Safe Sequential Path Planning Under Disturbances and Imperfect Information

Multi-UAV systems are safety-critical, and guarantees must be made to ensure no unsafe configurations occur. Hamilton-Jacobi (HJ) reachability is ideal for analyzing such safety-critical systems; however, its direct application is limited to small-scale systems of no more than two vehicles due to an exponentially-scaling computational complexity. Previously, the sequential path planning (SPP) method, which assigns strict priorities to vehicles, was proposed; SPP allows multi-vehicle path planning to be done with a linearly-scaling computational complexity. However, the previous formulation assumed that there are no disturbances, and that every vehicle has perfect knowledge of higher-priority vehicles' positions. In this paper, we make SPP more practical by providing three different methods to account for disturbances in dynamics and imperfect knowledge of higher-priority vehicles' states. Each method has different assumptions about information sharing. We demonstrate our proposed methods in simulations.Comment: American Control Conference, 201

Decentralized Connectivity-Preserving Deployment of Large-Scale Robot Swarms

We present a decentralized and scalable approach for deployment of a robot swarm. Our approach tackles scenarios in which the swarm must reach multiple spatially distributed targets, and enforce the constraint that the robot network cannot be split. The basic idea behind our work is to construct a logical tree topology over the physical network formed by the robots. The logical tree acts as a backbone used by robots to enforce connectivity constraints. We study and compare two algorithms to form the logical tree: outwards and inwards. These algorithms differ in the order in which the robots join the tree: the outwards algorithm starts at the tree root and grows towards the targets, while the inwards algorithm proceeds in the opposite manner. Both algorithms perform periodic reconfiguration, to prevent suboptimal topologies from halting the growth of the tree. Our contributions are (i) The formulation of the two algorithms; (ii) A comparison of the algorithms in extensive physics-based simulations; (iii) A validation of our findings through real-robot experiments.Comment: 8 pages, 8 figures, submitted to IROS 201

Safe Sequential Path Planning of Multi-Vehicle Systems via Double-Obstacle Hamilton-Jacobi-Isaacs Variational Inequality

We consider the problem of planning trajectories for a group of $N$ vehicles, each aiming to reach its own target set while avoiding danger zones of other vehicles. The analysis of problems like this is extremely important practically, especially given the growing interest in utilizing unmanned aircraft systems for civil purposes. The direct solution of this problem by solving a single-obstacle Hamilton-Jacobi-Isaacs (HJI) variational inequality (VI) is numerically intractable due to the exponential scaling of computation complexity with problem dimensionality. Furthermore, the single-obstacle HJI VI cannot directly handle situations in which vehicles do not have a common scheduled arrival time. Instead, we perform sequential path planning by considering vehicles in order of priority, modeling higher-priority vehicles as time-varying obstacles for lower-priority vehicles. To do this, we solve a double-obstacle HJI VI which allows us to obtain the reach-avoid set, defined as the set of states from which a vehicle can reach its target while staying within a time-varying state constraint set. From the solution of the double-obstacle HJI VI, we can also extract the latest start time and the optimal control for each vehicle. This is a first application of the double-obstacle HJI VI which can handle systems with time-varying dynamics, target sets, and state constraint sets, and results in computation complexity that scales linearly, as opposed to exponentially, with the number of vehicles in consideration.Comment: European Control Conference 201

Adaptive Governance and Evolving Solutions to Natural Resource Conflicts

New Zealand is facing increasing challenges in managing natural resources (land, freshwater, marine space and air quality) under pressures from domestic (population growth, agricultural intensification, cultural expectations) and international (climate change) sources. These challenges can be described in terms of managing ‘wicked problems’; i.e. problems that may not be understood fully until they have been solved, where stakeholders have different world views and frames for understanding the problem, the constraints affecting the problem and the resources required to solve it change over time, and no complete solution is ever actually found. Adaptive governance addresses wicked problems through a framework to engage stakeholders in a participative process to create a long term vision. The vision must identify competing goals and a process for balancing them over time that acknowledges conflicts cannot always be resolved in a single lasting decision. Circumstances, goals and priorities can all vary over time and by region. The Resource Management Act can be seen as an adaptive governance structure where frameworks for resources such as water may take years to evolve and decades to fully implement. Adaptive management is about delivery through an incremental/experimental approach, limits on the certainty that governments can provide and stakeholders can demand, and flexibility in processes and results. In New Zealand it also requires balancing central government expertise and resources, with local authorities which can reflect local goals and knowledge, but have varying resources and can face quite distinct issues of widely differing severity. It is important to signal the incremental, overlapping, iterative and time-consuming nature of the work involved in developing and implementing adaptive governance and management frameworks. Managing the expectations of those involved as to the nature of the process and their role in it, and the scope and timing of likely outcomes, is key to sustaining participation.Adaptive capacity; governance; resilience