Håvard Fjær Grip

Washington State University, Pullman, Washington, United States

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Publications (50)41.3 Total impact

  • Håvard Fjær Grip, Thor I. Fossen, Tor A. Johansen, Ali Saberi
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    ABSTRACT: This paper deals with the construction of nonlinear observers for navigation purposes. We first present a globally exponentially stable observer for attitude and gyro bias, based on gyro measurements and two or more pairs of vector measurements. We avoid the well-known topological obstructions to global stability by not confining the attitude estimate to SO(3), but rather estimating a full rotation matrix with nine degrees of freedom. We also show how the attitude can be estimated under a relaxed persistency-of-excitation condition, with a single vector measurement as a special case. Next, we use the attitude observer to construct a globally exponentially stable observer for gnss/ins integration, based on accelerometer, gyro, and magnetometer measurements, as well as gnss measurements of position and (optionally) velocity. We verify the stability properties of the design using experimental data from a light fixed-wing aircraft.
    Automatica. 11/2014;
  • Tao Yang, Ali Saberi, Anton A. Stoorvogel, Håvard Fjær Grip
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    ABSTRACT: In this paper, we consider the output synchronization problem for heterogeneous networks of right-invertible linear agents. We assume that all the agents are introspective, meaning that they have access to their own local measurements. Under this assumption, we then propose a decentralized control scheme for solving the output synchronization problem for a set of network topologies. The proposed scheme can also be applied to solve the output formation problem with arbitrary formation vectors. We also consider the regulation of output synchronization problem, where the output of each agent has to track an a priori specified reference trajectory, generated by an exosystem. In this case, we assume that the root agent has access to its own output relative to the reference trajectory.Copyright © 2013 John Wiley & Sons, Ltd.
    International Journal of Robust and Nonlinear Control 09/2014; 24(13). · 1.90 Impact Factor
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    ABSTRACT: Synchronization in networks has been an active research area in recent years. In this paper we consider networks where the only measurements available to an agent are relative output information from their neighbors. No direct information of its own internal agents is available nor is there an exchange of internal controller states with neighboring agents. We consider the homogeneous case where all agents are identical SISO linear systems of arbitrary order. The prime extension compared to earlier work is that we only assume the systems to be weakly-non-minimum-phase.
    2014 American Control Conference - ACC 2014; 06/2014
  • Havard Fjaer Grip, Ali Saberi, Anton A. Stoorvogel
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    ABSTRACT: We consider the synchronization problem for homogeneous networks of nonlinear SISO agents connected via diffusive partial-state coupling. The agents are non-introspective (i.e., they do not have access to their own state or output), and thus unable to manipulate their own dynamics in order to present themselves differently to the network. Moreover, the agents are not allowed to exchange additional information, such as internal controller states, over the network. Unlike many other designs for nonlinear synchronization, we do not require the agents to be passive; we rely instead on a canonical form that requires the nonlinearities to have a certain lower-triangular structure.
    2014 American Control Conference - ACC 2014; 06/2014
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    ABSTRACT: We consider two synchronization problems, namely, state synchronization for networks of identical linear agents, and regulated output synchronization for networks of non-identical linear agents, under a time-varying topology. Agents are assumed to be multiple-input multiple-output (MIMO), minimum-phase, right invertible and non-introspective (i.e., they only receive relative output information from their neighboring agents, but lack independent information about their own states or outputs). The time-varying topology is assumed to switch among a finite number of directed graphs containing a directed spanning tree with an arbitrarily a priori given non-vanishing dwell time. Moreover agents are unable to exchange of controller states with their neighboring agents. For solving each problem, we propose a distribute dynamic protocol based on a combination of low-gain and high-gain design techniques.
    2014 American Control Conference - ACC 2014; 06/2014
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    ABSTRACT: This paper brings forward the notion of “H∞H∞ almost output synchronization” for heterogeneous multi-agent systems under directed interconnection structures. Agents are assumed to be linear, right-invertible and introspective (i.e. agents have partial knowledge of their own states). The objective is to suppress the impact of disturbances on the synchronization error dynamics in terms of the H∞H∞ norm of the corresponding closed-loop transfer function. In addition, the problem of regulating the consensus trajectories to a reference signal is addressed. The application of the proposed method to the problem of formation is furthermore elucidated. Simulation results are provided to illustrate the method.
    Automatica 04/2014; · 2.92 Impact Factor
  • Håvard Fjær Grip, Ali Saberi
