Kumar, Vijay
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Computer Sciences
Mechanical Engineering
Mechanical Engineering
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UPS Foundation Professor
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108 results
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Publication Convergence of Time-Stepping Method For Initial and Boundary-Value Frictional Compliant Contact Problems(2005-12-30) Pang, Jong-Shi; 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 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 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 Abstraction and Control for Groups of Robots(2004-10-01) Belta, Calin; Kumar, R. VijayThis paper addresses the general problem of controlling a large number of robots required to move as a group. We propose an abstraction based on the definition of a map from the configuration space Q of the robots to a lower dimensional manifold A, whose dimension is independent of the number of robots. In this paper, we focus on planar fully actuated robots. We require that the manifold has a product structure A = G x S, where G is a Lie group, which captures the position and orientation of the ensemble in the chosen world coordinate frame, and S is a shape manifold, which is an intrinsic characterization of the team describing the “shape” as the area spanned by the robots. We design decoupled controllers for the group and shape variables. We derive controllers for individual robots that guarantee the desired behavior on A. These controllers can be realized by feedback that depends only on the current state of the robot and the state of the manifold A. This has the practical advantage of reducing the communication and sensing that is required and limiting the complexity of individual robot controllers, even for large numbers of robots.Publication Dynamics of Rigid Bodies Undergoing Multiple Frictional Contacts(1991-10-01) Wang, Yin-Tien; Kumar, R. Vijay; Abel, JacobThere 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 Stabilization of Multiple Robots on Stable Orbits via Local Sensing(2007-04-10) Hsieh, Mong-Ying A; Loizou, Savvas; Kumar, R. VijayWe develop decentralized controllers for a team of disk-shaped robots to converge to and circulate along the boundary of a desired two-dimensional geometric pattern specified by a smooth function with collision avoidance. The proposed feedback controllers rely solely on each robot's range and bearing sensors which allow them to obtain information about positions of neighbors within a given range. This is relevant for applications such as perimeter surveillance or containing hazardous regions where limited bandwidth must be preserved for situational awareness. The computational complexity of the decentralized controller for each agent is linear in the number of neighboring agents, making it scalable to robot swarms. We establish stability and convergence properties of the controllers and verify the feasibility of the method through computer simulations.Publication A Multiagent System for Intelligent Material Handling(1991-10-01) Bajcsy, Ruzena; Paul, Richard P; Yun, Xiaoping; Kumar, R. VijayThe goal of our research is to investigate manipulation, mobility, sensing, control and coordination for a multiagent robotic system employed in the task of material handling, in an unstructured, indoor environment. In this research, manipulators, observers, vehicles, sensors, and human operator(s) are considered to be agents. Alternatively, an agent can be a general-purpose agent (for example, a six degree of freedom manipulator on a mobile platform with visual force, touch and position sensors). Possible applications for such a system includes handling of waste and hazardous materials, decontamination of nuclear plants, and interfacing between special purpose material handling devices in warehouses. The fundamental research problems that will be studied are organization, or the decomposition of the task into subtasks and configuring the multiple agents with appropriate human interaction, exploration, or the process of exploring geometric, material and other properties about the environment and other agents, and coordination, or the dynamic control of multiple agents for manipulation and transportation of objects to a desired destination.Publication Exploration of Unknown Mechanical Assemblies Through Manipulation(1989-11-01) Kumar, R. Vijay; Yun, Xiaoping; Bajcsy, RuzenaIf robots must function in unstructured environments, they must also possess the ability to acquire information and construct appropriate models of the unknown environment. This paper addresses the automatic generation of kinematic models of unknown objects with moveable parts in the environment. If the relative motion between moving parts must be observed and characterized, vision alone cannot suffice. An approach in which manipulation is used with vision for sensing is better suited to the task of determining kinematic properties. In this paper, algorithms for constructing models of unknown mechanical assemblies and characterizing the relative motion are developed. Results of a simulation are described to demonstrate the role of manipulation in such an endeavor.Publication Computational Techniques for Analysis of Genetic Network Dynamics(2005-02-01) Belta, Calin; Esposito, Joel M; Kim, Jongwoo; Kumar, R. VijayIn this paper we propose modeling and analysis techniques for genetic networks that provide biologists with insight into the dynamics of such systems. Central to our modeling approach is the framework of hybrid systems and our analysis tools are derived from formal analysis of such systems. Given a set of states characterizing a property of biological interest P, we present the Multi-Affine Rectangular Partition (MARP) algorithm for the construction of a set of infeasible states I that will never reach P and the Rapidly Exploring Random Forest of Trees (RRFT) algorithm for the construction of a set of feasible states F that will reach P. These techniques are scalable to high dimensions and can incorporate uncertainty (partial knowledge of kinetic parameters and state uncertainty). We apply these methods to understand the genetic interactions involved in the phenomenon of luminescence production in the marine bacterium V. fischeri.Publication Hybrid Control of Formations of Robots(2001-05-21) Das, Aveek K.; Kumar, R. Vijay; Fierro, Rafael; Ostrowski, James P.We describe a framework for controlling a group of nonholonomic mobile robots equipped with range sensors. The vehicles are required to follow a prescribed trajectory while maintaining a desired formation. By using the leader-following approach, we formulate the formation control problem as a hybrid (mode switching) control system. We then develop a decision module that allows the robots to automatically switch between continuous-state control laws to achieve a desired formation shape. The stability properties of the closed-loop hybrid system are studied using Lyapunov theory. We do not use explicit communication between robots; instead we integrate optimal estimation techniques with nonlinear controllers. Simulation and experimental results verify the validity of our approach.Publication On the Generation of Smooth Three-Dimensional Rigid Body Motions(1998-08-01) Kumar, Vijay; Žefran, Miloš; Croke, ChristopherThis paper addresses the problem of generating smooth trajectories between an initial and final position and orientation in space. The main idea is to define a functional depending on velocity or its derivatives that measures the smoothness of a trajectory and find trajectories that minimize this functional. In order to ensure that the computed trajectories are independent of the parameterization of positions and orientations, we use the notions of Riemannian metric and covariant derivatives from differential geometry and formulate the problem as a variational problem on the Lie group of spatial rigid body displacements, SE (3). We show that by choosing an appropriate measure of smoothness, the trajectories can be made to satisfy boundary conditions on the velocities or higher order derivatives. Dynamically smooth trajectories can be obtained by incorporating the inertia of the system into the definition of the Riemannian metric. We state the necessary conditions for the shortest distance, minimum acceleration and minimum jerk trajectories. Analytical expressions for the smooth trajectories are derived for some special cases. We also provide several examples of the general case where the trajectories are computed numerically.