Kinematics of Norma, a Spherical Robot, Rolling Over 3D Terrains

Kinematics and dynamics of spherical robots (SRs) on horizontal and inclined flat surfaces are well-investigated, while their behavior on generic 3D terrains has remained unexplored. This paper studies the kinematics of a class of SRs rolling over 3D terrains. First, a brief description of the selected configuration for the SR is presented along with the characterization of the modeling method. Next, the kinematics equations of the SR are derived based on the mathematical description of the terrain and the mechanical constraints of the robot. Then, a path tracking method is utilized for tracking a 3D desired trajectory. Finally, simulations are carried out to validate the developed model and the effectiveness of the proposed control scheme.