# Publications

Book chapter/Contribution

• S. Rodrigues, N. Crasta, A. P. Aguiar, and F. Leite, “Dynamics, games and science II in honour of mauricio peixoto and david rand.” Berlin: Springer Verlag, 2011. [Bibtex]

@inbook{DYNA1I,
author = {S. Rodrigues, and N. Crasta, and A. P. Aguiar, and F. Leite},
abstract = {"This paper considers the state estimation problem of a class of systems described by implicit outputs and whose state lives in
the special Euclidean group {SE}(3). This type of systems are motivated by applications in dynamic vision such as the estimation of the motion of a camera from a sequence of images. We propose an observer in the group of motion {SE}(3) and discuss conditions under which the linearized state estimation error converges exponentially fast. We also analyze the problem when the system is subject to disturbances and noises. We show that the estimate converges to a neighborhood of the real solution. The size of the neighborhood increases/decreases gracefully with the bound of the disturbance and noise."}
editor = {Mauricio Matos Peixoto, and Alberto Adrego Pinto, and David A. Rand},
title = {Dynamics, Games and Science {II} in honour of Mauricio Peixoto and David Rand},
chapter = {An exponential observer for systems on SE(3) with implicit outputs},
publisher = {Springer Verlag},
year = {2011},
}
• D. S. Bernstein, “Matrix mathematics: Theory, facts, and formulas,” , Second ed., Princeton: Princeton Press University, 2009, p. 204. [Bibtex]

@inbook{DBS2,
author = {Dennis S. Bernstein},
title = {Matrix Mathematics: {T}heory, Facts, and Formulas},
pages = {204},
edition = {Second},
publisher = {Princeton Press University},
year = {2009},
}

Journal papers

• N. Crasta, Romeo Ortega, and H. K. Pillai, “On the matching equations of energy shaping controllers for mechanical systems,” International Journal of Control, 2014 (ACCEPTED). [Bibtex]

@article{NaveenEtAll:IJC:2014,
author = {N. Crasta, and Romeo Ortega, and Harish K. Pillai},
journal = { International {J}ournal of {C}ontrol},
title = {On the matching equations of energy shaping controllers for mechanical systems},
year = "2014 (ACCEPTED)"
}
• S. P. Bhat and N. Crasta, “Closed rotation sequences,” Discrete and Computational Geometry, 2014 (ACCEPTED). [Bibtex]

@article{Bhat \& Crasta:SPB:2014,
author = {Sanjay P. Bhat \& N. Crasta},
journal = {Discrete and {C}omputational {G}eometry},
title = {Closed rotation sequences},
year = "2014 (ACCEPTED)"
}
• M. Bayat, N. Crasta, A. P. Aguiar, and A. M. Pascoal, “Range-based underwater vehicle localization in the presence of unknown ocean currents: theory and experiments,” IEEE Transactions on Control Systems Technology, 2014 (ACCEPTED). [Bibtex]

@article{BehzadEtAll:TCST:2014,
author = {M. Bayat, and N. Crasta, and A. P. Aguiar, and A. M. Pascoal},
journal = {I{EEE} {T}ransactions on {C}ontrol {S}ystems {T}echnology},
title = {Range-based underwater vehicle localization in the presence of unknown ocean currents: Theory and experiments},
year = "2014 (ACCEPTED)"
}

Conference proceedings

• S. P. Bhat and N. Crasta, “Closed attitude trajectories,” in First indian control conference, 2015 (Accepted). [Bibtex]

@inproceedings{Bhat \& Crasta:2014,
author = "Sanjay P. Bhat \& N. Crasta",
abstract = "A closed angular velocity time history does not necessarily yield a closed attitude trajectory, where we use “closed” to mean
that the time history terminates at the same point that it starts from. We give a complete characterization of closed angular velocity time histories that yield a closed attitude trajectory. The characterization is an extension to the continuous case of recent results on discrete closed sequences of rotations. Our characterization yields special examples of closed attitude trajectories that may be seen as extensions to the continuous case of classical results on rotation sequences such as the Rodrigues-Hamilton theorem and Donkin’s theorem.",
title = "Closed attitude trajectories",
booktitle = "First Indian Control Conference",
year = "2015 (Accepted)",
month = "January",
}
• Thomas Glotzbach, N. Crasta, and C. Ament, “Observability analyses and trajectory planning for tracking of an underwater robot using empirical gramians,” in The 19th IFAC world congress, 2014. [Bibtex]

