## Robot Dynamics: Equations and Algorithms (2000)

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Venue: | IEEE Int. Conf. Robotics and Automation |

Citations: | 42 - 2 self |

### BibTeX

@INPROCEEDINGS{Featherstone00robotdynamics:,

author = {Roy Featherstone},

title = {Robot Dynamics: Equations and Algorithms},

booktitle = {IEEE Int. Conf. Robotics and Automation},

year = {2000},

pages = {826--834}

}

### Years of Citing Articles

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### Abstract

This paper reviews some of the accomplishments in the field of robot dynamics research, from the development of the recursive Newton-Euler algorithm to the present day. Equations and algorithms are given for the most important dynamics computations, expressed in a common notation to facilitate their presentation and comparison. 1

### Citations

292 |
A Unified Approach for Motion and Force Control of Robot Manipulators: The Operational Space Formulation, in
- Khatib
- 1987
(Show Context)
Citation Context ... inertia matrix. Their Modified Composite Rigid Body Method includes computation of the manipulator Jacobian so that it is very efficient for computing the inertia matrix in operational space. Khatib =-=[20]-=- developed an operational-space formulation of robot dynamics, in which the equations are expressed in the same coordinate system that is used to command the robot: Cartesian coordinates and orientati... |

98 | Linear-time dynamics using Lagrange multipliers
- Baraff
- 1996
(Show Context)
Citation Context ... As the size of the system matrix is (n+nc)× (n + nc), this method is O((n + nc) 3 ). Method 2 is particularly useful if n ≫ nc, and offers the opportunity to use O(n) algorithms on the spanning tree =-=[5]-=-. From Eq 20, L M −1 L T λ = c − L M −1 (τ − C + τ a) . (21) This equation can be formulated in O(n n2 c ) operations via O(n) algorithms, and solved in O(n3 c). Once λ is known, τ c can be calculated... |

97 |
On line computational scheme for mechanical manipulators
- Luh, Walker, et al.
- 1980
(Show Context)
Citation Context ...cused on the problem of computational efficiency. In fact, many of the most efficient algorithms in dynamics, that are applicable to a wide class of mechanisms, were developed by robotics researchers =-=[23, 33, 10]-=-. While computational efficiency continues to be important for the simulation and control of increasingly complex mechanisms operating at higher speeds, other aspects of the dynamics problem are also ... |

81 |
The calculation of robot dynamics using articulated-body inertias
- FEATHERSTONE
- 1983
(Show Context)
Citation Context ...cused on the problem of computational efficiency. In fact, many of the most efficient algorithms in dynamics, that are applicable to a wide class of mechanisms, were developed by robotics researchers =-=[23, 33, 10]-=-. While computational efficiency continues to be important for the simulation and control of increasingly complex mechanisms operating at higher speeds, other aspects of the dynamics problem are also ... |

79 |
E cient Dynamic Computer Simulation of Robotic Mechanisms
- Walker, Orin
- 1982
(Show Context)
Citation Context ...cused on the problem of computational efficiency. In fact, many of the most efficient algorithms in dynamics, that are applicable to a wide class of mechanisms, were developed by robotics researchers =-=[23, 33, 10]-=-. While computational efficiency continues to be important for the simulation and control of increasingly complex mechanisms operating at higher speeds, other aspects of the dynamics problem are also ... |

61 | Inertial Properties in Robotic Manipulation: An Object-Level Framework
- Khatib
- 1995
(Show Context)
Citation Context ...that is used to command the robot: Cartesian coordinates and orientation of the end-effector. This formulation has been particularly successful in hybrid motion/force control and related applications =-=[21]-=-. Rodriguez [28] recognized the parallels between the concepts and techniques of Kalman filtering and the forward dynamics problem, and developed the spatial operator algebra framework for the study o... |

61 | A Spatial Operator Algebra for Manipulator Modeling and Control
- Rodriguez, Kreutz-Delgado, et al.
- 1991
(Show Context)
Citation Context ...ere should be a clear relationship between these equations and the recursive set from which the greatest computational efficiency is obtained. The use of spatial notation and spatial operator algebra =-=[11, 29]-=- has been very effective in this regard. Also, it is important to develop algorithms which have applicability to robotic mechanisms with general geometries and joint structures. While the early algori... |

