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Performance characterization of a reconfigurable planararray digital microfluidic system
 IEEE Transactions on ComputerAided Design of Integrated Circuits and Systems
, 2006
"... Abstract—This paper describes a computational approach to designing a digital microfluidic system (DMFS) that can be rapidly reconfigured for new biochemical analyses. Such a “labonachip” system for biochemical analysis, based on electrowetting or dielectrophoresis, must coordinate the motions of ..."
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Abstract—This paper describes a computational approach to designing a digital microfluidic system (DMFS) that can be rapidly reconfigured for new biochemical analyses. Such a “labonachip” system for biochemical analysis, based on electrowetting or dielectrophoresis, must coordinate the motions of discrete droplets or biological cells using a planar array of electrodes. The authors have earlier introduced a layoutbased system and demonstrated its flexibility through simulation, including the system’s ability to perform multiple assays simultaneously. Since arraylayout design and dropletrouting strategies are closely related in such a DMFS, their goal is to provide designers with algorithms that enable rapid simulation and control of these DMFS devices. In this paper, the effects of variations in the basic arraylayout design, dropletrouting control algorithms, and droplet spacing on system performance are characterized. DMFS arrays with hardware limited rowcolumn addressing are considered, and a polynomialtime algorithm for coordinating droplet movement under such hardware limitations is developed. To demonstrate the capabilities of our system, we describe example scenarios, including dilution control and minimalist layouts, in which our system can be successfully applied. Index Terms—Array layout, biochips, digital microfluidics, droplet routing, labonachip, performance analysis, row–column addressing. I.
Coordinating Multiple Droplets in Planar Array . . .
"... In this paper we present an approach to coordinate the motions of droplets in digital microfluidic systems, a new class of labonachip systems for biochemical analysis. A digital microfluidic system typically consists of a planar array of cells with electrodes that control the droplets. The primar ..."
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In this paper we present an approach to coordinate the motions of droplets in digital microfluidic systems, a new class of labonachip systems for biochemical analysis. A digital microfluidic system typically consists of a planar array of cells with electrodes that control the droplets. The primary challenge in using dropletbased systems is that they require the simultaneous coordination of a potentially large number of droplets on the array as the droplets move, mix, and split. In this paper we describe a generalpurpose system that uses simple algorithms and yet is versatile. First, we present a semiautomated approach to generate the array layout in terms of components. Next, we discuss simple algorithms to select destination components for the droplets and a decentralized scheme for components to route the droplets on the array. These are then combined into a reconfigurable system that has been simulated in software to perform analyses such as the DNA polymerase chain reaction. The algorithms have been able to successfully coordinate hundreds of droplets simultaneously and perform one or more chemical analyses in parallel. Because it is challenging to analytically characterize the behavior of such systems, simulation methods to detect potential system instability are proposed.
Path planning for permutationinvariant multirobot formations
, 2002
"... In many multirobot applications, the specific assignment of goal configurations to robots is less important than the overall behavior of the robot formation. In such cases, it is convenient to define a permutationinvariant multirobot formation as a set of robot configurations, without assigning ..."
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Cited by 11 (0 self)
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In many multirobot applications, the specific assignment of goal configurations to robots is less important than the overall behavior of the robot formation. In such cases, it is convenient to define a permutationinvariant multirobot formation as a set of robot configurations, without assigning specific configurations to specific robots. For the case of robots that translate in the plane, we can represent such a formation by the coefficients of a complex polynomial whose roots represent the robot configurations. Since these coefficients are invariant with respect to permutation of the roots of the polynomial, they provide an effective representation for permutationinvariant formations. In this paper, we extend this idea to build a full representation of a permutationinvariant formation space. We describe the properties of the representation, and show how it can be used to construct collisionfree paths for permutationinvariant formations.
