Error propagation on the Euclidean group with applications to manipulator kinematics

Yunfeng Wang, G.S. Chirikjian
2006 IEEE Transactions on robotics  
Error propagation on the Euclidean motion group arises in a number of areas such as errors that accumulate from the base to the distal end of manipulators. We address error propagation in rigid-body poses in a coordinate-free way, and explain how this differs from other approaches proposed in the literature. In this paper, we show that errors propagate by convolution on the Euclidean motion group, (3). When local errors are small, they can be described well as distributions on the Lie algebra
more » ... n the Lie algebra (3). We show how the concept of a highly concentrated Gaussian distribution on (3) is equivalent to one on (3). We also develop closure relations for these distributions under convolution on (3). Numerical examples illustrate how convolution is a valuable tool for computing the propagation of both small and large errors. , motion planning, design, and implementation of hyper-redundant, metamorphic, and binary manipulators. In recent years, he has expanded the scope of his research to include applications of group theory in a variety of engineering disciplines and the mechanics of biological macromolecules.
doi:10.1109/tro.2006.878978 fatcat:orqfrmkwzvec3dslscffkew25e