Kumar, Vijay
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Mechanical Engineering
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UPS Foundation Professor
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108 results
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Publication Finite state abstraction of a stochastic model of the lactose regulation system of Escherichia coli(2006-12-15) Julius, Agung; Kumar, R. Vijay; Halász, Ádám; Pappas, George J; Kumar, R. Vijay; Pappas, George JThis paper focuses on the lactose regulation system in Escherichia coli bacteria, one of the most extensively studied examples of positive feedback in a naturally occurring gene network. State-of-the-art nonlinear dynamical system models predict a bi-stability phenomenon that is confirmed in experiments. However, such deterministic models fail to explain experimental observations of spontaneous transition between the two stable states in the system and the simultaneous occurrence of both steady states in a population of cells. In this paper, we propose a stochastic model that explains this phenomenon. Furthermore, we also extract a coarser two-state continuous-time Markov chain as a higher level abstraction of this model, and show that macroscopic properties are retained in the abstraction.Publication Visual Programming for Modeling and Simulation of Biomolecular Regulatory Networks(2002-12-18) Alur, Rajeev; Kumar, R. Vijay; Belta, Calin; Ivancic, Franjo; Sokolsky, Oleg; Rubin, Harvey; Schug, Jonathan; Sokolsky, Oleg; Webb, JonathanIn this paper we introduce our new tool BIOSKETCHPAD that allows visual programming and modeling of biological regulatory networks. The tool allows biologists to create dynamic models of networks using a menu of icons, arrows, and pop-up menus, and translates the input model into CHARON, a modeling language for modular design of interacting multi-agent hybrid systems. Hybrid systems are systems that are characterized by continuous as well as discrete dynamics. Once a CHARON model of the underlying system is generated, we are able to exploit the various analysis capabilities of the CHARON toolkit, including simulation and reachability analysis. We illustrate the advantages of this approach using a case study concerning the regulation of bioluminescence in a marine bacterium.Publication Motion generation for formations of robots: a geometric approach(2001-05-21) Kumar, R. Vijay; Kumar, R. VijayThis paper develops a method for generating smooth trajectories for mobile robots in formation. The problem of trajectory generation is cast in terms of designing optimal curves on the Euclidean group, SE(3). Specifically, the method generates the trajectory that minimizes the total energy associated with the translations and rotations of the robots, while maintaining a rigid formation. When the mobile robots are nonholonomic, trajectories that allow rigid formations to be maintained must satisfy appropriate constraints. An efficient non-iterative algorithm to obtain near-optimal trajectories is described. Finally, the approach is illustrated with examples involving formations of aircrafts.Publication Experimental Testbed for Large Multirobot Teams(2008-03-01) Michael, Nathan; Kumar, Vijay; Fick, Jonathan; Kumar, VijayExperimental validation is particularly important in multirobot systems research. The differences between models and real-world conditions that may not be apparent in single robot experiments are amplified because of the large number of robots, interactions between robots, and the effects of asynchronous and distributed control, sensing, and actuation. Over the last two years, we have developed an experimental testbed to support research in multirobot systems with the goal ofmaking it easy for users tomodel, design, benchmark, and validate algorithms. In this article, we describe our approach to the design of a large-scale multirobot system for the experimental verification and validation of a variety of distributed robotic applications in an indoor environment. Our research focusses on decentralized multirobot algorithms that rely on an integrated approach to mobility, perception, and communication, with such applications as environmental monitoring, surveillance and reconnaissance for security and defense, and support for first responders in search and rescue operations [1]. In all of these applications, robots must rely on local sensing, computation, and control and exploit the availability of communication links with other robots whenever possible. To enable scaling up to large numbers, computations must be decentralized, and the systemmust be robust to changes in the numbers of robots and to the dynamic addition and deletion of units. There is also the need to provide some degree of centralization with an interface to one or more human operators for programming, tasking, andmonitoring of the system. These research applications serve as the motivation for our experimental testbed. While there is a rich body of work to build on, there is currently no inexpensive multirobot system that allows users to move easily from conceptual ideas to algorithms and then to experimentation. We begin by motivating design considerations for the testbed in the context of our research and existing multirobot control and experimental architectures.We next arrive at a set of design requirements for the system based on the driving applications as well as practical considerations. Most importantly, we are driven by the pragmatic considerations of ease of use, robustness, flexibility, and scalability to enable the easy inclusion of more robots and sensors with minimal changes to the existing infrastructure. We also review some of the applicable hardware and software options currently available. The experimental testbed is discussed in detail with overviews of the robots, software, and the supporting infrastructure required for multirobot experiments. Since simulation is of great relevance in the experimental process and the testbed design, we discuss its role and detail the transition from simulation to reality. Finally, we present several multirobot experiments for formation control and cooperative manipulation, which demonstrate the capabilities of the system for verification purposes and elucidate the experiment design process with our testbed.Publication Distributed Search and Rescue with Robot and Sensor Teams(2003-07-14) Das, Aveek K; Kumar, R. Vijay; Kumar, R. Vijay; Pereira, Guilherme A. S.; Peterson, Ron; Rus, Daniela; Singh, Sanjiv; Spletzer, JohnWe consider search and rescue applications in which heterogeneous groups of agents (humans, robots, static and mobile sensors) enter an unknown building and disperse while following gradients in temperature and concentration of toxins, and looking for immobile humans. The agents deploy the static sensors and maintain line of sight visibility and communication connectivity whenever possible. Since different agents have different sensors and therefore different pieces of information, communication is necessary for tasking the network, sharing information, and for control. An ad-hoc network is formed