A new Coriolis matrix factorization

Bjerkeng, Magnus; Pettersen, Kristin Y.

doi:10.1109/icra.2012.6224820

Cited by 14 publications

(9 citation statements)

References 12 publications

(31 reference statements)

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“…The definition of the Coriolis matrix is not unique and that different choices are possible (e.g. [38]) having different properties. The choice herein has the property of Ṁ − 2C being skew-symmetric, a useful property for controller design [17].…”

Section: Equations Of Motionmentioning

confidence: 99%

A Hybrid Modelling Approach for Aerial Manipulators

Kremer,

Sanchez-Lopez,

Voos

2022

Preprint

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Aerial manipulators (AM) exhibit particularly challenging, non-linear dynamics; the UAV and the manipulator it is carrying form a tightly coupled dynamic system, mutually impacting each other. The mathematical model describing these dynamics forms the core of many solutions in non-linear control and deep reinforcement learning. Traditionally, the formulation of the dynamics involves Euler angle parametrization in the Lagrangian framework or quaternion parametrization in the Newton-Euler framework. The former has the disadvantage of giving birth to singularities and the latter being algorithmically complex. This work presents a hybrid solution, combining the benefits of both, namely a quaternion approach leveraging the Lagrangian framework, connecting the singularity-free parameterization with the algorithmic simplicity of the Lagrangian approach. We do so by offering detailed insights into the kinematic modeling process and the formulation of the dynamics of a general aerial manipulator. The obtained dynamics model is validated experimentally against a real-time physics engine. A practical application of the obtained dynamics model is shown in the context of a computed torque feedback controller (feedback linearization), where we analyze its real-time capability with increasingly complex models.

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Section: Equations Of Motionmentioning

confidence: 99%

A Hybrid Modelling Approach for Aerial Manipulators

Kremer,

Sanchez-Lopez,

Voos

2022

Preprint

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“…The Jacobian J mc mapsq to ν a = [v T 1 , w T 1 , ..., v T n , w T n ] T . A factorization c(q,q) = C(q,q)q of the Coriolis/centrifugal matrix C, which preserves the skew-symmetry ofṀ − 2C for motion control purposes, is given in [21]. g denotes gravitational torques obtained by projecting the vector F g = [δ T 1 , ..., δ T n ] T of gravity forces δ i = [0, 0, −9.81 * m i , 0, 0, 0] T for each body onto J T mc .…”

Section: A Robot Dynamics Capturementioning

confidence: 99%

Value-Driven Robotic Digital Twins in Cyber-Physical Applications

Kaigom¹,

Roßmann²

2021

Preprint

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<div> <b>To appear in IEEE Transactions on Industrial Informatics</b></div><div><br></div><div><b>Abstract</b>: Although the skills of robot manipulators are becoming technically more complex, the unprecedented cost-effective access to recently unveiled intelligent robots has the potential to unleash as yet unimagined automation capabilities. A key technology behind this opportunity for companies to gain a competitive edge through an informed and intelligent robotized automation is the robotic digital twin (RDT). As such, the RDT will be instrumental in mirroring targeted properties of a physical robot to obtain a digital sibling flexibly harnessed in virtual testbeds to understand, predict, and shape the robot performance. However, these objectives remain challenging to well-established simulators. This is because the architectural and functional capabilities they support are not sufficiently in-line with ever-growing and varying demands for agile and cost-efficient manipulations. As a consequence, robot stakeholders can hardly use RDTs to unlock opportunities and meet needs from prospective markets. This paper contributes to addressing this gap. We introduce a novel concept for the development of a RDT that helps create and add value to current and future robotized cyber-physical applications. Hereinafter referred to as the value-driven RDT (vdRDT), it systematically captures the robot dynamics and purposefully farms data, about which its services reason to facilitate insight and deliver capabilities and benefits to stakeholders. Experiment results show that vdRDTs enlarge the scope of, adapt to, and revitalize robotized applications carried out in different fields.</div>

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“…where e = (q d − q) is the joint position error and k p and k v are positive scalars. Substituting (15) into 3gives…”

Section: Error Dynamics In Joint Trajectory Trackingmentioning

confidence: 99%

“…Furthermore, a matrix C may or not satisfy the skew-symmetric property, and if it does, the factorization is not unique. One analytical factorization that satisfies the skew-symmetric property was proposed in[15].…”

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confidence: 99%

Robust Humanoid Control Using a QP Solver with Integral Gains

Cisneros¹,

Benallegue²,

Benallègue

et al. 2018

2018 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)

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We propose a control framework for torque controlled humanoid robots that efficiently minimizes the tracking error in a Quadratic Programming (QP) formulated as a multiobjective weighted tasks with constraints. It results in an optimal dynamically-feasible reference that can be tracked robustly, with exponential convergence, without joint torque feedback, in the presence of non modelled torque bias and low-frequency bounded disturbances. This is achieved by introducing integral gains in a Lyapunov-stable torque control, which exploit the passivity properties of the dynamical model of the robot and their effect on the dynamic constraints of the QP solver. The robustness of this framework is demonstrated in simulation by commanding our robot, the HRP-5P, to achieve simultaneously several objectives in the configuration and the Cartesian spaces, in the presence of non-modeled static and kinetic joint friction, as well as an uncertain torque scale.

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A new Coriolis matrix factorization

Cited by 14 publications

References 12 publications

A Hybrid Modelling Approach for Aerial Manipulators

A Hybrid Modelling Approach for Aerial Manipulators

Value-Driven Robotic Digital Twins in Cyber-Physical Applications

Robust Humanoid Control Using a QP Solver with Integral Gains

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