Design-by-Optimization and Control of Redundantly Actuated Parallel Kinematics Sliding Star

Valášek, Michael; Bauma, V.; Šika, Z.; Belda, Květoslav; Píša, Pavel

doi:10.1007/s11044-005-2278-4

Cited by 21 publications

(11 citation statements)

References 6 publications

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“…Almost all the aforementioned work use only simulations to test their control or force optimization algorithm. The types of parallel mechanisms considered are almost exclusively planar [12], [14], [15]. Few experiment results on practical spatial parallel mechanisms can be found in the literature.…”

Section: A Redundant and Antagonistic Actuation Of Parallel Mechanismsmentioning

confidence: 99%

Cartesian stiffness evaluation of a novel 2 DoF parallel wrist under redundant and antagonistic actuation

et al. 2013

2013 IEEE/RSJ International Conference on Intelligent Robots and Systems

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In this paper, we present an experimental evaluation of the Cartesian stiffness of a novel parallel wrist under redundant and antagonistic actuation. The mechanism in consideration is Omni-Wrist V (OW5), a two degrees-offreedom (DoF) parallel mechanism redundantly actuated by three subchains. We first give a brief review of its kinetostatics and derive its reduced Cartesian stiffness model. To illustrate the stiffness enhancement of OW5 under redundant and antagonistic actuation, its Cartesian stiffness is measured and evaluated under four control schemes: the non-redundant control, the minimum 2-norm torque control without or with redundant encoder, and the antagonistic actuation control. Measurement data are represented using stiffness matrices and stiffness ellipses. Our study offers a quick quantitative evaluation of stiffness enhancement of OW5 under redundant and antagonistic actuation.

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Section: A Redundant and Antagonistic Actuation Of Parallel Mechanismsmentioning

confidence: 99%

Cartesian stiffness evaluation of a novel 2 DoF parallel wrist under redundant and antagonistic actuation

et al. 2013

2013 IEEE/RSJ International Conference on Intelligent Robots and Systems

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“…This applies to serial manipulators as well as to PKM without actuation redundancy as summarized in Paccot et al (2009) and Thanh et al (2009). However, since in case of RA-PKM more actuators are activated than required, decentralized control of RA-PKM naturally leads to conflicting control forces, reflected by undesired prestresses and an increased power consumption as observed in Saglia et al (2009),Valasek et al (2005, Wang et al (2009). Hence antagonistic control forces cannot be attributed to model uncertainties alone, as analyzed in Müller (2010), which could be minimized using model identification methods.…”

Section: Peculiarities Of Pkm With Actuation Redundancymentioning

confidence: 99%

Robust Modeling and Control Issues of Parallel Manipulators with Actuation Redundancy

Mueller¹

2011

Recent Advances in Robust Control - Theory and Applications in Robotics and Electromechanics

