FABRIKc Delta: Extending the FABRIKc Algorithm to Solve the Forward Kinematics of a Continuum Delta Robot

Xiang Wang, Yue Ding, Chang Zhou, Kai Xu

Abstract: Parallel continuum robots have attracted lots of attention due to higher positioning accuracy and stiffness compared to the serial ones. In our previous work, a novel Continuum Delta Robot (CDR) was proposed with a pure translational motion property. The forward kinematics (FK) of the CDR was solved through a non-linear optimization process, which is time-consuming. In this paper, the FABRIKc algorithm, which was proposed for the inverse kinematics (IK) of serial continuum robots, is extended to solve the CDR's FK in a more efficient manner. Firstly, the CDR is converted into an open-loop two-end kinematic chain (named the Delta-Chain) by separating two of the three proximal prismatic joints of the CDR. The proximal end of one leg of the CDR is the base of the Delta-Chain, while those of the other legs are treated as the Delta-Chain's two end-effectors. The CDR's actuation values (translations of the three proximal prismatic joints) provide the base and two target positions of the Delta-Chain's end-effectors. Thus, the CDR's FK is transformed to the IK of the Delta-Chain, where the FABRIKc algorithm is applied. In this so-called FABRIKc Delta algorithm, the CDR's FK is solved without using any matrix manipulation as the FABRIKc algorithm is a geometrical method. The details of the FABRIKc Delta algorithm for the CDR's FK are elaborated, while its computational efficiency is demonstrated through two simulation studies.