@inproceedings{GlotzbachEtAll:2014b,
author = "Thomas Glotzbach, and N. Crasta, and Christoph Ament",
abstract = "In marine robotics, estimation of the position and orientation of an underwater agent requires lots of research efforts.
Especially the realization of robot teams has opened new horizons, allowing for relative navigation based on relative range measurements between the agents. Hence, there is the need for a better understanding of optimal sensor placement related to the positions of the robots relative to each other, and for improvement of observability, based on the concrete mission scenario. In this paper, we study the tracking of a moving target by a Reference Objects (RO) capable of performing acoustic range measurements. We employ the well-known theory of the Empirical Gramians, to evaluate different scenarios and their influence on the observability properties. Emphasis will be put on the computation of a trajectory for the RO that optimizes the observability criterion. We will compare our results with others found in literature that were derived by different procedures, to proof the usability of the Empirical Gramian approach for the area of underwater robotics.",
title = "Observability analyses and trajectory planning for tracking of an underwater robot using empirical gramians",
booktitle  = "The 19th {IFAC} World Congress",
year = "2014",
month = "August",
note = "August 24-29, 2014, Cape Town, South Africa",
}
• N. Crasta, M. Bayat, A. A. Pedro, and A. M. Pascoal, “Observability analysis of 3d auv trimming trajectories in the presence of ocean currents using single beacon navigation,” in The 19th IFAC world congress, 2014. [Bibtex]

@inproceedings{CrastaEtAll:2014,
author = "N. Crasta, and M. Bayat, and A. A. Pedro, and A. M. Pascoal",
abstract = "This paper addresses the observability properties of a 3{D} autonomous underwater vehicle ({AUV}) model in the presence of
ocean currents, under the assumption that the vehicle can only measure its distance to a fixed transponder using an acoustic
ranging device. In the set-up adopted, the {AUV} may undergo a wide range of maneuvers that are usually described as trimming trajectories. The latter are of paramount importance in flight dynamics and can be completely parametrized by three variables: i) linear body speed $v$, ii) flight-path angle $\gamma$, and iii) yaw rate $\dot \psi$. We assume that $v > 0,$ $\gamma$ and $\dot \psi$ are constant but otherwise arbitrary (within the constraints of the vehicle capabilities) and examine the observability of the resulting system with the output (measured) variable described above. We adopt weaker definitions of observability that are akin to those proposed by Herman and Krener (Hermann and Krener, 1977) but reflect the fact that we consider specific kinds of maneuvers in 3{D}. We show that in the presence of known constant ocean currents the 3D kinematic model of the AUV that corresponds to trimming trajectories with nonzero flight path angle and yaw rate is observable.
\par
In case the latter conditions fail, we give a complete characterization of the sets of states that are indistinguishable from a given initial state. We further show that in the case of unknown constant ocean currents the model is locally weakly observable for yaw rate different from zero but fails to be locally weakly observable for zero yaw rate. In both the cases we give a complete characterization of the sets of states that are indistinguishable from a given initial state.",
title = "Observability analysis of 3D AUV trimming trajectories in the presence of ocean currents using single beacon navigation",
booktitle  = "The 19th {IFAC} World Congress",
year = "2014",
month = "August",
note = "August 24-29, 2014, Cape Town, South Africa",
}
• Thomas Glotzbach, N. Crasta, and C. Ament, “Navigation for marine robots: observability analyses for tracking of an underwater robot using empirical gramians,” in Conference on computer applications and information technology in the maritime industries (COMPIT), 2014. [Bibtex]

@inproceedings{GlotzbachEtAll:2014a,
author = "Thomas Glotzbach, and N. Crasta, and Christoph Ament",
abstract = "The precise position information is of paramount importance for a fleet of autonomous vehicles to operate cooperatively in subsea environment. The problem of Optimal Sensor Placement becomes more important, aiming to find a constellation of sensors/agents that is optimal in some sense. In this paper, we investigate the observability properties for different sensor suites measuring distances to a moving target by using the Empirical Gramians. We show that the scenario referred to as single beacon navigation, where the target measures the distance to the reference objects and some of its own state variables, yields the best observability performance",
title = "Navigation for marine robots: Observability analyses for tracking of an underwater robot using empirical Gramians",
booktitle = "Conference on Computer Applications and Information Technology in the Maritime Industries ({COMPIT})",
year = "2014",
month = "May",
note = "May 12-14, Redworth/UK"
}
• N. Crasta, M. Bayat, A. A. Pedro, and A. M. Pascoal, “Observability analysis of 2d single beacon navigation in the presence of constant currents for two classes of maneuvers,” in The 19th IFAC conference on control applications in marine systems (CAMS), 2013. [Bibtex]

