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.

Time-Reversal Massive Multipath Effect and Bandwidth Heterogeneity

The proliferation of new mobile communication devices, such as smartphones and tablets, has led to an exponential growth in network traffic. The demand for supporting the fast-growing consumer data rates urges the wireless service providers and researchers to seek a new efficient radio access technology, which is the so-called 5G technology, beyond what current 4G LTE can provide. On the other hand, ubiquitous RFID tags, sensors, actuators, mobile phones and etc. cut across many areas of modern-day living, which offers the ability to measure, infer and understand the environmental indicators. The proliferation of these devices creates the term of the Internet of Things (IoT). For the researchers and engineers in the field of wireless communication, the exploration of new effective techniques to support 5G communication and the IoT becomes an urgent task, which not only leads to fruitful research but also enhance the quality of our everyday life. Massive MIMO, which has shown the great potential in improving the achievable rate with a very large number of antennas, has become a popular candidate. However, the requirement of deploying a large number of antennas at the base station may not be feasible in indoor scenarios. Does there exist a good alternative that can achieve similar system performance to massive MIMO for indoor environment? In this dissertation, we address this question by proposing the time-reversal technique as a counterpart of massive MIMO in indoor scenario with the massive multipath effect. It is well known that radio signals will experience many multipaths due to the reflection from various scatters, especially in indoor environments. The traditional TR waveform is able to create a focusing effect at the intended receiver with very low transmitter complexity in a severe multipath channel. TR's focusing effect is in essence a spatial-temporal resonance effect that brings all the multipaths to arrive at a particular location at a specific moment. We show that by using time-reversal signal processing, with a sufficiently large bandwidth, one can harvest the massive multipaths naturally existing in a rich-scattering environment to form a large number of virtual antennas and achieve the desired massive multipath effect with a single antenna. Further, we explore the optimal bandwidth for TR system to achieve maximal spectral efficiency. Through evaluating the spectral efficiency, the optimal bandwidth for TR system is found determined by the system parameters, e.g., the number of users and backoff factor, instead of the waveform types. Moreover, we investigate the tradeoff between complexity and performance through establishing a generalized relationship between the system performance and waveform quantization in a practical communication system. It is shown that a 4-bit quantized waveforms can be used to achieve the similar bit-error-rate compared to the TR system with perfect precision waveforms. Besides 5G technology, Internet of Things (IoT) is another terminology that recently attracts more and more attention from both academia and industry. In the second part of this dissertation, the heterogeneity issue within the IoT is explored. One of the significant heterogeneity considering the massive amount of devices in the IoT is the device heterogeneity, i.e., the heterogeneous bandwidths and associated radio-frequency (RF) components. The traditional middleware techniques result in the fragmentation of the whole network, hampering the objects interoperability and slowing down the development of a unified reference model for the IoT. We propose a novel TR-based heterogeneous system, which can address the bandwidth heterogeneity and maintain the benefit of TR at the same time. The increase of complexity in the proposed system lies in the digital processing at the access point (AP), instead of at the devices' ends, which can be easily handled with more powerful digital signal processor (DSP). Meanwhile, the complexity of the terminal devices stays low and therefore satisfies the low-complexity and scalability requirement of the IoT. Since there is no middleware in the proposed scheme and the additional physical layer complexity concentrates on the AP side, the proposed heterogeneous TR system better satisfies the low-complexity and energy-efficiency requirement for the terminal devices (TDs) compared with the middleware approach.

Spatial and Temporal Dynamics of Larval Atlantic Menhaden on the East Coast of the United States

Atlantic Menhaden Brevoortia tyrannus is a commercially and ecologically important forage fish abundant on the Atlantic Coast of the United States. We conducted spatial and temporal analyses of larval Atlantic Menhaden using data collected from two large-scale ichthyoplankton programs during 1977-1987 and 1999-2013 to construct indices of larval abundance and survival over time, evaluate how environmental factors affect early life survival, and examine how larvae are distributed in space to gain knowledge on spawning and larval dispersal. Over time, we found larval abundance to increase, while early life survival declined. Coastal temperature, wind speed, and Atlantic Multidecadal Oscillation were found to potentially explain some of this decline in survival. Over both periods, we found evidence spawning predominantly occurs near shore, from New York to North Carolina, increasing in intensity southwards. While the general spatial patterns were consistent, we observed some localized variation and overall expansion of occupied area by larvae.