A Dynamic Boundary Guarding Problem with Translating Targets

We introduce a problem in which a service vehicle seeks to guard a deadline (boundary) from dynamically arriving mobile targets. The environment is a rectangle and the deadline is one of its edges. Targets arrive continuously over time on the edge opposite the deadline, and move towards the deadline at a fixed speed. The goal for the vehicle is to maximize the fraction of targets that are captured before reaching the deadline. We consider two cases; when the service vehicle is faster than the targets, and; when the service vehicle is slower than the targets. In the first case we develop a novel vehicle policy based on computing longest paths in a directed acyclic graph. We give a lower bound on the capture fraction of the policy and show that the policy is optimal when the distance between the target arrival edge and deadline becomes very large. We present numerical results which suggest near optimal performance away from this limiting regime. In the second case, when the targets are slower than the vehicle, we propose a policy based on servicing fractions of the translational minimum Hamiltonian path. In the limit of low target speed and high arrival rate, the capture fraction of this policy is within a small constant factor of the optimal.Comment: Extended version of paper for the joint 48th IEEE Conference on Decision and Control and 28th Chinese Control Conferenc

Combining a hierarchical task network planner with a constraint satisfaction solver for assembly operations involving routing problems in a multi-robot context

This work addresses the combination of a symbolic hierarchical task network planner and a constraint satisfaction solver for the vehicle routing problem in a multi-robot context for structure assembly operations. Each planner has its own problem domain and search space, and the article describes how both planners interact in a loop sharing information in order to improve the cost of the solutions. The vehicle routing problem solver gives an initial assignment of parts to robots, making the distribution based on the distance among parts and robots, trying also to maximize the parallelism of the future assembly operations evaluating during the process the dependencies among the parts assigned to each robot. Then, the hierarchical task network planner computes a scheduling for the given assignment and estimates the cost in terms of time spent on the structure assembly. This cost value is then given back to the vehicle routing problem solver as feedback to compute a better assignment, closing the loop and repeating again the whole process. This interaction scheme has been tested with different constraint satisfaction solvers for the vehicle routing problem. The article presents simulation results in a scenario with a team of aerial robots assembling a structure, comparing the results obtained with different configurations of the vehicle routing problem solver and showing the suitability of using this approach.Unión Europea ARCAS FP7-ICT-287617Unión Europea H2020-ICT-644271Unión europea H2020-ICT-73166

A Framework for Developing and Integrating Effective Routing Strategies Within the Emergency Management Decision-Support System, Research Report 11-12

This report describes the modeling, calibration, and validation of a VISSIM traffic-flow simulation of the San José, California, downtown network and examines various evacuation scenarios and first-responder routings to assess strategies that would be effective in the event of a no-notice disaster. The modeled network required a large amount of data on network geometry, signal timings, signal coordination schemes, and turning-movement volumes. Turning-movement counts at intersections were used to validate the network with the empirical formula-based measure known as the GEH statistic. Once the base network was tested and validated, various scenarios were modeled to estimate evacuation and emergency vehicle arrival times. Based on these scenarios, a variety of emergency plans for San José’s downtown traffic circulation were tested and validated. The model could be used to evaluate scenarios in other communities by entering their community-specific data

A layered fuzzy logic controller for nonholonomic car-like robot

A system for real time navigation of a nonholonomic car-like robot in a dynamic environment consists of two layers is described: a Sugeno-type fuzzy motion planner; and a modified proportional navigation based fuzzy controller. The system philosophy is inspired by human routing when moving between obstacles based on visual information including right and left views to identify the next step to the goal. A Sugeno-type fuzzy motion planner of four inputs one output is introduced to give a clear direction to the robot controller. The second stage is a modified proportional navigation based fuzzy controller based on the proportional navigation guidance law and able to optimize the robot's behavior in real time, i.e. to avoid stationary and moving obstacles in its local environment obeying kinematics constraints. The system has an intelligent combination of two behaviors to cope with obstacle avoidance as well as approaching a target using a proportional navigation path. The system was simulated and tested on different environments with various obstacle distributions. The simulation reveals that the system gives good results for various simple environments

An Optimal Control Theory for the Traveling Salesman Problem and Its Variants

We show that the traveling salesman problem (TSP) and its many variants may be modeled as functional optimization problems over a graph. In this formulation, all vertices and arcs of the graph are functionals; i.e., a mapping from a space of measurable functions to the field of real numbers. Many variants of the TSP, such as those with neighborhoods, with forbidden neighborhoods, with time-windows and with profits, can all be framed under this construct. In sharp contrast to their discrete-optimization counterparts, the modeling constructs presented in this paper represent a fundamentally new domain of analysis and computation for TSPs and their variants. Beyond its apparent mathematical unification of a class of problems in graph theory, the main advantage of the new approach is that it facilitates the modeling of certain application-specific problems in their home space of measurable functions. Consequently, certain elements of economic system theory such as dynamical models and continuous-time cost/profit functionals can be directly incorporated in the new optimization problem formulation. Furthermore, subtour elimination constraints, prevalent in discrete optimization formulations, are naturally enforced through continuity requirements. The price for the new modeling framework is nonsmooth functionals. Although a number of theoretical issues remain open in the proposed mathematical framework, we demonstrate the computational viability of the new modeling constructs over a sample set of problems to illustrate the rapid production of end-to-end TSP solutions to extensively-constrained practical problems.Comment: 24 pages, 8 figure