A modal approach to hyper-redundant manipulator kinematics

Chirikjian, Gregory S.; Burdick, Joel W.

doi:10.1109/70.294209

Cited by 506 publications

(296 citation statements)

References 18 publications

(20 reference statements)

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“…[ 81 ] for details). If the system were completely deterministic (no actuator noise, and no slipping of the wheels), this approach might work well.…”

Section: 21mentioning

confidence: 99%

Kinematic state estimation and motion planning for stochastic nonholonomic systems using the exponential map

Park¹,

Liu²,

et al. 2008

Robotica

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SUMMARYA nonholonomic system subjected to external noise from the environment, or internal noise in its own actuators, will evolve in a stochastic manner described by an ensemble of trajectories. This ensemble of trajectories is equivalent to the solution of a Fokker-Planck equation that typically evolves on a Lie group. If the most likely state of such a system is to be estimated, and plans for subsequent motions from the current state are to be made so as to move the system to a desired state with high probability, then modeling how the probability density of the system evolves is critical. Methods for solving Fokker-Planck equations that evolve on Lie groups then become important. Such equations can be solved using the operational properties of group Fourier transforms in which irreducible unitary representation (IUR) matrices play a critical role. Therefore, we develop a simple approach for the numerical approximation of all the IUR matrices for two of the groups of most interest in robotics: the rotation group in three-dimensional space, SO(3), and the Euclidean motion group of the plane, SE(2). This approach uses the exponential mapping from the Lie algebras of these groups, and takes advantage of the sparse nature of the Lie algebra representation matrices. Other techniques for density estimation on groups are also explored. The computed densities are applied in the context of probabilistic path planning for kinematic cart in the plane and flexible needle steering in three-dimensional space. In these examples the injection of artificial noise into the computational models (rather than noise in the actual physical systems) serves as a tool to search the configuration spaces and plan paths. Finally, we illustrate how density estimation problems arise in the characterization of physical noise in orientational sensors such as gyroscopes.

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“…[ 81 ] for details). If the system were completely deterministic (no actuator noise, and no slipping of the wheels), this approach might work well.…”

Section: 21mentioning

confidence: 99%

Kinematic state estimation and motion planning for stochastic nonholonomic systems using the exponential map

Park¹,

Liu²,

et al. 2008

Robotica

View full text Add to dashboard Cite

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“…12 However, this approach has some limitations. 12 First, the Frenet-Serret frames assigned along the curve are not defined for straight line segments. Second, the vector function describing the spatial curve requires a numerical solution of a cumbersome differential equation.…”

Section: Backbone Curves and Continuum Robotsmentioning

confidence: 99%

“…[12]) is a way of handling these limitations. The backbone curve is defined as "a piecewise continuous curve that captures the important macroscopic geometric features of a hyper-redundant robot" 12 and it typically runs through the spine of the snake robot. A set of orthonormal reference frames are found along the backbone curve at a set of "fitting" points in order to specify the actual snake robot configuration.…”

Section: Backbone Curves and Continuum Robotsmentioning

confidence: 99%

“…12,[33][34][35][36] The Frenet-Serret apparatus 37 is employed in a classical handling of the geometry of curves. 12 However, this approach has some limitations. 12 First, the Frenet-Serret frames assigned along the curve are not defined for straight line segments.…”

Section: Backbone Curves and Continuum Robotsmentioning

confidence: 99%

“…Some examples are multi-link mobile robot, 4 snake-like or snake robot, 5−11 hyper-redundant robot, 12 and G-snake. 13 To emphasize that this paper deals with robots that mainly resemble the locomotion of snakes, the term "snake robot" will be employed.…”

Section: Introductionmentioning

confidence: 99%

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A survey on snake robot modeling and locomotion

2009

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SUMMARYSnake robots have the potential to make substantial contributions in areas such as rescue missions, firefighting, and maintenance where it may either be too narrow or too dangerous for personnel to operate. During the last 10-15 years, the published literature on snake robots has increased significantly. The purpose of this paper is to give a survey of the various mathematical models and motion patterns presented for snake robots. Both purely kinematic models and models including dynamics are investigated. Moreover, the different approaches to biologically inspired locomotion and artificially generated motion patterns for snake robots are discussed.

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