@inproceedings{CrastaEtAll:2013,
author = "N. Crasta, and M. Bayat, and A. A. Pedro, and A. M. Pascoal",
abstract = "We analyze the observability properties of an underwater vehicle (moving in 2{D}) performing single beacon navigation for two
specific classes of maneuvers, whereby the vehicle measures its distance to a fixed transponder located at a known position using an acoustic ranging device. We show that in the presence of known ocean currents, the system is found to be globally observable for constant relative course and constant (nonzero) relative course rate inputs in the sense of Herman and Krener. On the other hand, with unknown ocean currents the system fails to be locally weakly observable with constant relative course but we characterize the set of indistinguishable states from a given initial position and ocean current configuration. Interestingly, observability can be achieved with constant (nonzero) relative course rate in the presence of unknown, constant ocean currents.",
title = "Observability analysis of 2D single beacon navigation in the presence of constant currents for two classes of maneuvers",
booktitle  = "The 19th {IFAC} Conference on Control Applications in Marine Systems ({CAMS})",
year = "2013",
month = "September",
note = "September 17-20, Osaka, Japan, 2013",
}
• Cheikh A.B. Hann, Vincent Van A., N. Crasta, and F. Lamnabhi-lagarrigue, “Dynamical continuous high gain observer for sampled measurements systems,” in IEEE Control and Decision Conference, 2012. [Bibtex]

@inproceedings{CheikhEtAll:2012,
author = "Cheikh A.B. Hann, and Vincent Van A., and N. Crasta and Francoise Lamnabhi-lagarrigue",
abstract = "This paper presents the design of an observer for a class of nonlinear Lipschitz sampled-data systems. The proposed observer
uses a predictor of the output between the sampling times. This predictor is re-initialized at each sampling time. Besides, unlike the conventional high gain observer, the observer introduced herein has a dynamic observation gain. Using a Lyapunov approach, we will derive an explicit relation between the bound on maximum allowable sampling period and the parameters of the observer in order to guarantee an asymptotic convergence of the observation error.",
title = "Dynamical continuous high gain observer for sampled measurements systems",
booktitle  = "{IEEE} {C}ontrol and {D}ecision {C}onference ",
year = "2012",
month = "December",
note = "December 10-12, Hawaii, 2012",
}
• N. Crasta, Tarek Ahmed-Ali, and F. Lamnabhi-Lagarrigue, “Dynamical high-gain observer design with sampled measurements,” in Advances in control and optimization of dynamic systems, 2012. [Bibtex]

@inproceedings{CrastaEtAll:2012,
author = "N. Crasta, and Tarek Ahmed-Ali, and Francoise Lamnabhi-Lagarrigue",
abstract = "Continuous time observers are often employed for nonlinear systems even in the presence of discrete measurements. In this
paper, a structure for predicting the output of a class of uniformly observable nonlinear system coupled with adaptive high-gain observer is proposed and prove the convergence of the proposed observer with a suitable Lyapunov function. We compare the maximum allowable sampling time of constant high-gain observer with the proposed observer in the paper.",
title = "Dynamical high-gain observer design with sampled measurements",
booktitle  = "Advances in Control and Optimization of Dynamic Systems",
year = "2012",
month = "February",
note = "February, IISc Bangalore, India, 2012",
}
• S. Rodrigues, N. Crasta, A. P. Aguiar, and F. Leite, “State estimation for systems on SE(3) with implicit outputs: An application to visual servoying,” in Nonlinear control systems (NOLCOS), 2010. [Bibtex]

@inproceedings{RodriguesEtAll:2010,
author = "S. Rodrigues, and N. Crasta, and A. P. Aguiar, and F. Leite",
abstract = "Motivated by applications in visual servoing, we consider the state estimation problem for a class of systems described by
implicit outputs and whose state lives in the special Euclidean group SE(3). We propose an observer in the group of motion SE(3) that preserves invariance and therefore takes explicitly into consideration the geometry of the problem, and discuss conditions under which the linearized state estimation error converges exponentially fast. Furthermore, we analyze the problem when the system is subject to disturbances and noises and show that the estimate converges to a neighborhood of the real solution. The size of the neighborhood increases/decreases gracefully with the bound of the disturbance and noise. We
apply and illustrate these results through an application of position and attitude estimation of a rigid body using measurements from a camera attached to the rigid body.",
title = "State estimation for systems on {SE(3)} with implicit outputs: {A}n application to visual servoying",
booktitle  = "NOnLinear Control Systems ({NOLCOS})",
year = "2010",
month = "August",
note = "Bolonga, Italy, 2910",
}
• N. Crasta and S. P. Bhat, “Observability of nonlinear input-affine systems,” in Eighteenth international symposium on mathematical theory of networks and systems (MTNS), 2008. [Bibtex]

