Motion of a Ball Wheel Based Omnidirectional Platform Over Uneven Terrain

Recent work by the present authors has presented a redundant, reconfigurable ball wheel mechanism, and the motion of an associated omnidirectional platform was simulated on flat terrain (Lee et al., 2007 Lee , Y.-C. , Lee , D. V. , Chung , J. H. , Velinsky , S. A. ( 2007 ). Control of a redundant, reconfigurable ball wheel drive mechanism for an omnidirectional mobile platform . Robotica 25 ( 4 ): 385 – 395 . [Google Scholar]). The outdoor environment usually contains uneven terrain, and in this article, motion of an omnidirectional-wheeled mobile platform based on three ball wheel drive mechanisms is studied when the platform moves on uneven terrain that is modeled as a smooth surface. A critical issue that arises for uneven terrain is that the point of contact of the wheel and the terrain is changing. This introduces three more degrees of freedom, which cannot be directly controlled and should also be considered in uneven terrain motion. Herein, Euler–Rodrigues parameters are used to derive the necessary transformations, and Montana's contact equations with the geometric parameters of the terrain are used for tracing the contact point. Simulation results are then presented for motion on flat terrain and both concave and convex spherically shaped terrain. The results clearly show the effectiveness of the proposed method, which can accommodate other more complex terrains provided that the surface configuration is given in an orthogonal coordinate chart.