Quartic Oscillator Model with Applications in Locomotion
André Carvalho, Miguel Botto, Jorge Martins
AI summary
Problem
Designing compliant locomotion models that balance biological relevance with parameter transparency, particularly for generating stable, self-sustained running gaits without force discontinuities at touchdown.
Approach
The authors introduce a quartic oscillator that pairs linear leg stiffness with a nonlinear, velocity-proportional energy regulation term, deriving parametric conditions via linearization to predict and tune gait characteristics.
Key results
- Derivation of a quartic oscillator with guaranteed unique limit cycle convergence.
- Development of a hopping model that accurately estimates stance parameters and flight/stance transitions.
- Extension to a 2D running model that emulates marathon-pace gait dynamics with high fidelity.
- Transparent parameterization method linking desired velocity, mass, leg length, and contact times to model coefficients.
Why it matters
Provides a biologically inspired, mathematically transparent template for designing and controlling stable legged robots and prosthetics.
Abstract
This work introduces a novel compliant model for running gaits. The model consists of a linear leg stiffness paired with a nonlinear energy regulation term. This new model, termed the quartic model, is shown to reproduce the external dynamics of a running gait. The characteristics of the gait are imposed through parametric conditions which are derived through linearization of the model. The nonlinear nature of the model ensures convergence towards a limit cycle, which makes the model a useful template for the control of legged systems.