Modeling and motion planning for mechanisms on a non-inertial base

From, Pål Johan; Duindam, Vincent; Gravdahl, Jan Tommy; Sastry, S. Shankar

doi:10.1109/robot.2009.5152666

Cited by 19 publications

(22 citation statements)

References 14 publications

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Section: General Multibody Dynamicsmentioning

confidence: 99%

“…The approach is based on Duindam and Stramigioli (2008) and From et al (2009) where the dynamics of vehicle-manipulator systems are derived and the boundedness property holds. However, for the Coriolis matrix presented in From et al (2009) the symmetry property does not hold. In this section we thus present a new formulation of the dynamic equations for vehiclemanipulator systems where both the boundedness and the symmetry properties hold and which allows us to include the vehicle configuration in the representation.…”

Section: General Multibody Dynamicsmentioning

confidence: 99%

“…We can also follow the generalised Lagrangian method introduced by Duindam and Stramigioli (2008) and From et al (2009). This method gives the dynamic equations for a general mechanism described by a set Q = {Q i } of configuration states Q i (not necessarily Euclidean), a vector v of velocity states v i ∈ R ni , and several mappings that describe the local Euclidean structure of the configuration states and their relation to the velocity states.…”

Section: Multibody Dynamics In Terms Of Quasi-coordinatesmentioning

confidence: 99%

See 2 more Smart Citations

On the Boundedness and Skew-Symmetric Properties of the Inertia and Coriolis Matrices for Vehicle-Manipulator Systems

From¹,

Schjølberg

Gravdahl³

et al. 2010

IFAC Proceedings Volumes

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This paper addresses the boundedness property of the inertia matrix and the skewsymmetric property of the Coriolis matrix for vehicle-manipulator systems. These properties are widely used in Lyapunov-based stability proofs and are therefore important to identify. For example, the skew-symmetric property does not depend on the system at hand, but on the choice of parameterisation of the Coriolis matrix, which is not unique. It is the authors' experience that many researchers take this assumption for granted without taking into account that there exist several parameterisations for which this is not true. In fact, most researchers refer to references that do not show this property for vehicle-manipulator systems, but for other systems such as single rigid bodies or manipulators on a fixed base. As a result, the otherwise rigorous stability proofs fall apart. In this paper we point out several references that are widely used, but that do not show this property and we refer to the correct references. As most references on this topics are not easily accessible, we also give the correct proofs for commonly used parameterisations of the Coriolis matrix and thus provide a proof for future reference. The same is the case for the boundedness property of the inertia matrix which for a bad choice of state variables will not necessarily hold. This can be solved by deriving the dynamics for vehiclemanipulator systems in terms of quasi-velocities, which allows us to describe the dynamics without the presence of the Euler angle singularities that normally arise in vehicle-manipulator dynamics. To the authors' best knowledge we derive for the first time the dynamic equations with both the skew-symmetric property of the Coriolis matrix and the boundedness property of the inertia matrix for vehicle-manipulator systems with non-Euclidean joints.

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Section: General Multibody Dynamicsmentioning

confidence: 99%

Section: General Multibody Dynamicsmentioning

confidence: 99%

Section: Multibody Dynamics In Terms Of Quasi-coordinatesmentioning

confidence: 99%

See 1 more Smart Citation

On the Boundedness and Skew-Symmetric Properties of the Inertia and Coriolis Matrices for Vehicle-Manipulator Systems

From¹,

Schjølberg

Gravdahl³

et al. 2010

IFAC Proceedings Volumes

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“…Finally, the terms C qV and C qq depend only on the first part of (6) and can be written as (From et al, 2009)…”

Section: Vehicles With Configurations Space Se(3)mentioning

confidence: 99%

“…A wide range of dynamical systems can be described by the Lagrange equations (Goldstein et al, 2001) …”

Section: State Of the Art Auv Dynamicsmentioning

confidence: 99%

Singularity-Free Dynamic Equations of AUV-Manipulator Systems

From

Pettersen

Gravdahl

2010

IFAC Proceedings Volumes

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In this paper we derive the singularity-free dynamic equations of AUV-manipulator systems using a minimal representation. Autonomous underwater vehicles (AUVs) are normally modeled using the singularity-prone Euler angles, but introducing quasi-coordinates allows us to derive the dynamics using minimal and globally valid non-Euclidean configuration coordinates. This is a great advantage as the configuration space of an AUV is non-Euclidean. We thus obtain a computationally efficient and singularity-free formulation of the dynamic equations with the same complexity as the conventional Lagrangian approach. The closed form formulation makes the proposed approach well suited for system analysis and model-based control. This paper focuses on the kinematic and dynamic properties of AUV-manipulator systems and we present the explicit matrices needed for implementation together with several mathematical relations that can be used to speed up the algorithms. The hydrodynamic and damping forces are also included in the equations. By presenting the explicit equations needed for implementation, the approach presented becomes more accessible and engineers and programmers can implement the results without extensive knowledge of the mathematical background.

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Singularity-free dynamic equations of spacecraft-manipulator systems

From¹,

Pettersen²,

Gravdahl³

2011

Acta Astronautica

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In this paper we derive the singularity-free dynamic equations of spacecraftmanipulator systems using a minimal representation. Spacecraft are normally modeled using Euler angles, which leads to singularities, or Euler parameters, which is not a minimal representation and thus not suited for Lagrange's equations. We circumvent these issues by introducing quasi-coordinates which allows us to derive the dynamics using minimal and globally valid non-Euclidean configuration coordinates. This is a great advantage as the configuration space of a spacecraft is non-Euclidean. We thus obtain a computationally efficient and singularity-free formulation of the dynamic equations with the same complexity as the conventional Lagrangian approach. The closed form formulation makes the proposed approach well suited for system analysis and model-based control. This paper focuses on the dynamic properties of free-floating and free-flying spacecraft-manipulator systems and we show how to calculate the inertia and Coriolis matrices in such a way that this can be implemented for simulation and control purposes without extensive knowledge of the mathematical background.

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Modeling and motion planning for mechanisms on a non-inertial base

Cited by 19 publications

References 14 publications

On the Boundedness and Skew-Symmetric Properties of the Inertia and Coriolis Matrices for Vehicle-Manipulator Systems

On the Boundedness and Skew-Symmetric Properties of the Inertia and Coriolis Matrices for Vehicle-Manipulator Systems

Singularity-Free Dynamic Equations of AUV-Manipulator Systems

Singularity-free dynamic equations of spacecraft-manipulator systems

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