Journal of Computer Science & Systems Biology

Determinant Analysis to Detect the Singularity of the Extended Theo Jansen Mechanism in the Phase-Rotation-Amplitude Parameter Space

Abstract

Kazuma Komoda and Hiroaki Wagatsuma

Legged robots have a potential of being a walking machine on irregular ground. Eleven-bar linkages, Theo Jansen mechanism reproduces a smooth locomotion pattern as gait. Parallel motions have widely used in the heavy machinery and recently highlighted in a model of biological motions. The close-loop linkage simply provides a designed end-effector trajectory, whereas the trajectory is considered to be less modifiable due to the singularity problem. In the present study, the singularity on the modified Theo Jansen mechanism was addressed by introducing the parametric orbit as a new freedom point in the joint center, and analyzed its kinematics and dynamics by using multibody dynamics (MBD). The extendability of the mechanism in the viewpoint of flexibility in the gait trajectory was clearly demonstrated in the numerical simulation, providing new functional gait trajectories controlled by two control parameters that change the shape of the parametric oval in the joint center. In systematic determinant analyses of how broken trajectories were generated depending on four parameters, i.e., horizontal and vertical amplitudes and rotation angle of the joint center movement and its phase difference with the driving link, morpho-logical changes of generated trajectories in the phase-rotation-amplitude parameter space were revealed. Thus the extension capability of Theo Jansen mechanism was validated not only in smooth walking but also in jumping, climbing and running-like motions. In considering the ways of control, the present results indicated that there exists a inverse relationship between the rotation angle and the phase difference to significantly reduce the occurrence of the singularity and breakage failures of the mechanism, which is consistent with biological evidences of coupling oscillators that enables the nervous system to control the complex musculoskeletal system by using a few of simple parameters frequently represented by the phase and rotation in a torus state space.