Recursive Estimation of Rigid Body Motions

• Applicant: Professor Dr.-Ing. Uwe D. Hanebeck
• Subject Area: Automation, Mechatronics, Control Systems, Intelligent Technical Systems, Robotics
• Term: from 2016 to 2020
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 325035548

In this proposal, we focus on algorithms for recursive estimation of rigid body motions. A rigid body motion consists of a translation and a rotation. The group of rigid body motions in three dimensions is called SE(3) and plays an important role in a variety of applications in robotics, aerospace, and computer vision. Consider for example the problem of accurate motion tracking of a moving object, say, a robotic arm, an airplane, or a head-mounted camera. All these problems necessitate estimation of the pose of the considered object, i.e., the rigid body motion of a reference coordinate frame to the body coordinate frame.For this purpose, we propose a new probability distribution on SE(3) that can be used to represent uncertain rigid body motions. Unlike most approaches in literature, the novel distribution is based on so-called unit dual quaternions, a generalization of unit quaternions to the case of rigid body motions. The novel distribution can be seen as a generalization of the hyperspherical Bingham distribution, which has been applied to estimation on the rotation group SO(3) based on unit quaternions. Similar to the Bingham density, the novel density is antipodally symmetric, i.e., x and -x always have the same probability density, which resolves the problem that unit dual quaternions q and -q represent the same rigid body motion.Based on this new probability density, we plan to develop recursive estimation algorithms that have several key advantages compared to state-of-the-art algorithms. First of all, we can represent all rigid body motions, whereas methods based on the corresponding Lie algebra typically cannot represent rotations by exactly 180 degrees. Second, there are no singularities and there is no need to switch between different parameterizations. Furthermore, we do not need to make any assumptions that the uncertainty is low, that rotations are small, or that the density describing the rigid body motions is approximately Gaussian. Due to these advantages, we expect that recursive estimation algorithms based on the new density will outperform state-of-the-art approaches that rely on Gaussian assumptions or locally linear approximations.

• DFG Programme: Research Grants