Trajectory Planning for Spherical Robot Based on Differential Flatness

The spherical robot epitomizes an underactuated and non-holonomic system, where the control input is less than the system's degrees of freedom, thus rendering navigation and control complex. To equip the spherical robot with the ability to navigate various environments, perform multi-scene inspection tasks, and dynamically update its motion path in real time, necessitating the exploration of a path planning algorithm suitable for this mobile robot. In this research, a trajectory optimization method predicated on differential flatness for spherical robots has been proposed. We commence by elucidating the kinematic model of the spherical robot and the theoretical principles of differential flatness. Subsequently, we elaborate on deploying differential flatness in generating the robot's trajectory. This methodology not only facilitates the generation of a smooth trajectory but also ensures the feasibility and rationality of the trajectory. The research is concluded with a series of experimental demonstrations, reinforcing the superior efficacy of our methodology in a variety of scenarios and comparative experiments. In conclusion, our research furnishes a novel and efficacious approach to the trajectory optimization of spherical robots.