Triangularization of equations of motion for robotic systems

Rosenthal, Dan E.

doi:10.2514/3.20305

Cited by 7 publications

(7 citation statements)

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“…The analyst develops an expression for the angular velocity vector of each body B, «*. From each angular velocity, v terms called partial angular velocities are defined: (10) A partial angular velocity is simply a coefficient appearing in an expression for angular velocity. Because angular velocity is a vector, and speed is scalar, it follows that a partial angular velocity is always a vector.…”

Section: Dynamics Analysis Via Kane's Methodsmentioning

confidence: 99%

“…2 Minimal sets of dynamical equations involving Lagrangian generalized coordinates can be derived for tree-topology systems 3 and combined with algebraic constraint equations to handle kinematical loops. 4 ' 6 Kane's method 7 ' 10 and others are based on the principle that the virtual power of constraint forces and moments are identically zero. 4 ' 6 Although most formalisms produce the equations of motion in implicit form, as a set of coupled differential equations, recursive, order(fl) formalisms produce equations of motion in explicit form.…”

Section: Introductionmentioning

confidence: 99%

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Symbolic vector/dyadic multibody formalism for tree-topology systems

Sayers

1991

Journal of Guidance, Control, and Dynamics

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A multibody formalism is presented that can be applied to automatically generate efficient equations of motion for a system of rigid bodies in a tree topology. The formalism is built on Kane's analysis method and is described using vector/dyadic notation. In addition to defining a way to formulate equations of motion, it specifies many details of the analysis that have formerly involved judgments made by a dynamicist. These details include "rule of thumb" issues such as 1) making modeling simplifications, 2) choosing state variables, 3) introducing intermediate variables, 4) choosing coordinate systems to represent vectors, and 5) choosing recursive vs nonrecursive formulations. The formalism has been automated using a computer algebra language that supports vector/dyadic algebra, small variable simplification options, and the automated introduction of new symbols. A companion paper describes this language and provides details of an example of a spacecraft multibody system. Results shown in this paper for the example spacecraft illustrate the high computational efficiency of the simulation code.

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Section: Dynamics Analysis Via Kane's Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Symbolic vector/dyadic multibody formalism for tree-topology systems

Sayers

1991

Journal of Guidance, Control, and Dynamics

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“…The m kk terms in Ref . 6 correspond to D ~ \k) here, and the general m kj /m kk terms are precisely the elements where V. 0(91) Forward Dynamics Algorithms In this section, 0(91) algorithms for the computation of the forward dynamics of serial chains are discussed. We show that, aside from some minor differences, all of the 0(91) algorithms are closely related and have the same inherent structure.…”

Section: Tc = [/ + Hk]d[i + Hk]*mentioning

confidence: 99%

“…Thus the <t>( •) operators satisfy the semigroup property. Let us assume now that C is the center of mass of the rigid body and that the body has mass m and moment of inertia $(C) about C. The spatial inertia M(C) and the spatial momentum II(C) of the body about C are defined as 0 w/ y and (6) About the center of mass C, the equations of motion for the rigid body are given by…”

Section: Dynamics Of a Single Rigid Bodymentioning

confidence: 99%

“…These results provide a unifying perspective, within which these diverse dynamics algorithms arise naturally as a consequence of a progressive exploitation of the structure of the mass matrix. about G k = vector from 0^ to 0^_ i = spatial inertia of the Ath link about G k = mass of the Ath link = reference location of the Ath joint on the Ath link = reference location of the Arth joint on the (k + l)th link = vector from 0* to the center of mass of the Arth link = joint motion parameters for Ath joint = configuration variables for Ath joint Forces and Velocities a(k) €(R 6 = Coriolis and centrifugal spatial acceleration at 0* b(k) € (ft 6 = gyroscopic spatial force at G k F(k) € (R 3 = linear force of interaction between the accelerations v(k) at the Arth joint = articulated body relative joint acceleration at the Ath joint r(A:),7(A:) € (R 6 x 6 = articulated body projection operators for the Arth joint i/s8^ 6(R 6wx6rt = articulated body transformation operators for the full serial chain \l/(k + l,Ar) € (R 6x 6 = articulated body transformation operator from 0* to 0^ +1…”

mentioning

confidence: 99%

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Unified formulation of dynamics for serial rigid multibody systems

Jain

1991

Journal of Guidance, Control, and Dynamics

163

113

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There has been a growing interest in the development of new and efficient algorithms for multibody dynamics in recent years. Serial rigid multibody systems form the basic subcomponents of general multibody systems, and a variety of algorithms to solve the serial chain forward dynamics problem have been proposed. In this paper, the economy of representation and analysis tools provided by the spatial operator algebra are used to clarify the inherent structure of these algorithms, to identify those that are similar, and to study the relationships among the ones that are distinct. For the purposes of this study, the algorithms are categorized into three classes: algorithms that require the explicit computation of the mass matrix, algorithms that are completely recursive in nature, and algorithms of intermediate complexity. In addition, alternative factorizations for the mass matrix and closed form expressions for its inverse are derived. These results provide a unifying perspective, within which these diverse dynamics algorithms arise naturally as a consequence of a progressive exploitation of the structure of the mass matrix. Serial Chain oft €(R 9lx9l n .91 r p (k) r v (k) Link/ Joint Properties Nomenclature! = mass matrix for the serial chain = number of links in the serial chain = total number of motion DOF for the serial chain = number of positional DOF of the kth joint = number of motion DOF of the kth joint = joint matrix for the kth joint = moment of inertia of the Ath linkabout G k = vector from 0^ to 0^_ i = spatial inertia of the Ath link about G k = mass of the Ath link = reference location of the Ath joint on the Ath link = reference location of the Arth joint on the (k + l)th link = vector from 0* to the center of mass of the Arth link = joint motion parameters for Ath joint = configuration variables for Ath joint Forces and Velocities a(k) €(R 6 = Coriolis and centrifugal spatial acceleration at 0* b(k) € (ft 6 = gyroscopic spatial force at G k F(k) € (R 3 = linear force of interaction between the (k + l)th and kth links at 0* l(k,k-\) M(Ar) m(k)

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