Lagrangian dynamics of open multibody systems with generalized holonomic and nonholonomic joints

Duindam, Vincent

doi:10.1109/iros.2007.4399066

Cited by 14 publications

(11 citation statements)

References 9 publications

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“…For more details on how to derive the dynamics see From et al [3] or Duindam et al [17], [18]. We consider the setup of Figure 2 describing a general n-link robot manipulator arm attached to a moving base.…”

Section: Ship-manipulator Modelingmentioning

confidence: 99%

On the influence of ship motion prediction accuracy on motion planning and control of robotic manipulators on seaborne platforms

From

Gravdahl

Abbeel

2010

2010 IEEE International Conference on Robotics and Automation

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Abstract-Robotic manipulators on non-inertial platforms, such as ships, have to endure large inertial forces due to the non-inertial motion of the platform. When the non-inertial platform's motion is known, motion planning and control algorithms can eliminate these perturbations-in fact, in some situations the motion planning algorithms can even leverage the inertial forces to more cheaply move to a target point. However, for many non-inertial platforms, the motion is unknown.In this paper we investigate how prediction errors and the choice of the prediction horizon affect the motion planning and control of robots mounted on a non-inertial base with a particular focus on seaborne platforms. We study the following three aspects: (i) We study prediction of ship motion and how prediction errors affect the motion planning and control of the manipulator. (ii) We evaluate the relationship between prediction accuracy and control. In particular, we study what prediction horizon length is useful for motion planning and control. We also consider how uncertainties in the ship motion predictions map to uncertainties in the future state of the robot and how to include the variance in the cost function to increase the optimal horizon length. (iii) Finally, we study a receding horizon approach, which re-solves the optimal control problem on-line over a horizon as determined to be meaningful from (ii). Several simulations are presented and, to our knowledge, for the first time experiments of ship-manipulator systems based on real ship motion data are presented.

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Section: Ship-manipulator Modelingmentioning

confidence: 99%

On the influence of ship motion prediction accuracy on motion planning and control of robotic manipulators on seaborne platforms

From

Gravdahl

Abbeel

2010

2010 IEEE International Conference on Robotics and Automation

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“…To derive the dynamics of the complete mechanism (including the 6-DoF between Ψ 0 and Ψ b ), we follow the generalized Lagrangian method introduced by Duindam et al [12], [13]. This method gives the dynamics 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: B Manipulator Dynamics On a Non-inertial Basementioning

confidence: 99%

“…Our approach differs from previous work in that the dynamic equations are derived for rigid multibody systems including both Euclidean joints and generalized joints with configuration spaces different from R n . We follow the generalized Lagrangian approach presented in Duindam et al [12], [13], which allows us to combine the Euclidean joints (the manipulator) and more general joints (the base), i.e. joints that can be described by the Lie group SE(3) or one of its ten subgroups.…”

Section: Introductionmentioning

confidence: 99%

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

From

Duindam

Gravdahl

et al. 2009

2009 IEEE International Conference on Robotics and Automation

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Abstract-Robotic manipulators on ships and platforms suffer from large inertial forces due to the non-inertial motion of the ship or platform. When operating in high sea state, operation of such manipulators can be made more efficient and robust if these non-inertial effects are taken into account in the motion planning and control systems.Motivated by this application, we present a rigorous and singularity-free formulation of the dynamics of a robotic manipulator mounted on a non-inertial base. We extend the classical dynamics equations for a serial manipulator to include the 6-DoF motion of the non-inertial base. Then, we show two examples of a 1-DoF and a 4-DoF manipulator to illustrate how these non-inertial effects can be taken into account in the motion planning.

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“…In this paper we will derive in detail the explicit dynamic equations based on the correct formulation rst presented in brief in From et al (2012). and Stramigioli (2007and Stramigioli ( , 2008, for example, we would nd that these are dierent from the standard formulation of the dynamics and, more importantly, nor can they be reformulated into these. The equations presented in Duindam andStramigioli (2007, 2008) and From et al (2010) (Goldstein et al, 2001;Arnold, 1989).…”

Section: Introductionmentioning

confidence: 99%

n Explicit Formulation of Singularity-Free Dynamic Equations of Mechanical Systems in Lagrangian Form---Part one: Single Rigid Bodies

From¹

2012

MIC

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This paper presents the explicit dynamic equations of a mechanical system. The equations are presented so that they can easily be implemented in a simulation software or controller environment and are also well suited for system and controller analysis. The dynamics of a general mechanical system consisting of one or more rigid bodies can be derived from the Lagrangian. We can then use several well known properties of Lie groups to guarantee that these equations are well dened. This will, however, often lead to rather abstract formulation of the dynamic equations that cannot be implemented in a simulation software directly. In this paper we close this gap and show what the explicit dynamic equations look like.These equations can then be implemented directly in a simulation software and no background knowledge on Lie theory and dierential geometry on the practitioner's side is required. This is the rst of two papers on this topic. In this paper we derive the dynamics for single rigid bodies, while in the second part we study multibody systems. In addition to making the equations more accessible to practitioners, a motivation behind the papers is to correct a few errors commonly found in literature.For the rst time, we show the detailed derivations and how to arrive at the correct set of equations. We also show through some simple examples that these correspond with the classical formulations found from Lagrange's equations. The dynamics is derived from the BoltzmannHamel equations of motion in terms of local position and velocity variables and the mapping to the corresponding quasi-velocities. Finally we present a new theorem which states that the BoltzmannHamel formulation of the dynamics is valid for all transformations with a Lie group topology. This has previously only been indicated through examples, but here we also present the formal proof.

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Lagrangian dynamics of open multibody systems with generalized holonomic and nonholonomic joints

Cited by 14 publications

References 9 publications

On the influence of ship motion prediction accuracy on motion planning and control of robotic manipulators on seaborne platforms

On the influence of ship motion prediction accuracy on motion planning and control of robotic manipulators on seaborne platforms

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

n Explicit Formulation of Singularity-Free Dynamic Equations of Mechanical Systems in Lagrangian Form---Part one: Single Rigid Bodies

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