Symplectic reduction of holonomic open-chain multi-body systems with constant momentum

Chhabra, Robin; Emami, M. Reza

doi:10.1016/j.geomphys.2014.12.011

Cited by 11 publications

(8 citation statements)

References 27 publications

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“…In [54], a modeling approach was proposed that makes use of local exponential coordinates on the covering Lie subgroup defining the relative joint motions. A more holistic approach was taken by Chhabra [42,43] who introduced a generalized exponential formula.…”

Section: Open Issuesmentioning

confidence: 99%

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Geometric methods and formulations in computational multibody system dynamics

Müller

Terze

2016

Acta Mech

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Multibody systems are dynamical systems characterized by intrinsic symmetries and invariants. Geometric mechanics deals with the mathematical modeling of such systems and has proven to be a valuable tool providing insights into the dynamics of mechanical systems, from a theoretical as well as from a computational point of view. Modeling multibody systems, comprising rigid and flexible members, as dynamical systems on manifolds, and Lie groups in particular, leads to frame-invariant and computationally advantageous formulations. In the last decade, such formulations and corresponding algorithms are becoming increasingly used in various areas of computational dynamics providing the conceptual and computational framework for multibody, coupled, and multiphysics systems, and their nonlinear control. The geometric setting, furthermore, gives rise to geometric numerical integration schemes that are designed to preserve the intrinsic structure and invariants of dynamical systems. These naturally avoid the long-standing problem of parameterization singularities and also deliver the necessary accuracy as well as a long-term stability of numerical solutions. The current intensive research in these areas documents the relevance and potential for geometric methods in general and in particular for multibody system dynamics. This paper provides an exhaustive summary of the development in the last decade, and a panoramic overview of the current state of knowledge in the field.

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Section: Open Issuesmentioning

confidence: 99%

“…Recently, it was attempted in [42,43] and [54] to generalize this approach to non-holonomic systems. Along this line, an approach to model kinematic couplings that do not generate a motion subgroup was presented in [158].…”

Section: Open Issuesmentioning

confidence: 99%

Geometric methods and formulations in computational multibody system dynamics

Müller

Terze

2016

Acta Mech

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“…Provided the connection between screw motions and Lie group theory, kinematic mappings from the joint space to the task space (a subset of SE(3)) of a serial chain manipulator can be formulated [36,28,7]. In establishing a space manipulator's equations of motion, Hamiltonian and Lagrangian approaches prove beneficial due to their accommodation to Lie group formulations [7,8,38]. Note that due to the low-gravity orbital environment, space manipulators are often considered to possess negligible potential energy.…”

Section: Introductionmentioning

confidence: 99%

Singularity-Robust Full-Pose Workspace Control of Space Manipulators with Non-Zero Momentum

Rousso¹,

Chhabra²

2023

Preprint

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<p> We address the end-effector full-pose tracking control problem in free-floating space manipulators, experiencing constant non-zero linear and angular momentum. The aim is to develop an output-tracking (workspace) control law free of singularities due to parameterizing the end-effector motion and being robust against singularities of the input-output decoupling matrix (generalized Jacobian matrix). Space manipulators are modelled as open-chain multi-body systems with single- and multidegree-of-freedom joints, whose kinematics and dynamics are formulated on the Special Euclidean group SE(3). Such systems exhibit conserved (not necessarily zero) total momentum when operating in the free-floating regime, which we use to systematically reduce their dynamical equations by eliminating the base spacecraft’s motion. To avoid parameterizing the end-effector motion, we consider its full pose as the system output and develop a novel feedback linearization technique on the matrix Lie group SE(3) in the reduced phase space of the space manipulator. We then propose an intrinsic feedforward, feedback proportional-integral-derivative workspace controller involving a coordinate-free pose error function on SE(3) and velocity error on its Lie algebra. Using a Lyapunov candidate, this controller is proven to stabilize the end-effector pose to a feasible desired trajectory. The input-output decoupling matrix in the proposed control law can lose rank at some regions of the configuration space; hence, we implement a singularity-robust inverse, derived from the damped least squares method, to avoid impractical joint torques in these regions. The developed controller is implemented on a 7-degree-of-freedom manipulator onboard a spacecraft and its efficacy and robustness are demonstrated trough series of simulations. </p>

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“…Provided the connection between screw motions and Lie group theory, kinematic mappings from the joint space to the task space of a serial chain manipulator can be formulated [48,49,50]. In establishing a space manipulator's equations of motion from a geometric background, Hamiltonian and Lagrangian approaches prove beneficial due to their accommodation to Lie group formulations [50,51,52]. Note that due to the low-gravity orbital environment, space manipulators are often considered to possess negligible potential energy.…”

Section: Gnc Of Single-arm Free-floating Space Manipulatorsmentioning

confidence: 99%

Workspace Control of Free-Floating Space Manipulators for Implementation in a Novel On-Orbit Servicing Mission Architecture

Rousso¹

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An industrialized On-Orbit Servicing (OOS) mission architecture is proposed in this thesis which signifies the role of space manipulators in performing OOS missions. This mission architecture summarizes a procedure for OOS mission design based on a series of multi-objective optimization problems. To enhance proximity operations, it is concluded that the existence of an output tracking control system for space manipulators is beneficial. This thesis develops an output tracking controller to control the end-effector pose of an N-link free-floating space manipulator, with non-zero momentum. We employ feedback linearization on the Lie algebra of the Special Euclidean group SE(3) to remove the nonlinear influence from the system's dynamics and momentum in the controlled end-effector motion. Space manipulators are modelled as open-chain rigid multi-body systems, connected by either single or multi degree of freedom joints. The dynamics and kinematics of free-floating space manipulators are formulated on SE(3) using the exponential parameterization of screw motions. Multi-degree of freedom joints are modelled as the combination of the joints' individual exponential screw motion mappings to describe their motions as homogeneous transformations. The free-floating systems' equations of motion are obtained through an Euler-Lagrange derivation and decoupled into the base and manipulator motions. The conservation of linear and angular momentum is then considered as an affine nonholonomic constraint to the system, allowing for the dynamic reduction of a space manipulator system with conserved non-zero momentum. Due to the system's free-floating nature, the equations of motion are restricted to the manipulator's joint space which defines the region of controlled states.Two control cases are considered in this thesis, the first involving control over the output's linear motion and the second considering control over the end-effector pose. The first control case performs feedback linearization on R 3 where the resulting linear end-effector motion is controlled by a classical PID controller defined to impart a critically damped response in the error dynamics. For full pose control, feedback linearization is employed on se(3) for subsequent control using a modified feedforward, feedback PID control structure I first and foremost would like to extend my significant gratitude to my supervisor Dr. Robin Chhabra for providing me with constant support and the wonderful research experience. Aside from the tremendous technical insight and knowledge you have shared with me, you have also been a figure of compassion, perseverance and professionalism for which I very much appreciate. It has been a pleasure to conduct my research under your supervision. I would also like to acknowledge my colleagues in the ASRoM lab who have given their support and feedback in my research and have shared their friendship.I cannot describe the appreciation and love I have for my mom, Maria, my dad, Gilles, and my brother, Chris. To my parents in particular, th...

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Symplectic reduction of holonomic open-chain multi-body systems with constant momentum

Cited by 11 publications

References 27 publications

Geometric methods and formulations in computational multibody system dynamics

Geometric methods and formulations in computational multibody system dynamics

Singularity-Robust Full-Pose Workspace Control of Space Manipulators with Non-Zero Momentum

Workspace Control of Free-Floating Space Manipulators for Implementation in a Novel On-Orbit Servicing Mission Architecture

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