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G (q)q + C (q,q)q + Q (q,q, t) + J T (q) λ = u. ( 2 ) G is the generalized mass matrix of the tree-system, Cq represents generalized Coriolis and centrifugal forces, Q represents all remaining forces, including EE loads, and u are the generalized control forces. The Lagrange multipliers λ can be identified with the constraint reactions in cut-joints. The vector q ∈ V n represents the PKM configuration. The configuration space (c-space) of the PKM model is defined by the geometric constraints:V := {q ∈ V n |h (q) = 0} . ( 3 ) If J has locally full rank r, one can select δ := n − r joint variables, called independent coordinates, such that the admissible configurations q ∈ V are functions of these independent coordinates. This induces a coordinate partitioning. If the rank of J is constant, the c-space is smooth δ-dimensional manifold and δ is the DOF of the PKM, see Müller (2009). A configuration q where the rank of J changes is called a c-space singularity since then V is not a smooth manifold in q. Denote with q 1 and q 2 respectively the vector of dependent and independent coordinates, the velocity constraints can be written aswhere J = (J 1 , J 2 ),withJ 1 (q) ∈ R r,r , J 2 (q) ∈ R r,δ . By definition of independent coordinates J 1 has full rank, and the generalized velocities can be expressed aṡ q = Fq 2 ,w h e r eF :where the matrix F is an orthogonal complement of J because JF ≡ 0 . The time derivative of (5) yields the accelerationsq = Fq 2 +Ḟq 2 . Due to the existence of kinematic loops, PKM comprise passive joints and only the m control forces corresponding to the active joints are present in u.D e n o t ew i t hc ≡ (c 1 ,...,c m ) the vector of generalized control forces in the actuated joints, and let A be that part of F so that F T u = A T c. This means that if q a denote the vector of m actuator coordinates, thenq a = Aq 2 . Recent Advances in Robust Control -Theory and Applications in Robotics and Electromechanics www.intechopen.com Robust Modeling and Control Issues of Parallel Manipulators with Actuation Redundancy 5Projecting the motion equations (2) of the tree-system to the configuration space V,w i t ht h e help of the orthogonal complement F,andwith(5),yields G(q)q 2 + C (q,q)q 2 + Q(q,q, t) = A T (q) cwhere G := F T GF, C :=F T (CF + GḞ), Q := F T Q.The δ = n − m equations (6) together with the r dynamic constraints Jq +Jq = 0 yield a system of n ODE's in the n generalized coordinates q that govern the PKM dynamics when controlled via the generalized control forces c. The equations (6) have been first proposed by Voronets (1901) and are a special kind of Maggi's equations, Maggi (1901). They have been proposed for use in multibody dynamics in Angles & Lee (1988); Wehage & Haug (1982), and were put forward for PKM modeling in Cheng et al. (2003); Müller (2005); Thanh et al. (2009). The PKM control problem can now be represented as the control-affine control systeṁwith state vector x := (q 2 ,q 2 ),wheref is the drift vector field, and the columns g i , i = 1,...,m are the control vector f...

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“…A universal joint is installed between the central strut and the platform to constrain the mobility of the platform to two degrees of freedom. This results in an over-actuated mechanism with a singularity-free workspace [14] and a high stiffness capability.…”

Section: The Redundantly Actuated Platform Mechanismmentioning

confidence: 99%

“…In particular, compared to other devices, this platform has a higher number of inputs than the required outputs. This raises the issue of redundant control of the device and synchronization [14]. The paper presents the work of implementing online inverse kinematics to provide the desired actuation parameters in order for the platform to follow the expected orientation in sprained ankle physiotherapy.…”

Section: Introductionmentioning

confidence: 99%

Inverse-kinematics-based control of a redundantly actuated platform for rehabilitation

Saglia

Tsagarakis

Dai

et al. 2008

Proceedings of the Institution of Mechanical Engineers, Part I:

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The paper introduces the control of a redundantly actuated parallel mechanism for ankle rehabilitation which is based on online inverse kinematics calculation to generate required actuating parameters to control the mechanism and achieve the required dynamic response. The geometry of the mechanism is described and the design parameters are investigated in the analysis of singularity and dexterity. The dynamic model is developed and the tuning of the control gains is performed by analysing the level of actuation conflict and tracking error that have been minimized by varying the controller parameters. The paper further examines the actuation conflict and evaluates its association with the control parameters. Both simulation and experiments were carried out to implement the analysis and control strategy in the mechanism.

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Design-by-Optimization and Control of Redundantly Actuated Parallel Kinematics Sliding Star

Cited by 21 publications

References 6 publications

Cartesian stiffness evaluation of a novel 2 DoF parallel wrist under redundant and antagonistic actuation

Cartesian stiffness evaluation of a novel 2 DoF parallel wrist under redundant and antagonistic actuation

Robust Modeling and Control Issues of Parallel Manipulators with Actuation Redundancy

Inverse-kinematics-based control of a redundantly actuated platform for rehabilitation

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