47 |
Dynamics of multibody systems
- Roberson, Schwertassek
- 1988
(Show Context)
Citation Context ...ystems Systems with closed kinematic loops are much more complicated than tree-structure systems, and need a lengthy explanation to do them justice; so we refer readers to the lengthy explanations in =-=[27, 34]-=-. The main problem is that the joint variables are no longer independent, since they are subject to (potentially very complicated) loop-closure constraints. It is usually impractical to identify an in... |

46 |
A recursive Lagrangian formulation of manipulator dynamics and a comparative study of dynamics formulation complexity
- Hollerbach
- 1980
(Show Context)
Citation Context ... leg of a walking machine. Luh, Walker, and Paul [23] developed a very efficient Recursive NE Algorithm (RNEA) by referring most quantities to link coordinates. The RNEA is the most cited. Hollerbach =-=[16]-=- developed an O(N) recursive Lagrangian formulation, but found that it was much less efficient than the RNEA in terms of the number of multiplications and additions/subtractions required in the algori... |

46 |
Dynamics of Systems of Rigid Bodies
- Wittenburg
- 1985
(Show Context)
Citation Context ...ystems Systems with closed kinematic loops are much more complicated than tree-structure systems, and need a lengthy explanation to do them justice; so we refer readers to the lengthy explanations in =-=[27, 34]-=-. The main problem is that the joint variables are no longer independent, since they are subject to (potentially very complicated) loop-closure constraints. It is usually impractical to identify an in... |

39 |
Robot motion: planning and control
- Brady, Hollerbach, et al.
- 1982
(Show Context)
Citation Context ... most often cited. Unfortunately, space does not permit us to provide a comprehensive review of the extensive literature in the area. See some of the early books in the area for additional references =-=[7, 11]-=-. The classic approach to expressing the equations of motion was based on a Lagrangian formulation [18, 31] of the problem. Algorithms developed using Lagrangian dynamics were O(N 4 ), and had to be a... |

31 | Unified formulation of dynamics for serial rigid multibody systems
- Jain
- 1991
(Show Context)
Citation Context ...ed the spatial operator algebra framework for the study of multibody dynamics. This enabled him and others at JPL [29] to develop alternative factorizations of the mass matrix to derive the ABA. Jain =-=[17]-=- used the spatial operator algebra framework to provide a unified formulation for manipulator dynamics. From this, he was able to compare the various O(N 3 ), O(N 2 ), and O(N) algorithms that had bee... |

28 |
A very efficient algorithm for the simulation of robots and similar multibody systems without inversion of the mass matrix
- Brandl, Johanni, et al.
- 1986
(Show Context)
Citation Context ... of arithmetic operations required, the ABA was more efficient than the CRBA for N > 9 [11]. Also, using similar efficient transformations and link coordinates as Featherstone [11, 10], Brandl et al. =-=[8]-=- made further improvements on the ABA so that it was roughly comparable to the CRBA for N = 6. Further gains have been made in efficiency over the years, with McMillan and Orin [24] being representati... |

23 | Forward dynamics, elimination methods, and formulation stiffness in robot simulation
- Ascher, Pai, et al.
- 1997
(Show Context)
Citation Context ...ovide a unified formulation for manipulator dynamics. From this, he was able to compare the various O(N 3 ), O(N 2 ), and O(N) algorithms that had been previously published. Ascher,sPai, and Cloutier =-=[2]-=- used the spatial operator framework to unify the derivation of both the CRBA and the ABA, as two elimination methods to solve the same linear system. They also showed that the ABA is more accurate th... |

20 |
The near-minimum-time control of open-loop articulated kinematic chains
- Kahn, Roth
(Show Context)
Citation Context ...ive literature in the area. See some of the early books in the area for additional references [7, 11]. The classic approach to expressing the equations of motion was based on a Lagrangian formulation =-=[18, 31]-=- of the problem. Algorithms developed using Lagrangian dynamics were O(N 4 ), and had to be adapted for real-time control. Efficient low-order algorithms were sought for three major computations: 1. i... |

19 |
Recursive solution to the equations of motion of an n-link manipulator
- Armstrong
- 1979
(Show Context)
Citation Context ...e Articulated-Body Algorithm (ABA), but the paper was way ahead of its time and languished in obscurity for a decade. Later, Armstrong developed an O(N) algorithm for mechanisms with spherical joints =-=[1]-=-, and then Featherstone developed the ABA [10]. The first version of this algorithm was applicable to manipulators with singledegree-of-freedom joints, but the second included a general joint model an... |

