The Geometric Mechanics of Undulatory Robotic Locomotion

Ostrowski, James; Burdick, Joel W.

doi:10.1177/027836499801700701

Cited by 337 publications

(324 citation statements)

References 27 publications

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“…The aim is to show how this method can be employed in practice in order to investigate the stability properties of a time-periodic dynamical system. 1) Calculating the Poincaré map: It is difficult to determine the Poincaré map analytically since it requires the solution of the differential equation (3). However, the Poincaré map of (3) is simply the forward integration of this differential equation.…”

Section: B Practical Application Of Poincaré Mapsmentioning

confidence: 99%

“…Hirose [2] studied biological snakes and developed mathematical relationships characterizing their motion, such as the serpenoid curve. Ostrowski [3] studied the controllability properties of a wheeled snake robot on a purely kinematic level. Prautsch et al [4] modelled the dynamics of a wheeled snake robot and proposed an asymptotically stable controller for the position of the robot.…”

Section: Introductionmentioning

confidence: 99%

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Controllability and Stability Analysis of Planar Snake Robot Locomotion

Liljebäck

Pettersen

Stavdahl

et al. 2011

IEEE Trans. Automat. Contr.

103

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Abstract-This paper contributes to the understanding of snake robot locomotion by employing nonlinear system analysis tools for investigating fundamental properties of snake robot dynamics. The paper has five contributions: 1) A partially feedback linearized model of a planar snake robot influenced by viscous ground friction is developed. 2) A stabilizability analysis is presented proving that any asymptotically stabilizing control law for a planar snake robot to an equilibrium point must be time-varying. 3) A controllability analysis is presented proving that planar snake robots are not controllable when the viscous ground friction is isotropic, but that a snake robot becomes strongly accessible when the viscous ground friction is anisotropic. The analysis also shows that the snake robot does not satisfy sufficient conditions for small-time local controllability (STLC). 4) An analysis of snake locomotion is presented that easily explains how anisotropic viscous ground friction enables snake robots to locomote forward on a planar surface. The explanation is based on a simple mapping from link velocities normal to the direction of motion into propulsive forces in the direction of motion. 5) A controller for straight line path following control of snake robots is proposed and a Poincaré map is investigated to prove that the resulting state variables of the snake robot, except for the position in the forward direction, trace out an exponentially stable periodic orbit.

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Section: B Practical Application Of Poincaré Mapsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Controllability and Stability Analysis of Planar Snake Robot Locomotion

Liljebäck

Pettersen

Stavdahl

et al. 2011

IEEE Trans. Automat. Contr.

103

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show abstract

“…84 Results on the controllability of snake robots are given by Kelly et al 32 and Ostrowski and Burdick. 86 McIsaac and Ostrowski 21,58,87 have derived and implemented closed-loop heading control based on imagebased position feedback for an underwater snake robot, and a controller for stopping the underwater snake robot during forwards and circular motion is presented. The motion pattern for underwater locomotion is similar to lateral undulation.…”

Section: Lateral Undulation For Snake Robotsmentioning

confidence: 99%

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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“…For the snakelike robot there have existed modeling methods as followings: Ma and Saito [1,2] developed dynamics equations based on Newton-Euler equations considering the friction between the snake robot and the environment as the Coulomb friction and viscous friction. Ostrowski and Burdick [3,4] developed the kinematic model considering the nonholonomic constraints. Transeth [5] developed the Euler-Lagrange equations and decoupled the equations based on VSOP.…”

Section: Introductionmentioning

confidence: 99%

Modeling and optimal torque control of a snake-like robot based on the fiber bundle theory

Guo

et al. 2015

Sci. China Inf. Sci.

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For the snake-like robot with passive wheels, the side constraint force provides the required thrust which is less than the maximum static friction. Minimizing the side constraint force can reduce possibility of skidding which is important to ensure stable and efficient motion of the robot. In this paper we model the snakelike robot based on the fiber bundle theory. This method can reduce the complexity of the dynamics and derive the exact analytical solution for the side constraint force which is linear to the redundant torque. Using the linear relation, we can derive directly the optimal torque by minimizing the side constraint force. Additionally the nonholonomic constraint can be used for constructing the connection of the fiber bundle. Using the connection, we can select the gait of the snake-like robot. The position and orientation of the head can be described in terms of the special Euclidean group SE(2) which is also the structure group of the fiber bundle. Using the symmetry of the structure group, we can reduce the dynamics equations and derive the analytical solution for the side constraint force. Kinematics and dynamics simulations validate the proposed methods.Keywords snake-like robot, redundant torque, fiber bundle theory, nonholonomic, optimal control Citation Guo X, Ma S G, Li B, et al. Modeling and optimal torque control of a snake-like robot based on the fiber bundle theory. Sci China Inf Sci, 2015, 58: 032205(13),

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The Geometric Mechanics of Undulatory Robotic Locomotion

Cited by 337 publications

References 27 publications

Controllability and Stability Analysis of Planar Snake Robot Locomotion

Controllability and Stability Analysis of Planar Snake Robot Locomotion

A survey on snake robot modeling and locomotion

Modeling and optimal torque control of a snake-like robot based on the fiber bundle theory

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