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.

RESILIENCE OF NETWORKED INFRASTRUCTURE WITH EVOLVING COMPONENT CONDITIONS: A PAVEMENT NETWORK APPLICATION

This thesis deals with quantifying the resilience of a network of pavements. Calculations were carried out by modeling network performance under a set of possible damage-meteorological scenarios with known probability of occurrence. Resilience evaluation was performed a priori while accounting for optimal preparedness decisions and additional response actions that can be taken under each of the scenarios. Unlike the common assumption that the pre-event condition of all system components is uniform, fixed, and pristine, component condition evolution was incorporated herein. For this purpose, the health of the individual system components immediately prior to hazard event impact, under all considered scenarios, was associated with a serviceability rating. This rating was projected to reflect both natural deterioration and any intermittent improvements due to maintenance. The scheme was demonstrated for a hypothetical case study involving Laguardia Airport. Results show that resilience can be impacted by the condition of the infrastructure elements, their natural deterioration processes, and prevailing maintenance plans. The findings imply that, in general, upper bound values are reported in ordinary resilience work, and that including evolving component conditions is of value.