in order to prolong the battery lifetime and to reduce the HESS power losses. This optimization problem is numerically solved for standard drive cycle datasets using Dynamic Programming (DP). Trained using the DP optimal results, an effective real-time implementation of the optimal power split is realized based on Neural Network (NN). This proposed online energy management controller is applied to a midsize EV model with a 360V/34kWh battery pack and a 270V/203Wh UC pack. The proposed online energy management controller effectively splits the load demand with high power efficiency and also effectively reduces the battery peak current. More importantly, a 38V-385Wh battery and a 16V-2.06Wh UC HESS hardware prototype and a real-time experiment platform has been developed. The real-time experiment results have successfully validated the real-time implementation feasibility and effectiveness of the real-time controller design for the battery-UC HESS. A battery State-of-Health (SoH) estimation model is developed as a performance metric to evaluate the battery cycle life extension effect. It is estimated that the proposed online energy management controller can extend the battery cycle life by over 60%.

POSITIVE FILTERED P_N METHOD FOR LINEAR TRANSPORT EQUATIONS AND THE ASSOCIATED OPTIMIZATION ALGORITHM

We propose a positive, accurate moment closure for linear kinetic transport equations based on a filtered spherical harmonic (FP_N) expansion in the angular variable. The FP_N moment equations are accurate approximations to linear kinetic equations, but they are known to suffer from the occurrence of unphysical, negative particle concentrations. The new positive filtered P_N (FP_N+) closure is developed to address this issue. The FP_N+ closure approximates the kinetic distribution by a spherical harmonic expansion that is non-negative on a finite, predetermined set of quadrature points. With an appropriate numerical PDE solver, the FP_N+ closure generates particle concentrations that are guaranteed to be non-negative. Under an additional, mild regularity assumption, we prove that as the moment order tends to infinity, the FP_N+ approximation converges, in the L2 sense, at the same rate as the FP_N approximation; numerical tests suggest that this assumption may not be necessary. By numerical experiments on the challenging line source benchmark problem, we confirm that the FP_N+ method indeed produces accurate and non-negative solutions. To apply the FP_N+ closure on problems at large temporal-spatial scales, we develop a positive asymptotic preserving (AP) numerical PDE solver. We prove that the propose AP scheme maintains stability and accuracy with standard mesh sizes at large temporal-spatial scales, while, for generic numerical schemes, excessive refinements on temporal-spatial meshes are required. We also show that the proposed scheme preserves positivity of the particle concentration, under some time step restriction. Numerical results confirm that the proposed AP scheme is capable for solving linear transport equations at large temporal-spatial scales, for which a generic scheme could fail. Constrained optimization problems are involved in the formulation of the FP_N+ closure to enforce non-negativity of the FP_N+ approximation on the set of quadrature points. These optimization problems can be written as strictly convex quadratic programs (CQPs) with a large number of inequality constraints. To efficiently solve the CQPs, we propose a constraint-reduced variant of a Mehrotra-predictor-corrector algorithm, with a novel constraint selection rule. We prove that, under appropriate assumptions, the proposed optimization algorithm converges globally to the solution at a locally q-quadratic rate. We test the algorithm on randomly generated problems, and the numerical results indicate that the combination of the proposed algorithm and the constraint selection rule outperforms other compared constraint-reduced algorithms, especially for problems with many more inequality constraints than variables.

