Kumar, Vijay

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Computer Sciences
Mechanical Engineering
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UPS Foundation Professor
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Now showing 1 - 10 of 108
  • Publication
    From Discrete to Continuous and Back: Abstractions and Mesoscopic Phenomena in Cells
    (2008-05-28) Halász, Ádám M; Pappas, George J; Julius, A. Agung; Kumar, R. Vijay
    We discuss the interplay between stochasticity and multistability in bio-molecular networks. The resulting cell-level stochastic behavior reflects the fundamentally discrete and random nature of the underlying molecular processes. These ideas are illustrated on the well studied example of the lac operon. We first describe the switching behavior predicted by a differential-equation based model and then show how cell-level stochastic behavior emerges. Finally we point out that the observed macroscopic behavior may not be enough to determine both the dynamic and stochastic parameters.
  • Publication
    Convergence of Time-Stepping Method For Initial and Boundary-Value Frictional Compliant Contact Problems
    (2005-12-30) Pang, Jong-Shi; Kumar, Vijay; Song, Peng
    Beginning 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
    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
    This 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
    Cooperative Air and Ground Survaillance
    (2006-09-01) Grocholsky, Ben; Kumar, Vijay; Keller, James; Pappas, George J
    Unmanned aerial vehicles (UAVs) can be used to cover large areas searching for targets. However, sensors on UAVs are typically limited in their accuracy of localization of targets on the ground. On the other hand, unmanned ground vehicles (UGVs) can be deployed to accurately locate ground targets, but they have the disadvantage of not being able to move rapidly or see through such obstacles as buildings or fences. In this article, we describe how we can exploit this synergy by creating a seamless network of UAVs and UGVs. The keys to this are our framework and algorithms for search and localization, which are easily scalable to large numbers of UAVs and UGVs and are transparent to the specificity of individual platforms. We describe our experimental testbed, the framework and algorithms, and some results.
  • Publication
    Usability Study of a Control Framework for an Intelligent Wheelchair
    (2005-04-01) Grassi, Valdir; Parikh, Sarangi P; Kumar, Vijay; Okamoto, Jun
    We describe the development and assessment of a computer controlled wheelchair called the SMARTCHAIR. A shared control framework with different levels of autonomy allows the human operator to stay in complete control of the chair at each level while ensuring her safety. The framework incorporates deliberative motion plans or controllers, reactive behaviors, and human user inputs. At every instant in time, control inputs from these three different sources are blended continuously to provide a safe trajectory to the destination, while allowing the human to maintain control and safely override the autonomous behavior. In this paper, we present usability experiments with 50 participants and demonstrate quantitatively the benefits of human-robot augmentation.
  • Publication
    Incorporating User Inputs in Motion Planning for a Smart Wheelchair
    (2004-04-26) Parikh, Sarangi P; Kumar, R. Vijay; Grassi, Valdir; Okamoto, Jun
    We 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.
  • Publication
    A Framework for Scalable Cooperative Navigation of Autonomous Vehicles
    (2001-01-01) Fierro, Rafael; Song, Peng; Das, Aveek K; Kumar, R. Vijay
    We 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) Wang, Yin-Tien; Kumar, R. Vijay
    There 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
    The Effect of Feedback and Feedforward on Formation ISS
    (2002-05-11) Kumar, R. Vijay; Tanner, Herbert G.; Pappas, George J
    A new type of stability of leader follower formations is defined, based on input-to-state stability (ISS) properties of cascade interconnections. Formation ISS links leader input to internal state of the formation and characterizes the way this input affects performance. The effect of feedforward and feedback inter-agent communication is then investigated in this framework and it is indicated how the structure of interconnections and the amount of available information can affect stability performance.
  • Publication
    Euclidean metrics for motion generation on SE(3)
    (2002-01-01) Belta, Calin Andrei; Kumar, R. Vijay
    Previous approaches to trajectory generation for rigid bodies have been either based on the so-called invariant screw motions or on ad hoc decompositions into rotations and translations. This paper formulates the trajectory generation problem in the framework of Lie groups and Riemannian geometry. The goal is to determine optimal curves joining given points with appropriate boundary conditions on the Euclidean group. Since this results in a two-point boundary value problem that has to be solved iteratively, a computationally efficient, analytical method that generates near-optimal trajectories is derived. The method consists of two steps. The first step involves generating the optimal trajectory in an ambient space, while the second step is used to project this trajectory onto the Euclidean group. The paper describes the method, its applications and its performance in terms of optimality and efficiency.