SE(n)++: An Efficient Solution to Multiple Pose Estimation Problems.

Area of Science:

• Robotics
• Computer Vision
• Lie Group Theory

Background:

• Robotic pose estimation often involves solving homogeneous transformations within the special Euclidean group SE(n).
• Existing SE(n) solvers face challenges due to the group's nonconvexity, leading to separate treatment of rotation and translation and suboptimal computational efficiency.

Purpose of the Study:

• To introduce a novel technique, SE(n)++, for addressing pose problems in robotics.
• To improve the computational efficiency and analytical performance of solving homogeneous transformations in SE(n).
• To provide a unified formulation for coupled rotation and translation problems on Lie groups.

Main Methods:

• A novel mapping from the special Euclidean group SE(n) to SO(n+1) is proposed.
• This mapping transforms the coupled rotation-translation problem into a unified formulation within the Lie group framework.
• The method is applied to three key robotic pose problems: point-cloud registration, hand-eye calibration, and SE(n) synchronization.

Main Results:

• The SE(n)++ method demonstrates enhanced analytical results and computational performance compared to traditional approaches.
• Experimental validation on open datasets confirms the effectiveness of the SE(n)++ technique.
• The unified formulation successfully addresses the coupling between rotation and translation.

Conclusions:

• The proposed SE(n)++ method offers a significant advancement in solving robotic pose problems.
• This technique provides a more efficient and analytically superior approach by unifying rotation and translation.
• SE(n)++ shows strong potential for practical applications in robotics, particularly in registration, calibration, and synchronization.