17 |
A Divide-and-Conquer Articulated-Body Algorithm for Parallel O(log(n)) Calculation of Rigid-Body Dynamics. Part 1: Basic Algorithm
- Featherstone
- 1999
(Show Context)
Citation Context ... inertia, are represented using 6 × 6 matrices. The underlying algebra is a dual system of vector spaces. A brief description of the current version of spatial algebra can be found in the appendix of =-=[12]-=-, and a detailed description of the previous version in [11]. 3.1 The Recursive Newton-Euler Algorithm A general robot mechanism with tree structure can be modelled by a set of N movable links (rigid ... |

16 |
Kinematic and kinetic analysis of open-chain linkages utilizing Newton-Euler methods, Math Biosci
- Orin, McGhee, et al.
- 1979
(Show Context)
Citation Context ...rithms for inverse dynamics for robotics used a Newton-Euler (NE) formulation of the problem. Stepanenko and Vukobratovic [30] developed a recursive NE method for human limb dynamics, and Orin et al. =-=[26]-=- made the recursive method more efficient by referring forces and moments to local link coordinates for real-time control of a leg of a walking machine. Luh, Walker, and Paul [23] developed a very eff... |

14 | Efficient computation of articulatedbody inertias using successive axial screws - McMillan, Orin - 1995 |

12 | Dynamics of articulated open-chain active mechanisms - Stepanenko, Vukobratović - 1976 |

12 |
Computer simulation of the dynamics of complicated mechanisms of robot manipulators, Engineering Cybernetics 12(6): 65–70
- Vereshchagin
- 1974
(Show Context)
Citation Context ... was O(N 3 ). For small N, the first-order terms dominated the computation so that the result was quite efficient. The earliest known O(N) algorithm for forward dynamics was developed by Vereshchagin =-=[32]-=-. This algorithm uses a recursive formula to evaluate the GibbsAppel form of the equation of motion, and is applicable to unbranched chains with revolute and prismatic joints. The recursive formula wa... |

11 |
Recursive lagrangian dynamics of flexible manipulator arms,” The
- Book
- 1984
(Show Context)
Citation Context ...s of non-rigid behaviour, like compliance in the joint bearings, are relatively easy to incorporate into a rigid-body model; but elastic links are more complicated. This problem was addressed by Book =-=[6]-=-, who developed an efficient, recursive Lagrangian formulation (using 4 × 4 matrices) of both inverse and forward dynamics for serial chains with flexible links. A general modal formulation of elastic... |

8 |
Parallel o(log n) algorithms for computation of manipulator forward dynamics
- FIJANY, SHARF, et al.
- 1995
(Show Context)
Citation Context ...cient matrix in Eq. 28 is block-tridiagonal. This means that it can be solved in O(log(N)) time on a parallel computer with O(N) processors; and this is the key step in the Constraint-Force Algorithm =-=[14, 13]-=-. 4 Conclusion This paper has reviewed some of the major contributions made in the field of robot dynamics. The main algorithms and associated equations have been given using a common, concise notatio... |

8 |
The use of Kane's Dynamical Equations in Robotics
- Kane, Levison
(Show Context)
Citation Context ...cular classes of systems. For a particular robot configuration, the equations of motion when expressed in symbolic form usually involve the least computation to implement. The use of Kane’s equations =-=[19]-=- may be of value in this regard, although their use may also involve considerable manipulation of the basic equations to reduce them to the simplest form. Through the use of parallel algorithms, resea... |

8 |
Recursive Robot Arm Forward and Inverse Dynamics
- Rodriguez, Smoothing
(Show Context)
Citation Context ...command the robot: Cartesian coordinates and orientation of the end-effector. This formulation has been particularly successful in hybrid motion/force control and related applications [21]. Rodriguez =-=[28]-=- recognized the parallels between the concepts and techniques of Kalman filtering and the forward dynamics problem, and developed the spatial operator algebra framework for the study of multibody dyna... |

6 |
Efficient Modelling and Computation of Manipulator Dynamics Using Orthogonal Cartesian Tensors
- Balafoutis, Patel, et al.
- 1988
(Show Context)
Citation Context ...an the RNEA in terms of the number of multiplications and additions/subtractions required in the algorithm. Further gains have been made in efficiency over the years. The results of Balafoutis et al. =-=[3]-=- and He and Goldenberg [15] are representative of those that are up to a factor of 1.7 faster than early implementations of the RNEA (for a 6-DoF robot). Walker and Orin [33] used the RNEA for inverse... |

