Qualitative and quantitative characterisation of lorenz like chaos in a single leg hopping robot

Abstract The dynamic performance of the Single Leg Hopping Robot (SLHR) is thoroughly investigated in this paper. A linear electrical circuit analogy based on the force voltage formulation, is employed. The electrical equivalent provides a controlled and experimentally feasible platform. Our system performs a thorough qualitative as well as quantitative characterisation of SLHR dynamics. For qualitative characterization phase portrait, time series and for quantitative characterization return maps, Poincare sections, bifurcation diagrams, correlation dimension (D 2 ), Lyapunov exponent and permutation entropy (PE) are used. Evolution of the system as parameter values change reveals the emergence of reverse-time chaos, high sensitivity to initial conditions and the presence of a bounded butterfly like attractor. The study demonstrates that a simple linear electromechanical representations can reproduce complex dynamical patterns like nonlinear systems. This framework provides a practical method for exploring chaos in legged locomotion models. It also offers fresh insights into reverse-time instabilities within mechanical systems.