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    ABSTRACT: In this paper, we consider the observer design problem for a class of observable linear systems perturbed by nonlinear, time-varying terms. Our design methodology is based on a canonical form, similar to canonical forms used elsewhere in the literature, that allows the nonlinearities to be dominated using high gain. We show that linear state and output transformations to this canonical form exist if, and only if, the data of the system satisfies a certain admissibility property. Moreover, the appropriate transformations can easily be constructed using available tools. We furthermore show that, if a system does not satisfy the admissibility property, it may be possible to extend it with an invertible output filter that makes the data of the extended system admissible. We refer to the problem of constructing such a filter as the output shaping problem and introduce an algorithm that solves the problem whenever it is solvable. Copyright © 2012 John Wiley & Sons, Ltd.
    International Journal of Robust and Nonlinear Control 04/2014; 24(6). · 1.90 Impact Factor
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    ABSTRACT: The National Aeronautics and Space Administration is currently considering an Asteroid Redirect Mission (ARM), the goal of which is to bring a near-Earth asteroid into lunar orbit for inspection by a team of human astronauts. In this paper we present the results of a simulation study that focuses on the challenge of capturing a target asteroid using a robotic spacecraft. This simulation study was conducted in parallel with an ongoing mechanical design process, with the goal of providing feedback on specific design concepts, deriving high-level design targets via optimization, and exploring the trade space of the capture problem independently. We present and discuss several simulation models, the results of which have influenced the evolution of the ARM project to date.
    2014 IEEE Aerospace Conference; 03/2014
  • Tao Yang, Anton A. Stoorvogel, Håvard Fjær Grip, Ali Saberi
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    ABSTRACT: In this paper, we consider the semi-global regulation of output synchronization problem for heterogeneous networks of invertible linear agents subject to actuator saturation. That is, we regulate the output of each agent according to an a priori specified reference model. The network communication infrastructure provides each agent with a linear combination of its own output relative to that of neighboring agents, and it allows the agents to exchange information about their own internal observer estimates while some agents have access to their own outputs relative to the reference trajectory.Copyright © 2012 John Wiley & Sons, Ltd.
    International Journal of Robust and Nonlinear Control 02/2014; 24(3). · 1.90 Impact Factor
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    ABSTRACT: This paper studies the synchronization problem for a network of identical discrete-time agents with unknown uniform constant communication delay. When the agents are non-introspective, the problem is solvable via a decentralized low-gain-based synchronization controller if the delay satisfies the proposed upper bound. When the agents are introspective, the synchronization problem can be solved with arbitrary bounded communication delay. Copyright © 2013 John Wiley & Sons, Ltd.
    International Journal of Robust and Nonlinear Control 07/2013; · 1.90 Impact Factor
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    ABSTRACT: For applications with limited computational capacity, observers designed based on nonlinear stability theory offer an alternative to computationally demanding extended Kalman filters. In this paper, we present a semiglobally stable nonlinear observer for estimating position, velocity, attitude, and gyro bias by combining a GNSS receiver with an inertial measurement unit including a magnetometer. Previous work by the authors on this topic was based on local navigation equations that ignored the Earth's rotation and curvature. Moreover, the attitude was represented by an over-parameterized 9-degrees-of-freedom matrix. The current paper improves on these aspects by using navigation equations that take the Earth's rotation and curvature into account, and by representing the attitude estimate as a unit quaternion. Furthermore, the observer is tested experimentally on data from a light fixed-wing aircraft.
    American Control Conference (ACC), 2013; 06/2013
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    ABSTRACT: In this paper, synchronization for multi-agent systems subject to external disturbances is studied, and the notion of H∞ almost synchronization” is introduced. The objective is to suppress the impact of disturbances on the synchronization error dynamics in terms of the H∞ norm of the corresponding closed-loop transfer function to any arbitrarily value. We focus on networks of non-identical linear, right-invertible agents under directional communication links. The key assumption is that agents are introspective; that is, they have a partial knowledge about their own states.
    American Control Conference (ACC), 2013; 06/2013
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    ABSTRACT: We introduce the notions of “ℌ∞ almost regulated synchronization” and “ℌ∞ almost formation” for multi-agent systems subject to external disturbances and under directed interconnection structures. We assume that agents are linear, right-invertible and introspective with non-identical dynamics. The objective is to suppress the impact of disturbances on the synchronization error dynamics in terms of the ℌ∞ norm of the corresponding closed-loop transfer function. Inspired by the time-scale structure assignment techniques based on the singular perturbation theory, a family of observer-based protocols is introduced to achieve synchronization with any desired accuracy.
    Control Conference (ECC), 2013 European; 01/2013
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    ABSTRACT: In this paper we study the problem of achieving regulated output synchronization in a network of minimum-phase SISO agents. Our problem formulation is characterized by the combination of three different challenges: the network is heterogeneous (meaning that the agents are governed by non-identical models); the agents are non-introspective (meaning that they do not have access to information about their own state or output); and the agents are not allowed to exchange internal controller states via the network. To handle these challenges, we present an observer-based control methodology that combines elements of low-gain and high-gain design techniques.