by a group of mobile hosts upon a wireless local network interface. It is a temporary network formed without the aid of any established infrastructure or centralized administration. A sensor network consists of a collection of sensors and distributed over some area that form an ad-hoc network. Our heterogeneous teams of agents (sensors, robots, and humans) constitute distributed adaptive sensor networks and are well-suited for tasks in extreme environments, especially when the environmental model and the task specifications are uncertain and the system has to adapt to it. Applications of this work cover search and rescue for first responders, monitoring and surveillance, and infrastructure protection. We combine networking, sensing, and control to control the flow of information in search and rescue in unknown environments. Specifically, this research examines (1) localization in an environment with no infrastructure such as a burning building (for both sensors and robots) (2) information flow across a sensor network that can localize on the fly for delivering the most relevant and current information to its consumer, maintaining current maps, and automating localization; (3) using feedback from the sensor network to control the autonomous robots for placing sensors, collecting data from sensors, and locating targets; and (4) delivering the information gathered from the sensor network (integrated as a global picture) to human users. The paper will detail our technical results in these 4 areas and describe an integrated experiment for navigation in burning buildings.Publication Weak Input-to-State Stability Properties for Navigation Function Based Controllers(2006-12-01) Kumar, R. Vijay; Kumar, R. VijayDue to topological constraints, Navigation Functions, are not, except from trivial cases, equivalent to quadratic Lyapunov functions, hence systems based on Navigation Functions cannot directly accept an Input-to-State stability (ISS) characterization. However a relaxed version of Input-to-State stability, namely almost global ISS (aISS), is shown to be applicable. The proposed framework provides compositional capability for navigation function based systems. Cascade as well as feedback interconnections of aISS navigation systems are shown to also possess the aISS property under certain assumptions on the interconnections. Several simulated examples of navigation systems are presented to demonstrate the effectiveness of the proposed scheme.Publication Convergence of Time-Stepping Method For Initial and Boundary-Value Frictional Compliant Contact Problems(2005-12-30) Kumar, Vijay; Kumar, Vijay; Song, PengBeginning with a proof of the existence of a discrete-time trajectory, this paper establishes the convergence of a time-stepping method for solving continuous-time, boundary-value problems for dynamic systems with frictional contacts characterized by local compliance in the normal and tangential directions. Our investigation complements the analysis of the initial-value rigid-body model with one frictional contact encountering inelastic impacts by Stewart [Arch. Ration. Mech. Anal., 145 (1998), pp. 215–260] and the recent analysis by Anitescu [Optimization-Based Simulation for Nonsmooth Rigid Multibody Dynamics, Argonne National Laboratory, Argonne, IL, 2004] using the framework of measure differential inclusions. In contrast to the measure-theoretic approach of these authors, we follow a differential variational approach and address a broader class of problems with multiple elastic or inelastic impacts. Applicable to both initial and affine boundary-value problems, our main convergence result pertains to the case where the compliance in the normal direction is decoupled from the compliance in the tangential directions and where the friction coefficients are sufficiently small.Publication A Framework for Scalable Cooperative Navigation of Autonomous Vehicles(2001-01-01) Fierro, Rafael; Song, Peng; Kumar, R. Vijay; Kumar, R. VijayWe describe a general framework for controlling and coordinating a group of non-holonomic mobile robots equipped with range sensors, with applications ranging from scouting and reconnaissance, to search and rescue and manipulation tasks. We first describe a set of control laws that allows each robot to control its position and orientation with respect to neighboring robots or obstacles in the environment. We then develop a coordination protocol that allows the robots to automatically switch between the control laws to follow a specified trajectory. Finally, we describe two simple trajectory generators that are derived from potential field theory. The first allows each robot to plan its reference trajectory based on the information available to it. The second scheme requires sharing of information and results in a trajectory for the designated leader. Numerical simulations illustrate the application of these ideas and demonstrate the scalability of the proposed framework for a large group of robots.Publication Simulation of Mechanical Systems With Multiple Frictional Contacts(1992-03-01) Kumar, R. Vijay; Kumar, R. VijayThere are several applications in robotics and manufacturing in which nominally rigid objects are subject to multiple frictional contacts with other objects. In most previous work, rigid body models have been used to analyze such systems. There are two fundamental problems with such an approach. Firstly, the use of frictional laws, such as Coulomb's law, introduce inconsistencies and ambiguities when used in conjunction with the principles of rigid body dynamics. Secondly, hypotheses traditionally used to model frictional impacts can lead to solutions which violate principles of energy conservation. In this paper these problems are explained with the help of examples. A new approach to the simulation of mechanical systems with multiple, frictional constraints is proposed which is free of inconsistencies.Publication Incorporating User Inputs in Motion Planning for a Smart Wheelchair(2004-04-26) Parikh, Sarangi P; Kumar, R. Vijay; Grassi, Valdir; Kumar, R. Vijay; Okamoto, JunWe describe the development and assessment of a computer controlled wheelchair equipped with a suite of sensors and a novel interface, called the SMARTCHAIR. The main focus of this paper is a shared control framework which allows the human operator to interact with the chair while it is performing an autonomous task. At the highest level, the autonomous system is able to plan paths using high level deliberative navigation behaviors depending on destinations or waypoints commanded by the user. The user is able to locally modify or override previously commanded autonomous behaviors or plans. This is possible because of our hierarchical control strategy that combines three independent sources of control inputs: deliberative plans obtained from maps and user commands, reactive behaviors generated by stimuli from the environment, and user-initiated commands that might arise during the execution of a plan or behavior. The framework we describe ensures the user's safety while allowing the user to be in complete control of a potentially autonomous system.