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Nonparametric Second-Order Theory of Error Propagation on Motion Groups.
Yunfeng Wang1, Gregory S Chirikjian
1Department of Mechanical Engineering, The College of New Jersey, Ewing, NJ 08628. jwang@tcnj.edu.
The International Journal of Robotics Research
|March 25, 2010
Summary
This study introduces a second-order approximation for error propagation in rigid-body poses on the Euclidean motion group, SE(3). The new recursive formula accurately models accumulated errors in systems like robot manipulators.
Area of Science:
- Robotics
- Mechanical Engineering
- Computational Geometry
Background:
- Error propagation is critical in mobile robot navigation and kinematic chains.
- Existing methods often linearize errors, limiting accuracy for small but non-negligible uncertainties.
Purpose of the Study:
- To develop a coordinate-free, second-order approximation for error propagation on the Euclidean motion group, SE(3).
- To introduce a novel recursive formula for propagating small errors beyond linear approximations.
Main Methods:
- Utilizing Lie algebras and Lie groups theory for error approximation.
- Deriving a nonparametric recursive formula for second-order error propagation.
- Conducting numerical tests on manipulator arms and flexible needles.
Main Results:
- A second-order approximation for error propagation on SE(3) was achieved.
- A new recursive formula was derived, improving accuracy over first-order methods.
- The nonparametric approach accommodates various probability density functions.
Conclusions:
- The developed second-order theory and recursive formula accurately model error propagation in complex systems.
- This method enhances precision in applications like robot kinematics and biomechanics.
- The nonparametric formulation offers broad applicability beyond Gaussian error assumptions.
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