Nonpositive curvature and Paretooptimal coordination of robots
 SIAM J. Control & Optimization
"... Abstract. Given a collection of robots sharing a common environment, assume that each possesses a graph (a 1d complex also known as a roadmap) approximating its configuration space and, furthermore, that each robot wishes to travel to a goal while optimizing elapsed time. We consider vectorvalued ..."
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Cited by 10 (1 self)
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Abstract. Given a collection of robots sharing a common environment, assume that each possesses a graph (a 1d complex also known as a roadmap) approximating its configuration space and, furthermore, that each robot wishes to travel to a goal while optimizing elapsed time. We consider vectorvalued (or Pareto) optima for collisionfree coordination on the product of these roadmaps with collisiontype obstacles. Such optima are by no means unique: in fact, continua of Pareto optimal coordinations are possible. We prove a finite bound on the number of optimal coordinations in the physically relevant case where all obstacles are cylindrical (i.e., defined by pairwise collisions). The proofs rely crucially on perspectives from geometric group theory and cat(0) geometry. In particular, the finiteness bound depends on the fact that the associated coordination space is devoid of positive curvature. We also demonstrate that the finiteness bounds holds for systems with moving obstacles following known trajectories. 1. Introduction. 1.1. Motivation. In numerous settings, the coordination of multiple robots remains a basic and challenging research issue. Autonomous guided vehicles (AGVs) are used in a
Centralized Path Planning for Multiple Robots: Optimal Decoupling into Sequential Plans
, 2009
"... We develop an algorithm to decouple a multirobot path planning problem into subproblems whose solutions can be executed sequentially. Given an external path planner for general configuration spaces, our algorithm finds an execution sequence that minimizes the dimension of the highestdimensional s ..."
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Cited by 9 (0 self)
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We develop an algorithm to decouple a multirobot path planning problem into subproblems whose solutions can be executed sequentially. Given an external path planner for general configuration spaces, our algorithm finds an execution sequence that minimizes the dimension of the highestdimensional subproblem over all possible execution sequences. If the external planner is complete (at least up to this minimum dimension), then our algorithm is complete because it invokes the external planner only for spaces of dimension at most this minimum. Our algorithm can decouple and solve path planning problems with many robots, even with incomplete external planners. We show scenarios involving 16 to 65 robots, where our algorithm solves planning problems of dimension 32 to 130 using a PRM planner for at most eight dimensions.
Time complexity of sensorbased vehicle routing
 in Robotics: Science and Systems
, 2005
"... Abstract — In this paper, we study the following motion coordination problem: given n vehicles and n origindestination pairs in the plane, what is the minimum time needed to transfer each vehicle from its origin to its destination, avoiding conflicts with other vehicles? The environment is free of ..."
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Cited by 9 (2 self)
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Abstract — In this paper, we study the following motion coordination problem: given n vehicles and n origindestination pairs in the plane, what is the minimum time needed to transfer each vehicle from its origin to its destination, avoiding conflicts with other vehicles? The environment is free of obstacles and a conflict occurs when distance between any two vehicles is smaller than a velocitydependent safety distance. In the case where the origin and destination points can be chosen arbitrarily, we show that the transfer takes Θ ( √ n ¯ L) time to complete, where ¯ L is the average distance between the origin and destination points. We also analyze the case in which origin and destination points are generated randomly according to a uniform distribution, and present an algorithm providing a constructive upper bound on the time needed to transfer vehicles from origins to their corresponding destination, proving that the transfer takes Θ ( √ n) time for this case. I.
Computing Pareto optimal coordinations on roadmaps
 Intl. J. Robotics Research
, 2005
"... ABSTRACT. We consider coordination of multiple robots in a common environment, each robot having its own (distinct) roadmap. Our primary contribution is a classification of and exact algorithm for computing vectorvalued — or Pareto — optima for collisionfree coordination. We indicate the utility o ..."