@inproceedings{Crasta_Bhat:2008a,
author = "N. Crasta \& S. P. Bhat",
abstract = "The objective of this paper is to characterize sets of indistinguishable states of a general, smooth, nonlinear, input-affine
system. For this purpose, the extended observation space is introduced, and it is shown that sets of indistinguishable states are common level sets of functions from the extended observation space. Under additional conditions, connected components of sets of indistinguishable states are shown to be related to orbits and prolongations of the annihilator of the extended observation space. It is also shown that the closure of the extended observation space under pointwise limits is same as the closure of the observation space under pointwise limits in the case of an analytic system. The results are used to identify sets of indistinguishable states of the reduced dynamics of an unactuated, inertially symmetric rigid body carrying a single attitude sensor.",
title = "Observability of nonlinear input-affine systems",
booktitle  = "Eighteenth International Symposium on Mathematical Theory of Networks and Systems ({MTNS})",
year = "2008",
month = "August",
note = "July 26- August 1, Virginia Tech, Blacksburg, VA, USA, 2008",
}
• N. Crasta and S. P. Bhat, “Tools for analyzing observability of nonlinear systems,” in Eighteenth international symposium on mathematical theory of networks and systems (MTNS), 2008. [Bibtex]

@inproceedings{Crasta_Bhat:2008b,
author = "N. Crasta \& S. P. Bhat",
abstract = "The paper presents tools for analyzing the effect of introducing additional inputs and outputs on the observability of a smooth, nonlinear, input-affine system. We also present a result that makes it possible to relate the observability of a
system to that of its projection onto a lower-dimensional manifold. To illustrate the utility of our results, we show how our results can be used to deduce observability properties of the full attitude dynamics of an inertially symmetric rigid body under different sensor-actuator configurations from the observability properties of the reduced attitude dynamics of an unactuated, inertially symmetric rigid body equipped with a single attitude sensor.",
title = "Tools for analyzing observability of nonlinear systems",
booktitle  = "Eighteenth International Symposium on Mathematical Theory of Networks and Systems ({MTNS})",
year = "2008",
month = "August",
note = "July 26- August 1, Virginia Tech, Blacksburg, VA, USA, 2008",
}
• N. Crasta and S. P. Bhat, “Observability of nonlinear input-affine systems,” in International conference on advances in control and optimization of dynamical systems (ACODS), 2007. [Bibtex]

@inproceedings{Crasta_Bhat:2007,
author = "N. Crasta \& S. P. Bhat",
abstract = "The main aim of this paper is to characterize the set of states indistinguishable from a given state of a general nonlinear
input-affine control system with complete and smooth vector fields and smooth output functions. For this purpose, we introduce the extended observation space, and show that the set of states indistinguishable from a given state is the intersection of level sets containing that state, of functions from the extended observation space. A partial relationship between the annihilator of the extended observation space and the set of states indistinguishable from a given state is also established. In the case of an analytic system, the closure of observation space under pointwise limits considered in the literature and the closure of the extended observation space under pointwise limits introduced here are the same. ",
title = "Observability of nonlinear input-affine systems",
booktitle  = "International Conference on Advances in Control and Optimization of Dynamical Systems ({ACODS})",
year = "2007",
month = "February",
note = "February 1-2, Indian Institute of Science, Bangalore, India, 2007",
}

PhD Thesis

• N. Crasta, PhD Thesis , Indian Institute of Technology Bombay , Department of Aerospace Engineering, Powai Mumbai 400 076, India, 2009. [Bibtex]

@phdthesis{Phdthesis,
author = "Naveena Crasta",
abstract = {"The main objective of this thesis is to characterize sets of indistinguishable states of a general, smooth, nonlinear input-affine system. For this purpose, the extended observation space is introduced, and it is shown that sets of indistinguishable states are common level sets of functions from the extended observation space. Under additional conditions, connected components of sets of indistinguishable states are shown to be related to orbits of the annihilator of the extended observation space. Further, it is shown that sets of indistinguishable states contains prolongations of the annihilator of the extended observation space. In the case of an analytic system, it is also shown that the closures of the extended observation space and the observation space considered in the literature under pointwise limits are equal. We present tools for analyzing the effect of introducing additional actuators and sensors on the observability of asmooth, nonlinear, input-affinesystem. We also present a result that makes it possible to relate the observability properties of a system to that of its projection onto a lower-dimensional manifold. To illustrate the utility of our results, we show how our results can be used to deduce observability properties of the full attitude dynamics of an inertially symmetric rigid body under different actuator-sensor configurations from the observability properties of the reduced attitude dynamics of an unactuated, inertially symmetric rigid body equipped with a single attitude sensor. Characterization of sets of indistinguishable states of the full attitude dynamics require the angular rotations required about each axis of a given specific set of three axes such that the composition of rotations about these three axes produce no net rotational displacement and hence we provide explicit analytical solutions to this problem."}
title = "Observability of Nonlinear Input-affine Systems with Application to Attitude Dynamics",
school = "Indian Institute of Technology Bombay",
address  = "Department of Aerospace Engineering, Powai Mumbai 400 076, India",
year = "2009",
month = "August",
keywords = "Nonlinear input-affine systems, sets of indistinguishable states, observability, level sets, extended observation space, observation space, attitude dynamics, closed sequences."
}