Results 1  10
of
249
Nonholonomic motion planning: Steering using sinusoids
 IEEE fins. Auto. Control
, 1993
"... AbstractIn this paper, we investigate methods for steering systems with nonholonomic constraints between arbitrary configurations. Early work by Brockett derives the optimal controls for a set of canonical systems in which the tangent space to the configuration manifold is spanned by the input vec ..."
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Cited by 353 (15 self)
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AbstractIn this paper, we investigate methods for steering systems with nonholonomic constraints between arbitrary configurations. Early work by Brockett derives the optimal controls for a set of canonical systems in which the tangent space to the configuration manifold is spanned by the input vector fields and their first order Lie brackets. Using Brockett’s result as motivation, we derive suboptimal trajectories for systems which are not in canonical form and consider systems in which it takes more than one level of bracketing to achieve controllability. These trajectories use sinusoids at integrally related frequencies to achieve motion at a given bracketing level. We define a class of systems which can be steered using sinusoids (chained systems) and give conditions under which a class of twoinput systems can be converted into this form. I.
Randomized Kinodynamic Motion Planning with Moving Obstacles
, 2000
"... This paper presents a novel randomized motion planner for robots that must achieve a specified goal under kinematic and/or dynamic motion constraints while avoiding collision with moving obstacles with known trajectories. The planner encodes the motion constraints on the robot with a control syst ..."
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Cited by 264 (10 self)
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This paper presents a novel randomized motion planner for robots that must achieve a specified goal under kinematic and/or dynamic motion constraints while avoiding collision with moving obstacles with known trajectories. The planner encodes the motion constraints on the robot with a control system and samples the robot's state x time space by picking control inputs at random and integrating its equations of motion. The result is a probabilistic roadmap of sampled state x time points, called milestones, connected by short admissible trajectories. The planner does
Nonholonomic mechanics and locomotion: The snakeboard example
 In Proc. IEEE Int. Conf. Robotics and Automation
, 1994
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A Kalman Filterbased Algorithm for IMUCamera Calibration
, 2007
"... Visionaided Inertial Navigation Systems (VINS) can provide precise state estimates for the 3D motion of a vehicle when no external references (e.g., GPS) are available. This is achieved by combining inertial measurements from an IMU with visual observations from a camera under the assumption that ..."
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Cited by 72 (14 self)
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Visionaided Inertial Navigation Systems (VINS) can provide precise state estimates for the 3D motion of a vehicle when no external references (e.g., GPS) are available. This is achieved by combining inertial measurements from an IMU with visual observations from a camera under the assumption that the rigid transformation between the two sensors is known. Errors in the IMUcamera calibration process causes biases that reduce the accuracy of the estimation process and can even lead to divergence. In this paper, we present a Kalman filterbased algorithm for precisely determining the unknown transformation between a camera and an IMU. Contrary to previous approaches, we explicitly account for the time correlations of the IMU measurements and provide a figure of merit (covariance) for the estimated transformation. The proposed method does not require any special hardware (such as spin table or 3D laser scanner) except a calibration target. Simulation and experimental results are presented that validate the proposed method and quantify its accuracy.
A geometric approach to nonlinear fault detection and isolation
 IEEE TRANS. AUTOMAT. CONTR
, 2000
"... We present in this article a differentialgeometric approach to the problem of fault detection and isolation for nonlinear systems. A necessary condition for the problem to be solvable is derived in terms of an unobservability distribution, which is computable by means of suitable algorithms. The ex ..."
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Cited by 68 (4 self)
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We present in this article a differentialgeometric approach to the problem of fault detection and isolation for nonlinear systems. A necessary condition for the problem to be solvable is derived in terms of an unobservability distribution, which is computable by means of suitable algorithms. The existence and regularity of such a distribution implies the existence of changes of coordinates in the state and in the output space which induce an “observable” quotient subsystem unaffected by all fault signals but one. For this subsystem a fault detection filter is designed.
A LieBäcklund approach to equivalence and flatness of nonlinear systems
 922–937. IN INDIRECT OPTIMAL CONTROL OF MULTIVARIABLE SYSTEMS 317
, 1999
"... Abstract — In this paper, a new system equivalence relation, using the framework of differential geometry of jets and prolongations of infinite order, is studied. In this setting, two systems are said to be equivalent if any variable of one system may be expressed as a function of the variables of t ..."
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Cited by 62 (7 self)
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Abstract — In this paper, a new system equivalence relation, using the framework of differential geometry of jets and prolongations of infinite order, is studied. In this setting, two systems are said to be equivalent if any variable of one system may be expressed as a function of the variables of the other system and of a finite number of their time derivatives. This is a Lie–Bäcklund isomorphism. This quite natural, though unusual, equivalence is presented in an elementary way by the inverted pendulum and the vertical takeoff and landing (VTOL) aircraft. The authors prove that, although the state dimension is not preserved, the number of input channels is kept fixed. They also prove that a Lie–Bäcklund isomorphism can be realized by an endogenous feedback, i.e., a special type of dynamic feedback. Differentially flat nonlinear systems, which were introduced by the authors in 1992 via differential algebraic techniques, are generalized here and the new notion of orbitally flat systems is defined. They correspond to systems which are equivalent to a trivial one, with time preservation or not. Trivial systems are, in turn, equivalent to any linear controllable system with the same number of inputs, and consequently flat systems are linearizable by endogenous feedback. The endogenous linearizing feedback is explicitly computed in the case of the VTOL aircraft to track given reference trajectories with stability; simulations are presented. Index Terms — Dynamic feedback, flatness, infiniteorder prolongations, Lie–Bäcklund equivalence, nonlinear systems.
