Geometric Algorithms for Robot Dynamics: A Tutorial Review

[ Information ]

Applied Mechanics Reviews, vol. 70, no. 1, 2018.

[ Authors ]

Frank C. Park, Beobkyoon Kim, Cheongjae Jang, and Jisoo Hong

[ Abstract ]

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.