0
Review Article

Geometric Algorithms for Robot Dynamics: A Tutorial Review

[+] Author and Article Information
Frank C. Park

Department of Mechanical and
Aerospace Engineering,
Seoul National University,
Seoul 08826, Korea
e-mail: fcp@snu.ac.kr

Beobkyoon Kim, Cheongjae Jang, Jisoo Hong

Department of Mechanical and
Aerospace Engineering,
Seoul National University,
Seoul 08826, Korea

Manuscript received April 25, 2017; final manuscript received December 12, 2017; published online February 7, 2018. Editor: Harry Dankowicz.

Appl. Mech. Rev 70(1), 010803 (Feb 07, 2018) (18 pages) Paper No: AMR-17-1029; doi: 10.1115/1.4039078 History: Received April 25, 2017; Revised December 12, 2017

We provide a tutorial and review of the state-of-the-art in robot dynamics algorithms that rely on methods from differential geometry, particularly the theory of Lie groups. After reviewing the underlying Lie group structure of the rigid-body motions and the geometric formulation of the equations of motion for a single rigid body, we show how classical screw-theoretic concepts can be expressed in a reference frame-invariant way using Lie-theoretic concepts and derive recursive algorithms for the forward and inverse dynamics and their differentiation. These algorithms are extended to robots subject to closed-loop and other constraints, joints driven by variable stiffness actuators, and also to the modeling of contact between rigid bodies. We conclude with a demonstration of how the geometric formulations and algorithms can be effectively used for robot motion optimization.

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Figures

Grahic Jump Location
Fig. 1

Differential of the left translation map LX−1

Grahic Jump Location
Fig. 2

A screw motion with screw axis ω̂ and pitch h

Grahic Jump Location
Fig. 3

Statics of a single rigid body

Grahic Jump Location
Fig. 4

Illustration of the PoE formula for a six-link open chain (UR5 robot visualized in V-REP [19])

Grahic Jump Location
Fig. 5

Point contact between two rigid bodies

Grahic Jump Location
Fig. 6

An example of multibody systems subject to multiple point contacts

Grahic Jump Location
Fig. 7

A revolute joint (left) and variable stiffness rotary actuator (right)

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