Dynamic modeling and obstacle-crossing capability of flexible pendulum-driven ball-shaped robots

Ball-shaped robots present a novel and widely studied approach for mobile robotics. Despite the essential benefit of the ball-robot that it cannot flip over or fall down, the robot's physical construction often severely limits the ball mobility in uneven terrain. The customarily applied quasi-static motion model makes the anticipated theoretical robot mobility even worse, because it completely ignores ball dynamics and therefore seriously under-estimates the robot's obstacle-crossing capability. The energy-based model, sometimes applied instead of the quasi-static model, over-estimates ball mobility and becomes inconvenient when an active driving motor is added to the system. This paper introduces a new extended dynamic model for flexible pendulum-driven ball-shaped robots, as well as a simulation-based method to predict the robot's step-crossing capability. The extended dynamic model allows rolling, bouncing and slipping of the robot, and it includes a simplified contact model for the ball-obstacle-interaction. The simulation results have been compared to experimental results obtained with a physical robot. The comparison shows that the new dynamic model and contact model outperform the traditionally applied quasi-static and energy-based models. The new dynamic model may be applied in mobility analysis of ball-robot designs, for path planning, as well as for control algorithm development.