Waqar A. Malik

An approximation algorithm for a symmetric Generalized Multiple Depot, Multiple Travelling Salesman Problem

In this paper, we present an algorithm with an approximation factor of 2 for a Generalized, Multiple Depot, Multiple Travelling Salesman Problem (GMTSP) when the costs are symmetric and satisfy the triangle inequality. The algorithm requires finding a degree constrained minimum spanning tree which we compute using a Lagrangian relaxation.

A Mixed Integer Linear Program for Solving a Multiple Route Taxi Scheduling Problem

Aircraft movements on taxiways at busy airports often create bottlenecks. This paper introduces a mixed integer linear program to solve a Multiple Route Aircraft Taxi Scheduling Problem. The outputs of the model are in the form of optimal taxi schedules, which include routing decisions for taxiing aircraft. The model extends an existing single route formulation to include routing decisions. An efficient comparison framework compares the multi-route formulation and the single route formulation. The multi-route model is exercised for east side airport surface traffic at Dallas/Fort Worth International Airport to determine if any arrival taxi time savings can be achieved by allowing arrivals to have two taxi routes: a route that crosses an active departure runway and a perimeter route that avoids the crossing. Results indicate that the multi-route formulation yields reduced arrival taxi times over the single route formulation only when a perimeter taxiway is used. In conditions where the departure aircraft are given an optimal and fixed takeoff sequence, accumulative arrival taxi time savings in the multi-route formulation can be as high as 3.6 hours more than the single route formulation. If the departure sequence is not optimal, the multi-route formulation results in less taxi time savings made over the single route formulation, but the average arrival taxi time is significantly decreased.

On the Modeling of the Viscoelastic Response of Embryonic Tissues

Forgacs et al. have developed a continuum model for cellular aggregates that has at its basis the work of Steinberg and co-workers concerning the coalescence of cells that takes into account surface tension effects, to describe the response of embryonic tissues. Here, we propose a solid model that reflects the fact that such embryonic tissues in the bulk (not at the cellular level) behave like solids rather than as fluids. The model stems from a robust thermodynamic framework and we show that our model fits the experimental data exceptionally well.

A lagrangian-based algorithm for a combinatorial motion planning problem

We consider a combinatorial motion planning problem (CMP) that naturally arises in many applications involving unmanned aerial vehicles (UAVs) with fuel and motion constraints. The motion constraint we consider is the inability of a vehicle to turn at an arbitrary yaw rate. The CMP is a generalization of a single travelling salesman problem and is NP-hard. In this paper, we exploit the combinatorial structure of the problem and provide heuristics with computational results to address the same.

Combinatorial Motion Planning of Multiple Vehicle Systems

In this paper, we are concerned with the development of approximation algorithms for the combinatorial motion planning of a collection of m vehicles. Specifically, we consider the following multiple depot, generalized multiple traveling salesmen problem (GMTSP). We are given m vehicles that start at possibly different locations and n targets that must be visited. The problem is to choose at most p les m vehicles so that (1) each target is visited by exactly one of the chosen vehicles and (2) the cost of the tours of the chosen vehicles is a minimum among all possible choices and their corresponding tours of vehicles. The criteria for the cost of tours considered is the total distance (total cost of edges) traveled by the entire collection. This problem is a generalization of the symmetric traveling salesman problem (TSP) and is NP-hard. We show that there is a 2-approx algorithm for this problem. We also provide a branch and bound procedure for this problem

On the Synthesis of Fixed Structure Controllers Satisfying given Performance Criteria

Abstract Many practical applications require the design of fixed order and structure feedback controllers. It is often required that these feedback controllers satisfy some specified criterion. This class of fixed structure controller synthesis problems can be reduced to the determination of a real controller parameter vector (or simply a controller), K, so that a family of complex polynomials, linear in the parameters of the controllers, is Hurwitz. A novel feature of this paper is the exploitation of the Interlacing Property (IP) of complex Hurwitz polynomials to systematically generate an arbitrarily large number of sets of linear inequalities in K. The simultaneous stabilization of the family of complex polynomials provides an approximation of the required set of controllers. We provide examples of the applicability of the proposed methodology to the synthesis and design of fixed order controllers.

Sensor based localization for multiple mobile robots using virtual link

An approach for multiple mobile robot localization using inexpensive infrared sensors and CMOS cameras is presented. A multiple robot system is treated as a virtual linked robot. Using the virtual link length and the relative heading information in conjunction with sensor scan data for each robot in the system, the entire system can effectively be localized without investing heavily in sensors. In order to facilitate collaboration and exploit geometry, a team must be able to extract salient information from the collective sensing of all its members. By collecting and fusing sensor information from multiple, distinct positions, the effective resolution of the space can be improved beyond that of the individual measurements. The proposed localization method is verified via both simulation and experiment.

Synthesis of absolutely stabilizing controllers

In this paper, we consider the synthesis of fixed order controllers for nonlinear systems with sector bounded nonlinearities. We construct an inner and outer approximation of the set of absolutely stabilizing linear controllers by casting the closed loop system as a Lure-Postnikov system. The inner approximation is based on the well-known sufficient conditions that require strict positive realness (SPR) of open loop transfer function (possibly with some multipliers) and a characterization of SPR transfer functions that require a family of complex polynomials to be Hurwitz. The outer approximation is based on the condition that the open loop transfer function must have infinite gain margin, which translates to a family of real polynomials being Hurwitz. We illustrate the proposed methodology through the construction of an inner and outer approximation of absolutely stabilizing controllers for a mechanical system.

SYNTHESIS OF FIXED STRUCTURE CONTROLLERS FOR DISCRETE TIME SYSTEMS

In this paper, we develop a linear programming approach to the synthesis of stabilizing fixed structure controllers for a class of linear time invariant discretetime systems. The stabilization of this class of systems requires the determination of a real controller parameter vector (or simply, a controller), K, so that a family of real polynomials, affine in the parameters of the controllers, is Schur. An attractive feature of the paper is the exploitation of the interlacing property of Schur polynomials (based on the characterization in terms of Tchebyshev polynomials) to systematically generate an arbitrarily large large number of sets of linear inequalities in K. The union of the feasible sets of linear inequalities provides an approximation of the set of all controllers, K, which render P (z, K) Schur. Illustrative examples are provided to show the applicability of the proposed methodology. Copyright c ©2005 IFAC

A Recursive Algorithm for Reducing the Order of Controller while Guaranteeing Performance

In this paper, a procedure for the recursive reduction of the order of the stabilizing controller is introduced for SISO systems. Since all achievable closed loop maps are affine in the Q (Youla) parameter, we devise a sufficient condition for order reduction: Suppose there exists a Q parameter to induce a pole zero cancellation in the closed loop map to decrease the order of the closed loop system by m, then the corresponding controller is reduced in order by m. By appropriately choosing Q, we formulate a procedure for the recursive reduction of the order of the stabilizing controller and guarantee a performance describable through a complex stabilization technique.