Joint Optimization for Social Content Delivery in Wireless Networks

Over the last decade, success of social networks has significantly reshaped how people consume information. Recommendation of contents based on user profiles is well-received. However, as users become dominantly mobile, little is done to consider the impacts of the wireless environment, especially the capacity constraints and changing channel. In this dissertation, we investigate a centralized wireless content delivery system, aiming to optimize overall user experience given the capacity constraints of the wireless networks, by deciding what contents to deliver, when and how. We propose a scheduling framework that incorporates content-based reward and deliverability. Our approach utilizes the broadcast nature of wireless communication and social nature of content, by multicasting and precaching. Results indicate this novel joint optimization approach outperforms existing layered systems that separate recommendation and delivery, especially when the wireless network is operating at maximum capacity. Utilizing limited number of transmission modes, we significantly reduce the complexity of the optimization. We also introduce the design of a hybrid system to handle transmissions for both system recommended contents ('push') and active user requests ('pull'). Further, we extend the joint optimization framework to the wireless infrastructure with multiple base stations. The problem becomes much harder in that there are many more system configurations, including but not limited to power allocation and how resources are shared among the base stations ('out-of-band' in which base stations transmit with dedicated spectrum resources, thus no interference; and 'in-band' in which they share the spectrum and need to mitigate interference). We propose a scalable two-phase scheduling framework: 1) each base station obtains delivery decisions and resource allocation individually; 2) the system consolidates the decisions and allocations, reducing redundant transmissions. Additionally, if the social network applications could provide the predictions of how the social contents disseminate, the wireless networks could schedule the transmissions accordingly and significantly improve the dissemination performance by reducing the delivery delay. We propose a novel method utilizing: 1) hybrid systems to handle active disseminating requests; and 2) predictions of dissemination dynamics from the social network applications. This method could mitigate the performance degradation for content dissemination due to wireless delivery delay. Results indicate that our proposed system design is both efficient and easy to implement.

RISK-BASED MULTIOBJECTIVE PATH PLANNING AND DESIGN OPTIMIZATION FOR UNMANNED AERIAL VEHICLES

Safe operation of unmanned aerial vehicles (UAVs) over populated areas requires reducing the risk posed by a UAV if it crashed during its operation. We considered several types of UAV risk-based path planning problems and developed techniques for estimating the risk to third parties on the ground. The path planning problem requires making trade-offs between risk and flight time. Four optimization approaches for solving the problem were tested; a network-based approach that used a greedy algorithm to improve the original solution generated the best solutions with the least computational effort. Additionally, an approach for solving a combined design and path planning problems was developed and tested. This approach was extended to solve robust risk-based path planning problem in which uncertainty about wind conditions would affect the risk posed by a UAV.

Multi-level, Multi-stage and Stochastic Optimization Models for Energy Conservation in Buildings for Federal, State and Local Agencies

Energy Conservation Measure (ECM) project selection is made difficult given real-world constraints, limited resources to implement savings retrofits, various suppliers in the market and project financing alternatives. Many of these energy efficient retrofit projects should be viewed as a series of investments with annual returns for these traditionally risk-averse agencies. Given a list of ECMs available, federal, state and local agencies must determine how to implement projects at lowest costs. The most common methods of implementation planning are suboptimal relative to cost. Federal, state and local agencies can obtain greater returns on their energy conservation investment over traditional methods, regardless of the implementing organization. This dissertation outlines several approaches to improve the traditional energy conservations models. Any public buildings in regions with similar energy conservation goals in the United States or internationally can also benefit greatly from this research. Additionally, many private owners of buildings are under mandates to conserve energy e.g., Local Law 85 of the New York City Energy Conservation Code requires any building, public or private, to meet the most current energy code for any alteration or renovation. Thus, both public and private stakeholders can benefit from this research. The research in this dissertation advances and presents models that decision-makers can use to optimize the selection of ECM projects with respect to the total cost of implementation. A practical application of a two-level mathematical program with equilibrium constraints (MPEC) improves the current best practice for agencies concerned with making the most cost-effective selection leveraging energy services companies or utilities. The two-level model maximizes savings to the agency and profit to the energy services companies (Chapter 2). An additional model presented leverages a single congressional appropriation to implement ECM projects (Chapter 3). Returns from implemented ECM projects are used to fund additional ECM projects. In these cases, fluctuations in energy costs and uncertainty in the estimated savings severely influence ECM project selection and the amount of the appropriation requested. A risk aversion method proposed imposes a minimum on the number of “of projects completed in each stage. A comparative method using Conditional Value at Risk is analyzed. Time consistency was addressed in this chapter. This work demonstrates how a risk-based, stochastic, multi-stage model with binary decision variables at each stage provides a much more accurate estimate for planning than the agency’s traditional approach and deterministic models. Finally, in Chapter 4, a rolling-horizon model allows for subadditivity and superadditivity of the energy savings to simulate interactive effects between ECM projects. The approach makes use of inequalities (McCormick, 1976) to re-express constraints that involve the product of binary variables with an exact linearization (related to the convex hull of those constraints). This model additionally shows the benefits of learning between stages while remaining consistent with the single congressional appropriations framework.