Mimicking Lorenz attractor behavior in a simple linear single-leg hopping robot

The dynamics of the Single-Leg Hopping Robot (SLHR) are explored, revealing a form of reverse temporal chaos that resembles the reverse butterfly attractor of the Lorenz system. To facilitate analysis, an electrical equivalent circuit of the SLHR is proposed, leveraging the force-voltage analogy to transform the mechanical system into an electrical counterpart. This transformation enables a more controlled and feasible simulation approach, overcoming the challenges associated with mechanical experimentation. The study investigates how variations in system parameters lead to bifurcations, transitioning from periodic orbits to chaotic behavior, with particular emphasis on the emergence of reverse-time chaos. Additionally, a novel design of a simple linear SLHR is introduced, which mimics the Lorenz butterfly attractor despite the absence of nonlinearities and external circuitry. This work provides new insights into SLHR dynamics and underscores the utility of electrical network simulations and practical in the study of complex mechanical systems, offering a simplified platform for further experimentation and analysis.