Some flower-like gaits in the snakeboard’s locomotion

The snakeboard is a modified version of the skateboard in which the front and back pairs of wheels can pivot freely about a vertical axis (see Fig. 1). The rider can generate motion by coupling a turning of his/her feet which lie on wheel platforms with an appropriate twisting of his/her body without kicking off the ground. The snakeboard was first presented in details by [Lewis et al., in Proceedings of the 1994 IEEE International Conference on Robotics and Automation, San Diego, CA, USA, May 1994, pp. 2391–2400]. In literature, it also has been studied as a prototype of the symmetrical nonholonomic locomotion systems. Geometrical modeling, finding the gaits, presenting the controllability ideas and designing desired trajectories are the subjects that can be found in the literature of the snakeboard. In this paper, we present some symmetric sensitive flower-like gaits for the snakeboard by suitable tuning of the input parameters. The highly symmetric patterns generated by these gaits, besides their inherent beauty, sensitivity to parameter variations and coherency; exemplify the rich information content of the underlying nonlinear system.