arXiv:2610.37310v1 Announce Type: cross Abstract: This work investigates the use of event-based spiking controllers, implemented as spiking neural networks, for trajectory tracking in underactuated robots. Specifically, we address the problem of stabilizing a prescribed periodic orbit. It is well known that, by applying the method of transverse linearization to the robot dynamics in a neighborhood of a periodic trajectory, the dynamics can be approximately described by a linear time-varying system with periodic coefficients (a periodic LTV system). The problem of orbital stabilization can therefore be reduced to stabilizing the trivial solution of this LTV system. We show that a previously proposed Lyapunov-based greedy design, originally developed for LTI systems, can also be extended to the corresponding linearized transverse dynamics, which take the form of a periodic LTV system. This enables the construction of a feedback controller for orbital stabilization of the robot. The effectiveness of the proposed method is demonstrated on the trajectory stabilization problem for the butterfly robot.