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Cited by 9 (3 self)
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ABSTRACT. We consider coordination of multiple robots in a common environment, each robot having its own (distinct) roadmap. Our primary contribution is a classification of and exact algorithm for computing vectorvalued — or Pareto — optima for collisionfree coordination. We indicate the utility of new geometric techniques from CAT(0) geometry and give an argument that curvature bounds are the key distinguishing feature between systems for which the classification is finite and for those in which it is not. 1.
Exact ParetoOptimal Coordination of Two Translating Polygonal Robots On An Acyclic Roadmap
 In Proc. IEEE International Conference on Robotics and Automation
, 2004
"... We present an algorithm that computes the complete set of Paretooptimal coordination strategies for two translating polygonal robots in the plane. A collisionfree acyclic roadmap of piecewiselinear paths is given on which the two robots move. The robots have a maximum speed and are capable of ins ..."
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Cited by 8 (3 self)
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We present an algorithm that computes the complete set of Paretooptimal coordination strategies for two translating polygonal robots in the plane. A collisionfree acyclic roadmap of piecewiselinear paths is given on which the two robots move. The robots have a maximum speed and are capable of instantly switching between any two arbitrary speeds. Each robot would like to minimize its travel time independently. The Paretooptimal solutions are the ones for which there exist no solutions that are better for both robots. The algorithm computes exact solutions in time O(mn log n), in which m is the number of paths in the roadmap, n is the number of coordination space vertices. An implementation with computed examples is presented.
A Complete and Scalable Strategy for Coordinating Multiple Robots Within Roadmaps
, 2008
"... This paper addresses the challenging problem of finding collisionfree trajectories for many robots moving toward individual goals within a common environment. Most popular algorithms for multirobot planning manage the complexity of the problem by planning trajectories for robots individually; such ..."
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Cited by 7 (0 self)
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This paper addresses the challenging problem of finding collisionfree trajectories for many robots moving toward individual goals within a common environment. Most popular algorithms for multirobot planning manage the complexity of the problem by planning trajectories for robots individually; such decoupled methods are not guaranteed to find a solution if one exists. In contrast, this paper describes a multiphase approach to the planning problem that uses a graph and spanning tree representation to create and maintain obstaclefree paths through the environment for each robot to reach its goal. The resulting algorithm guarantees a solution for a welldefined number of robots in a common environment. The computational cost is shown to be scalable with complexity linear in the number of the robots, and demonstrated by solving the planning problem for 100 robots, simulated in an underground mine environment, in less than 1.5 s with a 1.5 GHz processor. The practicality of the algorithm is demonstrated in a realworld application requiring coordinated motion planning of multiple physical robots.
Coordinating the motions of multiple robots with kinodynamic constraints
 Proceedings of the IEEE International Conference on Robotics and Automation (ICRA
, 2003
"... This paper focuses on the coordination of multiple robots with kinodynamic constraints along specified paths. The presented approach generates continuous velocity profiles that avoid collisions and minimize the completion time for the robots. The approach identifies collision segments along each rob ..."
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Cited by 6 (2 self)
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This paper focuses on the coordination of multiple robots with kinodynamic constraints along specified paths. The presented approach generates continuous velocity profiles that avoid collisions and minimize the completion time for the robots. The approach identifies collision segments along each robot’s path and then optimizes the motions of the robots along their collision and collisionfree segments. For each path segment for each robot, the minimum and maximum possible traversal times that satisfy the dynamics constraints are computed by solving the corresponding twopoint boundary value problems. Then the collision avoidance constraints for pairs of robots can be combined to formulate a mixed integer nonlinear programming (MINLP) problem. Since this nonconvex MINLP model is difficult to solve, we describe two related mixed integer linear programming (MILP) formulations that provide schedules that are lower and upper bounds on the optimum; the upper bound schedule is a continuous velocity schedule. The approach is illustrated with robots modeled as double integrators subject to velocity and acceleration constraints. An implementation that coordinates 12 nonholonomic carlike robots is described. 1