    Control Conference (ECC), 2013 European; 01/2013
  • Xu Wang, Ali Saberi, Håvard Fjær Grip, Anton A. Stoorvogel
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    ABSTRACT: In this paper, we study the disturbance response of open‐loop neutrally stable linear systems with saturating linear feedback controller. It is shown that the closed‐loop states remain bounded if the disturbances consists of those signals that do not have large sustained frequency components corresponding to the system's eigenvalues on the imaginary axis (continuous‐time) or on the unit circle (discrete‐time). Copyright © 2011 John Wiley & Sons, Ltd.
    International Journal of Robust and Nonlinear Control 01/2013; 23(2). · 1.90 Impact Factor
  • Håvard Fjær Grip, Tao Yang, Ali Saberi, Anton A. Stoorvogel
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    ABSTRACT: In this paper we consider the output synchronization problem for heterogeneous networks of linear agents. The network’s communication infrastructure provides each agent with a linear combination of its own output relative to that of neighboring agents, and it allows the agents to exchange information about their own internal observer estimates. We design decentralized controllers based on setting the control input of a single root agent to zero and letting the remaining agents synchronize to the root agent. A distinguishing feature of our work is that the agents are assumed to be non-introspective, meaning that they possess no knowledge about their own state or output separate from what is received via the network. We also consider the problem of regulating the agreement trajectory according to an a priori specified reference model. In this case we assume that some of the agents have access to their own output relative to the reference trajectory.
    Proceedings of the American Control Conference 10/2012; 48(10):2444–2453.
  • Håvard Fjær Grip, Ali Saberi, Tor A. Johansen
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    ABSTRACT: In this paper we begin by assuming that an observer with a corresponding quadratic-type Lyapunov function has been designed for a given nonlinear system. We then consider the problem that arises when the output of that nonlinear system is not directly available; instead, it acts as an input to a second, linear system from which a partial-state measurement is in turn available. We develop an observer design methodology for the resulting cascade interconnection, based on estimating the unavailable output together with the states of the linear system. We also extend this methodology to a more general class of feedback-interconnected systems. Under a set of technical assumptions, the overall error dynamics is proven to be globally exponentially stable if the gains are chosen to satisfy an H∞H∞ condition. We illustrate application of the methodology by considering a navigation example based on integration of inertial and satellite measurements.
    Automatica 07/2012; 48(7):1339–1346. · 2.92 Impact Factor
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    ABSTRACT: We present an observer for estimating position, velocity, attitude, and gyro bias, by using inertial measurements of accelerations and angular velocities, magnetometer measurements, and satellite-based measurements of position and (optionally) velocity. The design proceeds in two stages: in Stage I, an attitude and gyro bias estimator is designed based on an unmeasured signal. In Stage II, that design is recovered using measured signals only, by combining it with a position and velocity estimator. We prove global exponential stability of the estimation error and test the design using realistic flight simulation.
    American Control Conference (ACC), 2012; 06/2012
  • [Show abstract] [Hide abstract]
    ABSTRACT: In this paper we consider the output synchronization problem for heterogeneous networks of linear agents. The network provides each agent with a linear combination of its own output relative to that of neighboring agents, and it allows the agents to exchange information about their own internal observer estimates. We design decentralized controllers based on setting the control input of a single root agent to zero and letting the remaining agents synchronize to the root agent. A distinguishing feature of our work is that the agents are assumed to be non-introspective, meaning that they possess no knowledge about their own state or output separate from what is received via the network.
    American Control Conference (ACC), 2012; 06/2012
  • Source
    Xu Wang, Ali Saberi, Anton A. Stoorvogel, Håvard Fjær Grip
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    ABSTRACT: In this paper, we study the response to external disturbances of a double integrator with a saturating feedback. For a class of disturbances that have bounded integrals over all intervals, we show that a linear static feedback law can always be designed to ensure boundedness of the states. Moreover, boundedness can be preserved if the disturbance is biased by a small DC signal. In the special case that the disturbance is made up of a finite number of sinusoids and a small bias, any linear static feedback ensures boundedness of the states. These results are an extension of previous results by Wen, Roy, and Saberi (2008).
    Automatica 01/2012; 48:430-435. · 2.92 Impact Factor

Publication Stats

120 Citations
41.30 Total Impact Points

Institutions

  • 2010–2014
    • Washington State University
      • School of Electrical Engineering and Computer Science
      Pullman, Washington, United States
  • 2006–2014
    • Norwegian University of Science and Technology
      • Department of Engineering Cybernetics
      Nidaros, Sør-Trøndelag, Norway
  • 2013
    • Universiteit Twente
      • Group of Electrical Engineering, Mathematics and Computer Science department
      Enschede, Overijssel, Netherlands
  • 2007–2010
    • NTNU Samfunnsforskning
      Nidaros, Sør-Trøndelag, Norway