Visualinertial sensor fusion: Localization, mapping and sensortosensor selfcalibration
 International Journal of Robotics Research
, 2011
"... Visual and inertial sensors, in combination, are able to provide accurate motion estimates and are wellsuited for use in many robot navigation tasks. However, correct data fusion, and hence overall performance, depends on careful calibration of the rigid body transform between the sensors. Obtainin ..."
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Cited by 60 (3 self)
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Visual and inertial sensors, in combination, are able to provide accurate motion estimates and are wellsuited for use in many robot navigation tasks. However, correct data fusion, and hence overall performance, depends on careful calibration of the rigid body transform between the sensors. Obtaining this calibration information is typically difficult and timeconsuming, and normally requires additional equipment. In this paper we describe an algorithm, based on the unscented Kalman filter, for selfcalibration of the transform between a camera and an inertial measurement unit (IMU). Our formulation rests on a differential geometric analysis of the observability of the cameraIMU system; this analysis shows that the sensortosensor transform, the IMU gyroscope and accelerometer biases, the local gravity vector, and the metric scene structure can be recovered from camera and IMU measurements alone. While calibrating the transform we simultaneously localize the IMU and build a map of the surroundings – all without additional hardware or prior knowledge about the environment in which a robot is To Appear in International Journal of Robotics Research operating. We present results from simulation studies and from experiments with a monocular camera and a lowcost IMU, which demonstrate accurate estimation of both the calibration parameters and the local scene structure. 1 1
Pricing of American PathDependent Contingent Claims
, 1994
"... We consider the problem of pricing pathdependent contingent claims. Classically, this problem can be cast into the BlackScholes valuation framework through inclusion of the pathdependent variables into the state space. This leads to solving a degenerate advectiondiffusion Partial Differential Eq ..."
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Cited by 53 (1 self)
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We consider the problem of pricing pathdependent contingent claims. Classically, this problem can be cast into the BlackScholes valuation framework through inclusion of the pathdependent variables into the state space. This leads to solving a degenerate advectiondiffusion Partial Differential Equation (PDE). Standard Finite Difference (FD) methods are known to be inadequate for solving such degenerate PDE. Hence, pathdependent European claims are typically priced through MonteCarlo simulation. To date, there is no numerical method for pricing pathdependent American claims. We first establish necessary and sufficient conditions amenable to a Lie algebraic characterization, under which degenerate diffusions can be reduced to lowerdimensional nondegenerate diffusions on a submanifold of the underlying asset space. We apply these results to pathdependent options. Then, we describe a new numerical technique, called Forward Shooting Grid (FSG) method, that efficiently copes with de...
Dynamic Nonprehensile Manipulation: Controllability, Planning, and Experiments
 International Journal of Robotics Research
, 1998
"... We are interested in using low degreeoffreedom robots to perform complex tasks by nonprehensile manipulation (manipulation without a form or forceclosure grasp). By not grasping, the robot can use gravitational, centrifugal, and Coriolis forces as virtual motors to control more degreesof freedo ..."
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Cited by 46 (15 self)
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We are interested in using low degreeoffreedom robots to perform complex tasks by nonprehensile manipulation (manipulation without a form or forceclosure grasp). By not grasping, the robot can use gravitational, centrifugal, and Coriolis forces as virtual motors to control more degreesof freedom of the part. The extra motion freedoms of the part are exhibited as rolling, slipping, and free flight.
Analysis and improvement of the consistency of extended Kalman filter based SLAM
"... Abstract — In this work, we study the inconsistency of EKFbased SLAM from the perspective of observability. We analytically prove that when the Jacobians of the state and measurement models are evaluated at the latest state estimates during every time step, the linearized errorstate system model of ..."
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Cited by 39 (14 self)
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Abstract — In this work, we study the inconsistency of EKFbased SLAM from the perspective of observability. We analytically prove that when the Jacobians of the state and measurement models are evaluated at the latest state estimates during every time step, the linearized errorstate system model of the EKFbased SLAM has observable subspace of dimension higher than that of the actual, nonlinear, SLAM system. As a result, the covariance estimates of the EKF undergo reduction in directions of the state space where no information is available, which is a primary cause of inconsistency. To address this issue, a new “First Estimates Jacobian ” (FEJ) EKF is proposed, which is shown to perform better in terms of consistency. In the FEJEKF, the filter Jacobians are calculated using the firstever available estimates for each state variable, which insures that the observable subspace of the errorstate system model is of the same dimension as that of the underlying nonlinear SLAM system. The theoretical analysis is validated through extensive simulations. I.