5 | Two numerical Issues in simulating constrained Robot Dynamics
- Ellis, Ricker
- 1994
(Show Context)
Citation Context ..., produces K T M K y = K T (τ − C + τ a − M ¨q0) . (22) This method also has cubic complexity, but it can be the most efficient if n − nc is small. It is also reported to be more stable than Method 1 =-=[9]-=-. 3.5 Global Analysis Techniques It is possible to express the equation of motion of a system of N independent rigid bodies in the form where f = I a + v × I v , (23) f = [f T 1 , . . . , f T N] T ∈ F... |

5 |
Alternate Formulations for the Manipulator Inertia Matrix
- Lilly, Orin
- 1991
(Show Context)
Citation Context ...mputation of the inertia matrix by about 30%. A number of other gains have been made over the years [4, 25] giving an overall improvement of close to a factor of two from that of [33]. Lilly and Orin =-=[22]-=- developed four methods for computation of the inertia matrix. Their Modified Composite Rigid Body Method includes computation of the manipulator Jacobian so that it is very efficient for computing th... |

5 |
Dynamic force analysis of spatial linkages
- Uicker
- 1967
(Show Context)
Citation Context ...ive literature in the area. See some of the early books in the area for additional references [7, 11]. The classic approach to expressing the equations of motion was based on a Lagrangian formulation =-=[18, 31]-=- of the problem. Algorithms developed using Lagrangian dynamics were O(N 4 ), and had to be adapted for real-time control. Efficient low-order algorithms were sought for three major computations: 1. i... |

4 |
A Technique for Analyzing Constrained Rigid-Body Systems and its Application to the Constraint Force Algorithm
- Featherstone, Fijany
- 1999
(Show Context)
Citation Context ...cient matrix in Eq. 28 is block-tridiagonal. This means that it can be solved in O(log(N)) time on a parallel computer with O(N) processors; and this is the key step in the Constraint-Force Algorithm =-=[14, 13]-=-. 4 Conclusion This paper has reviewed some of the major contributions made in the field of robot dynamics. The main algorithms and associated equations have been given using a common, concise notatio... |

4 |
An Algorithm for Efficient Computation of Dynamics of Robotic Manipulators
- Goldenberg, He
- 1989
(Show Context)
Citation Context ...e number of multiplications and additions/subtractions required in the algorithm. Further gains have been made in efficiency over the years. The results of Balafoutis et al. [3] and He and Goldenberg =-=[15]-=- are representative of those that are up to a factor of 1.7 faster than early implementations of the RNEA (for a 6-DoF robot). Walker and Orin [33] used the RNEA for inverse dynamics [23] as the basis... |

3 |
Efficient Computation of Manipulator Inertia Matrices and the Direct Dynamics Problem
- Balafoutis, Patel
- 1989
(Show Context)
Citation Context ... matrix [33]. Featherstone [11] used efficient transformations and link coordinates to reduce the computation of the inertia matrix by about 30%. A number of other gains have been made over the years =-=[4, 25]-=- giving an overall improvement of close to a factor of two from that of [33]. Lilly and Orin [22] developed four methods for computation of the inertia matrix. Their Modified Composite Rigid Body Meth... |

2 |
Robot Dynamics Algorithms. Boston-Dordrecht-Lancaster
- Featherstone
- 1987
(Show Context)
Citation Context ...ere should be a clear relationship between these equations and the recursive set from which the greatest computational efficiency is obtained. The use of spatial notation and spatial operator algebra =-=[11, 29]-=- has been very effective in this regard. Also, it is important to develop algorithms which have applicability to robotic mechanisms with general geometries and joint structures. While the early algori... |

2 |
Forward dynamics of multilegged vehicles using the composite rigid body method
- McMillan, Orin
- 1998
(Show Context)
Citation Context ... matrix [33]. Featherstone [11] used efficient transformations and link coordinates to reduce the computation of the inertia matrix by about 30%. A number of other gains have been made over the years =-=[4, 25]-=- giving an overall improvement of close to a factor of two from that of [33]. Lilly and Orin [22] developed four methods for computation of the inertia matrix. Their Modified Composite Rigid Body Meth... |