Dynamics and control of redundantly actuated parallel manipulators

Cheng, Hui; Yiu, Yiu-Kuen; Li, Zigang

doi:10.1109/tmech.2003.820006

Cited by 324 publications

(193 citation statements)

References 11 publications

Supporting

Mentioning

184

Contrasting

Unclassified

Order By: Relevance

“…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 systeṁ…”

Section: Wwwintechopencom Robust Modeling and Control Issues Of Parmentioning

confidence: 99%

“…Aiming for efficient real-time implementations model-based control schemes for PKM are based on a dynamic model in terms of minimal coordinates as pursued in Cheng et al (2003); Müller (2005); Nakamura & Ghodoussi (1989); Thanh et al (2009). A PKM is a force-controlled mechanism with kinematic loops.…”

Section: Manipulator Dynamicsmentioning

confidence: 99%

“…Now the feedforward term requires the inverse dynamics solution (11). These control methods, originally derived for non-redundantly actuated systems, can be directly adopted for RA-PKM as in Cheng et al (2003); Müller (2005); Paccot et al (2009). The APD can be used in the form (omitting null-space components)…”

Section: Augmented Pd and Computed Torque Controllermentioning

confidence: 99%

See 2 more Smart Citations

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

View full text Add to dashboard Cite

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...

show abstract

Section: Wwwintechopencom Robust Modeling and Control Issues Of Parmentioning

confidence: 99%

Section: Manipulator Dynamicsmentioning

confidence: 99%

Section: Augmented Pd and Computed Torque Controllermentioning

confidence: 99%

See 1 more Smart Citation

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

View full text Add to dashboard Cite

show abstract

“…It is well known that redundantly actuated PMs [19][20][21] have been investigated and utilized extensively, since redundant actuations can avoid kinematic singularities [22][23][24][25][26][27], enlarge load capability [28][29][30], improve dynamic characteristics [31,32], and eliminate backlash [33,34] of the mechanisms. The distribution of driving forces/torques of a redundantly actuated PM belongs to the statically indeterminate problem.…”

Section: Introductionmentioning

confidence: 99%

Methods for Force Analysis of Overconstrained Parallel Mechanisms: A Review

Liu

Yao

et al. 2017

Chin. J. Mech. Eng.

View full text Add to dashboard Cite

The force analysis of overconstrained PMs is relatively complex and difficult, for which the methods have always been a research hotspot. However, few literatures analyze the characteristics and application scopes of the various methods, which is not convenient for researchers and engineers to master and adopt them properly. A review of the methods for force analysis of both passive and active overconstrained PMs is presented. The existing force analysis methods for these two kinds of overconstrained PMs are classified according to their main ideas. Each category is briefly demonstrated and evaluated from such aspects as the calculation amount, the comprehensiveness of considering limbs' deformation, and the existence of explicit expressions of the solutions, which provides an important reference for researchers and engineers to quickly find a suitable method. The similarities and differences between the statically indeterminate problem of passive overconstrained PMs and that of active overconstrained PMs are discussed, and a universal method for these two kinds of overconstrained PMs is pointed out. The existing deficiencies and development directions of the force analysis methods for overconstrained systems are indicated based on the overview.

show abstract

“…The kinematic and dynamic control problems for parallel robots are considered in (Kövecses et al, 2003;Cheng et al, 2003;Rosario et al, 2007) and an autonomous control approach to reach the dynamic limits of parallel mechanisms is presented in (Pietsch et al, 2005).…”

Section: Introductionmentioning

confidence: 99%

Kinematic control of constrained robotic systems

Freitas

Leite

Lizarralde

2011

Sba Controle & Automação

View full text Add to dashboard Cite

RESUMO Controle de Sistemas Robóticos com Restrições CinemáticasEste artigo considera o problema de controle de postura para sistemas robóticos com restrições cinemáti-cas. A ideia principal é considerar as restrições cinemáticas dos mecanismos a partir de suas equações estruturais, ao invés de usar explicitamente a equação de restrição. Um estudo de caso para robôs paralelos e robôs cooperativos é discutido baseado nos conceitos de cinemática direta, cinemática diferencial, singularidades e controle cinemático. Resultados de simulação, obtidos a partir de um mecanismo F our-Bar linkage, uma plataforma de Gough-Stewart planar e dois robôs cooperativos, ilustram a aplicabilidade e versatilidade da metodologia proposta.PALAVRAS-CHAVE: robôs paralelos, robôs redundantes, coordenação multi-rôbos, singularidades cinemáticas . ABSTRACTThis paper addresses the posture control problem for robotic systems subject to kinematic constraints. The key idea is to consider the kinematic constraints of the mechanisms from their structure equations, instead of explicitly using the constraint equations. A case study for parallel robots and cooperating redundant robots is discussed based on the following concepts: forward kinematics, differential kinematics, singularities and kinematic control. Simulations results, obtained with a Four-Bar linkage mechanism, a planar Gough-Stewart platform and two cooperating robots, illustrate the applicability and versatility of the proposed methodology.

show abstract

Dynamics and control of redundantly actuated parallel manipulators

Cited by 324 publications

References 11 publications

Robust Modeling and Control Issues of Parallel Manipulators with Actuation Redundancy

Robust Modeling and Control Issues of Parallel Manipulators with Actuation Redundancy

Methods for Force Analysis of Overconstrained Parallel Mechanisms: A Review

Kinematic control of constrained robotic systems

Contact Info

Product

Resources

About