For the first time, scientists have shown that a greedy Lyapunov algorithm—originally written for simple linear systems—can be lifted to a robot that follows a repeating orbit. By turning the robot’s motion into a periodically varying linear model, the team built a controller that fires fixed‑amplitude spikes whenever a Lyapunov function drops. These spikes appear in two phases: no‑input flow periods (w = 0) and jump periods where the spike adds or subtracts a small amount, a time‑dependent vector aB(τ), to the robot’s state.

The switching rule is based on a quadratic Lyapunov function V(τ,ξ)=ξᵀP(τ)ξ. When the value V falls below a threshold, a spike is generated. The spike intensity a is chosen from {5,6,10,12,20} ×10⁻³ and the algorithm keeps the transverse state ξ close to zero, which translates into the robot staying near its desired path.

The method was tested on the Butterfly robot, a planar link with a rolling ball. The loop period is T = 2.38 s. Experiments show that the transverse coordinates converge to a small neighbourhood of the origin even when disturbances, measurement noise, and sensor delays are present. The spiking controller remained effective, and every spike was recorded and filtered at 20 Hz.

The authors emphasize that the stability claim applies only to the linearized hybrid model. A full nonlinear proof and robustness analysis are future work.

Still, the results demonstrate that neuromorphic, event‑triggered spikes can be engineered to stabilize periodic orbits of underactuated robots, opening a route to low‑power autonomous control.