Open-loop stiffness control of overconstrained mechanisms/robotic linkage systems

Freeman, Robert; Tesar, Delbert

doi:10.1109/robot.1989.100166

Cited by 43 publications

(26 citation statements)

References 20 publications

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“…The second part of the control vector c is the null-space component generating prestress that is closest to the desired c 0 . The possibility of generating control forces in the null-space has been used for backlash avoidance and stiffness control Müller (2005;2006); Valasek et al (2002); Yi et al (1989).…”

Section: Inverse Dynamics Solutionmentioning

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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Section: Inverse Dynamics Solutionmentioning

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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“…In order to exploit this effect, the control forces in the null-space of A T must be such that the change of A T due to a EE-perturbation yields a desired EE-wrench. This was attempted in (Müller, www.intechopen.com 2006; Yi et al, 1989). It turned out that, for the considered PKM, a large number of redundant actuators is required for stable control of all stiffness components.…”

Section: Stiffness Controlmentioning

confidence: 99%

Redundant Actuation of Parallel Manipulators

Mueller¹

2008

Parallel Manipulators, Towards New Applications

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“…Comparing with the ordinary parallel robot, the parallel robot with redundant actuation can optimize the load distribution between the actuators, reduce the energy consumption of each independent actuator, avoid driving force mutation, and improve force transmission properties of homogeneity and the rigidity of the agency (active stiffness). Thus the parallel robot with redundant actuation can obtain a better dynamic performance, higher stiffness and greater carrying capacity [5], [6]. In recent years, the redundant actuation parallel robot has widely been studied by many researchers.…”

Section: Introductionmentioning

confidence: 99%

The study of model predictive control algorithm based on the force/position control scheme of the 5-DOF redundant actuation parallel robot

Wen

Qin

Zhang

et al. 2016

Robotics and Autonomous Systems

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. (2016). The study of model predictive control algorithm based on the force/position control scheme of the 5-DOF redundant actuation parallel robot. Robotics and Autonomous Systems. DOI: 10.1016DOI: 10. /j.robot.2016 Citing this paper Please note that where the full-text provided on King's Research Portal is the Author Accepted Manuscript or Post-Print version this may differ from the final Published version. If citing, it is advised that you check and use the publisher's definitive version for pagination, volume/issue, and date of publication details. And where the final published version is provided on the Research Portal, if citing you are again advised to check the publisher's website for any subsequent corrections. General rightsCopyright and moral rights for the publications made accessible in the Research Portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognize and abide by the legal requirements associated with these rights.•Users may download and print one copy of any publication from the Research Portal for the purpose of private study or research.•You may not further distribute the material or use it for any profit-making activity or commercial gain •You may freely distribute the URL identifying the publication in the Research Portal Take down policy If you believe that this document breaches copyright please contact librarypure@kcl.ac.uk providing details, and we will remove access to the work immediately and investigate your claim. AbstractRedundant actuated parallel robot is a multi-input and multi-output (MIMO) system which usually works in an uncertain environment. In this paper, the force/position hybrid control structure of 6PUS-UPU redundant actuation parallel robot is designed, proportional-integral (PI) and model predictive control (MPC) cascade control strategy are used in the redundant branch of 6PUS-UPU redundant actuation parallel robot. The MPC algorithm is used in the current loop of the permanent magnet synchronous motor (PMSM) to restrain the motor parameter uncertainty and external disturbances influence on motor control. The MATLAB/ADAMS joint simulation method based on virtual 6PUS-UPU redundant actuation parallel robot prototype is used to test the performance of the proposed control strategy. The performance of proposed PI-MPC control strategy is compared with the traditional PI-PI control strategy. The simulation results show that the MPC controller can improve the tracking ability of the motor torque, guarantee the system robustness under the parameter variations and load disturbance environment.

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Open-loop stiffness control of overconstrained mechanisms/robotic linkage systems

Cited by 43 publications

References 20 publications

Robust Modeling and Control Issues of Parallel Manipulators with Actuation Redundancy

Robust Modeling and Control Issues of Parallel Manipulators with Actuation Redundancy

Redundant Actuation of Parallel Manipulators

The study of model predictive control algorithm based on the force/position control scheme of the 5-DOF redundant actuation parallel robot

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