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Register a new userVectorial Parameterizations of Pose
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Added by
Tim Barfoot
Publication date
2021
fields
Informatics Engineering
and research's language is
English
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Robotics and computer vision problems commonly require handling rigid-body motions comprising translation and rotation - together referred to as pose. In some situations, a vectorial parameterization of pose can be useful, where elements of a vector space are surjectively mapped to a matrix Lie group. For example, these vectorial representations can be employed for optimization as well as uncertainty representation on groups. The most common mapping is the matrix exponential, which maps elements of a Lie algebra onto the associated Lie group. However, this choice is not unique. It has been previously shown how to characterize all such vectorial parameterizations for SO(3), the group of rotations. Some results are also known for the group of poses, where it is possible to build a family of vectorial mappings that includes the matrix exponential as well as the Cayley transformation. We extend what is known for these pose mappings to the 4 x 4 representation common in robotics, and also demonstrate three different examples of the proposed pose mappings: (i) pose interpolation, (ii) pose servoing control, and (iii) pose estimation in a pointcloud alignment problem. In the pointcloud alignment problem our results lead to a new algorithm based on the Cayley transformation, which we call CayPer.
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Achieving human-like motion in robots has been a fundamental goal in many areas of robotics research. Inverse kinematic (IK) solvers have been explored as a solution to provide kinematic structures with anthropomorphic movements. In particular, numeric solvers based on geometry, such as FABRIK, have shown potential for producing human-like motion at a low computational cost. Nevertheless, these methods have shown limitations when solving for robot kinematic constraints. This work proposes a framework inspired by FABRIK for human pose imitation in real-time. The goal is to mitigate the problems of the original algorithm while retaining the resulting humanlike fluidity and low cost. We first propose a human constraint model for pose imitation. Then, we present a pose imitation algorithm (PIC), and its soft version (PICs) that can successfully imitate human poses using the proposed constraint system. PIC was tested on two collaborative robots (Baxter and YuMi). Fifty human demonstrations were collected for a bi-manual assembly and an incision task. Then, two performance metrics were obtained for both robots: pose accuracy with respect to the human and the percentage of environment occlusion/obstruction. The performance of PIC and PICs was compared against the numerical solver baseline (FABRIK). The proposed algorithms achieve a higher pose accuracy than FABRIK for both tasks (25%-FABRIK, 53%-PICs, 58%-PICs). In addition, PIC and its soft version achieve a lower percentage of occlusion during incision (10%-FABRIK, 4%-PICs, 9%-PICs). These results indicate that the PIC method can reproduce human poses and achieve key desired effects of human imitation.
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