Philip Twu

Controllability of homogeneous single-leader networks

This paper addresses an aspect of controllability in a single-leader network when the agents are homogeneous. In such a network, indices are not assigned to the individual agents and controllability, which is typically a point to point property, now becomes a point to set property, where the set consists of all permutations of the target point. Agent homogeneity allows for choice of the optimal target point permutation that minimizes the distance to the systems reachable subspace, which we show is equivalent to finding a minimum sum-of-squares clustering with constraints on the cluster sizes. However, finding the optimal permutation is NP-hard. Methods are presented to find suboptimal permutations in the general case and the optimal permutation when the agent positions are 1-D.

A controlled-precision algorithm for mode-switching optimization

This paper describes an adaptive-precision algorithm for solving a general optimal mode-scheduling problem in switched-mode dynamical systems. The problem is complicated by the fact that the controlled variable has discrete and continuous components, namely the sequence of modes and the switching times between them. Recently we developed a gradient-descent algorithm whose salient feature is that its descent at a given iteration is independent of the length (number of modes) of the schedule, hence it is suitable to situations where the schedule-lengths at successive iterations grow unboundedly. The computation of the descent direction requires grid-based approximations to solve differential equations as well as minimize certain functions on uncountable sets. However, the algorithms convergence analysis assumes exact computations, and it breaks down when approximations are used, because the descent directions are discontinuous in the problem parameters. The purpose of the present paper is to overcome this theoretical gap and its computational implications by developing an implementable, provably-convergent, adaptive-precision algorithm that controls the approximation levels by balancing precision with computational workloads.

On-line optimal timing control of switched systems

This paper considers a real-time algorithm for performance optimization of switched-mode hybrid dynamical systems. The controlled parameter consists of the switching times between the modes, and the cost criterion has the form of the integral of a performance function defined on the systems state trajectory. The dynamic response functions (state equations) associated with the modes are not known in advance; rather, at each time t, they are estimated for all future times s ≥ t. A first-order algorithm is proposed and its behavior is analyzed in terms of its convergence rate. Finally, an example of a mobile robot tracking a moving target while avoiding obstacles is presented.

Merging and Spacing of Heterogeneous Aircraft in Support of NextGen

The Federal Aviation Administration’s NextGen program aims to increase the capacity of the national airspace, while ensuring the safety of aircraft. This paper provides a distributed merging and spacing algorithm that maximizes the throughput at the terminal phase of flight, using information communicated between neighboring aircraft through the ADS-B framework. Aircraft belonging to a mixed fleet negotiate with each other and use dual decomposition to reach an agreement on optimal merging times, with respect to a pairwise cost, while ensuring proper interaircraft spacing for the respective aircraft types. A set of sufficient conditions on the geometry and operating conditions of merging forks is provided to identify when proper interaircraft spacing can always be achieved using the proposed algorithm for any combination of merging aircraft. Also, optimal decentralized controllers are derived for merging air traffic when operating under such conditions. The performance of the presented algorithm is verified through computer simulations.

Air traffic maximization for the terminal phase of flight under FAA's NextGen framework

The NextGen program is the FAAs response to the ever increasing air traffic, that provides tools to increase the capacity of national airspace, while ensuring the safety of aircraft. In support of this vision, this paper provides a decentralized algorithm based on dual decomposition for safe merging and spacing of aircraft at the terminal phase of the flight. Aircraft negotiate optimal merging times that ensure safety, while penalizing deviations from the nominal path. We provide feasibility conditions for the safe merging of all incoming legs of flight and put the viability of the proposed algorithm to the test through simulations.

Distributed scheduling for air traffic throughput maximization during the terminal phase of flight

FAAs NextGen program aims at increasing the capacity of the national airspace, while ensuring the safety of aircraft. This paper provides a distributed merging and spacing algorithm that maximizes the throughput at the terminal phase of flight using the information provided through the ADS-B framework. Using dual decomposition, aircraft negotiate with each other and reach an agreement on optimal merging times, with respect to an associated cost, that ensures proper inter-aircraft spacing. We provide a feasibility analysis that gives sufficient conditions to guarantee that proper spacing is achievable and derive maximum throughput controllers based on the air traffic characteristics of the merging flight paths.

A Hardware Testbed for Multi-UAV Collaborative Ground Convoy Protection in Dynamic Environments

In this paper, we will present a hardware testbed for multi-UAV systems that bridges the gap between algorithm design and field deployment. The testbed allows for UAV coordination algorithms, that have been shown to work in simulation, to be further tested in an environment where limited on-board computational resources, wireless communication constraints, environmental noise, and differences in the UAVs modeled versus actual dynamics come into effect. In particular, we will introduce an efficient assignment algorithm. This algorithm is used in a multi-UAV ground convoy protection scenario, where UAVs escort the ground convoy and are deployed to check potential threats along the way.

Optimal decentralization of multi-agent motions

This paper addresses how to optimally decentralize the execution of a multi-agent mission defined at the trajectory-level, where the information flow among agents in the system are limited by a predefined network topology. Each agents decentralized controllers are constrained to be parameterized functions of the relative distances and angles between itself and its neighbors. Starting with a discussion on what it means for a controller to be considered decentralized, the problem is posed as an optimal control problem for switched autonomous systems. We derive optimality conditions for the parameters defining each mode for each agent, which is combined with optimality conditions for when to switch between consecutive modes. Simulations are used to showcase the operation of the proposed optimal decentralization algorithm on a complex example.

Graph Process Specifications for Hybrid Networked Systems

Abstract Research in multi-agent systems has supplied a diverse collection of decentralized controllers to accomplish specific tasks. When agents execute a sequence of these controllers, the network behaves as a hybrid system, where the dynamics in each mode evolve according to a single controller in the sequence. This paper presents a formal specification for such a system that describes the underlying graph process associated with the information flow amongst agents in each mode. Since many decentralized controllers require specific information graph topologies in order to function properly, a problem that arises is that the information graph at the termination of one mode may not be sufficient to initiate the next mode in the sequence. We propose a Graph Process Specification (GPS) framework that describes the graph process. Furthermore, if two modes cannot be executed consecutively, a GPS provides a way to determine which modes can be inserted in between them to make the resulting sequence executable. We formally define a GPS, describe its execution, and provide examples that showcase its usage in composing together multiple decentralized controllers within a multi-agent system.

A measure of heterogeneity in multi-agent systems

Heterogeneous multi-agent systems have previously been studied and deployed to solve a number of different tasks. Despite this, we still lack a basic understanding of just what “heterogeneity” really is. For example, what makes one team of agents more heterogeneous than another? In this paper, we address this issue by proposing a measure of heterogeneity. This measure takes both the complexity and disparity of a system into account by combining different notions of entropy. The result is a formulation that is both easily computable and makes intuitive sense. An overview is given of existing metrics for diversity found in various fields such as biology, economics, as well as robotics, followed by a discussion of their relative merits and demerits. We show how our proposed measure of heterogeneity overcomes problematic issues identified across the previous metrics. Finally, we discuss how to apply the new measure of heterogeneity specifically to multi-agent systems by using the notion of a common task-space to compare agents with different capabilities.