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Geometric Algorithms for Robot Dynamics: A Tutorial Review
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DOI：10.1115/1.4039078.png)
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Abstract
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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 Lietheoretic 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.
Keywords:
SPATIAL OPERATOR ALGEBRA
LIE GROUP FORMULATION
BODY CONTACT PROBLEMS
FLEXIBLE MANIPULATORS
PARALLEL MANIPULATOR
KINEMATICS
OPTIMIZATION
MOTION
SIMULATION
SYSTEMS
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