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About this paper
Joan Solà, Jeremie Deray, Dinesh Atchuthan
This work introduces a "micro Lie theory," a simplified yet rigorous framework, to enhance the understanding and application of Lie theory for state estimation in robotics. It provides a comprehensive calculus for handling uncertainties and derivatives on Lie groups, supported by a new open-source C++ library, `manif`.
Key insights
- A carefully selected and simplified subset of Lie theory can provide a sufficient and rigorous mathematical foundation for designing optimal state estimators in robotics.
- Jacobians on Lie groups can be systematically defined and computed for various operations (inverse, composition, exponential map, group action) while adhering to the chain rule, enabling robust uncertainty propagation.
- The concepts of "composite manifolds" allow for the unified treatment of heterogeneous state variables, simplifying the formulation of complex multi-state estimation problems.
Summary by alphaXiv.
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