FABRIK

Inverse kinematics solutions using conformal geometric algebra. This paper describes a novel iterative Inverse Kinematics (IK) solver, FABRIK, that is implemented using Conformal Geometric Algebra (CGA). FABRIK uses a forward and backward iterative approach, finding each joint position via locating a point on a line. We use the IK of a human hand as an example of implementation where a constrained version of FABRIK was employed for pose tracking. The hand is modelled using CGA, taking advantage of CGA’s compact and geometrically intuitive framework and that basic entities in CGA, such as spheres, lines, planes and circles, are simply represented by algebraic objects. This approach can be used in a wide range of computer animation applications and is not limited to the specific problem discussed here. The proposed hand pose tracker is real-time implementable and exploits the advantages of CGA for applications in computer vision, graphics and robotics.


References in zbMATH (referenced in 10 articles )

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  1. El Mir, Ghina: A group of viewpoint changes in the conformal Clifford algebra (2018)
  2. Chai, Xinxue; Li, Qinchuan: Analytical mobility analysis of Bennett linkage using geometric algebra (2017)
  3. Papaefthymiou, Margarita; Hildenbrand, Dietmar; Papagiannakis, George: A conformal geometric algebra code generator comparison for virtual character simulation in mixed reality (2017)
  4. Wei, Feng; Wei, Shimin; Zhang, Ying; Liao, Qizheng: Forward displacement analysis of a general 6-3 Stewart platform using conformal geometric algebra (2017)
  5. Alastair Lansley, Peter Vamplew, Philip Smith, Cameron Foale: Caliko: An Inverse Kinematics Software Library Implementation of the FABRIK Algorithm (2016) not zbMATH
  6. Kim, Je Seok; Jeong, Yong Hoon; Park, Jahng Hyon: A geometric approach for forward kinematics analysis of a 3-SPS/S redundant motion manipulator with an extra sensor using conformal geometric algebra (2016)
  7. Ma, Sha; Shi, Zhiping; Shao, Zhenzhou; Guan, Yong; Li, Liming; Li, Yongdong: Higher-order logic formalization of conformal geometric algebra and its application in verifying a robotic manipulation algorithm (2016)
  8. Hitzer, Eckhard; Nitta, Tohru; Kuroe, Yasuaki: Applications of Clifford’s geometric algebra (2013)
  9. Aristidou, Andreas; Lasenby, Joan: Inverse kinematics solutions using conformal geometric algebra (2011)
  10. Aristidou, Andreas; Lasenby, Joan: FABRIK: a fast, iterative solver for the Inverse Kinematics problem (2011) ioport