The Euler-Poincaré equations for a spherical robot actuated by a pendulum

Gajbhiye, Sneha; Banavar, Ravi N.

doi:10.3182/20120829-3-it-4022.00011

Cited by 19 publications

(12 citation statements)

References 9 publications

(13 reference statements)

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“…Various mathematical methods, such as Kane's method, EulerLagrange equation, and Maggi's equations are often applied to create the coupled model Zhuang et al 2008;Liu and Sun 2010;Sang et al 2011;Yu et al 2011;Zheng, M. et al 2011;Zheng, Y.L. 2011;Gajbhiye and Banavar 2012;Balandin et al 2013 …”

Section: Related Workmentioning

confidence: 99%

Unified Representation Of Decoupled Dynamic Models For Pendulum-Driven Ball-Shaped Robots

Ylikorpi¹,

Forsman²,

Halme³

et al. 2014

ECMS 2014 Proceedings Edited By: Flaminio Squazzoni, Fabio Baronio, Claudia Archetti, Marco Castellani

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Dynamic models describing the ball-robot motion form the basis for developments in ball-robot mechanics and motion control systems. For this paper, we have conducted a literature review of decoupled forwardmotion models for pendulum-driven ball-shaped robots. The existing models in the literature apply several different conventions in system definition and parameter notation. Even if describing the same mechanical system, the diversity in conventions leads into dynamic models with different forms. As a result, it is difficult to compare, reproduce and apply the models available in the literature. Based on the literature review, we reformulate all common variations of decoupled dynamic forward-motion models using a unified notation and formulation. We have verified all reformulated models through simulations, and present the simulation results for a selected model. In addition, we demonstrate the different system behavior resulting from different ways to apply the pendulum reaction torque, a variation that can be found in the literature. For anyone working with the ball-robots, the unified compilation of the reformulated dynamic models provides an easy access to the models, as well as to the related work.

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Section: Related Workmentioning

confidence: 99%

Unified Representation Of Decoupled Dynamic Models For Pendulum-Driven Ball-Shaped Robots

Ylikorpi¹,

Forsman²,

Halme³

et al. 2014

ECMS 2014 Proceedings Edited By: Flaminio Squazzoni, Fabio Baronio, Claudia Archetti, Marco Castellani

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“…Lie group action and symmetry reduction has been successfully applied to model other types of nonholonomic mechanical systems in the differential geometric framework. See for example the works by Bloch et al [1996], Ostrowski [1999], Gajbhiye and Banavar [2012]. As shown, e. g., by Ostrowski [1999], the resulting equations can be put in a simplified form containing apart from the reduced equations of motion, also the momentum and reconstruction equation, which describe the dynamics of the system along the group directions.…”

Section: Introductionmentioning

confidence: 98%

Reduced equations of motion for a wheeled inverted pendulum

2015

Self Cite

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This paper develops the equations of motion in the reduced space for the wheeled inverted pendulum, which is an underactuated mechanical system subject to nonholonomic constraints. The equations are derived from the Lagrange-d'Alembert principle using variations consistent with the constraints. The equations are first derived in the shape space, and then, a coordinate transformation is performed to get the equations of motion in more suitable coordinates for the purpose of control.

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“…Euler-Poincaré equations were obtained in a geometric framework for spherical robot with internal rotors in [10], [11], for pendulum actuation in [12] and for sliding mass actuation in [10]. The controllability of the spherical robot kinematics was established in [10], [11], [13] for internal rotors and in [10] for sliding mass actuation.…”

Section: Introductionmentioning

confidence: 99%

Geometric Controllability and Stabilization of Spherical Robot Dynamics

Muralidharan

Mahindrakar

2015

IEEE Trans. Automat. Contr.

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Geometric control of a spherical robot rolling on a horizontal plane with three independent inertia disc actuators is considered in this note. The dynamic model of the spherical robot in the geometric framework is used to establish the strong accessibility and small-time local controllability properties. Smooth stabilizability to an equilibrium fails for the nonholonomic spherical robot. A novel contribution of this note is a smooth, asymptotically stabilizing geometric control law for position and reduced attitude, which corresponds to an equilibrium submanifold of dimension one. From Brockett's condition, this is the best possible dimension of a smoothly stabilized equilibrium submanifold. We also present a novel smooth global tracking controller for tracking position trajectories.Index Terms-Algebraic/geometric methods, stability of NL systems, robotics, spherical robot, position and attitude stabilization.

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The Euler-Poincaré equations for a spherical robot actuated by a pendulum

Cited by 19 publications

References 9 publications

Unified Representation Of Decoupled Dynamic Models For Pendulum-Driven Ball-Shaped Robots

Unified Representation Of Decoupled Dynamic Models For Pendulum-Driven Ball-Shaped Robots

Reduced equations of motion for a wheeled inverted pendulum

Geometric Controllability and Stabilization of Spherical Robot Dynamics

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