Pedal curves of fronts in the sphere

Notions of the pedal curves of regular curves are classical topics. T. Nishimura [T. Nishimura, Demonstratio Math., 43 (2010), 447-459] has done some work associated with the singularities of pedal curves of regular curves. But if the curve has singular points, we can not define the Frenet frame at these singular points. We also can not use the Frenet frame to define and study the pedal curve of the original curve. In this paper, we consider the differential geometry of pedal curves of singular curves in the sphere. We define the pedal curve of a front and give properties of such pedal curve by using a moving frame along a front. At last, we give the classification of singularities of the pedal curves of fronts.