Rolling Balance Board Robust Stabilization: A MID-based Design

Amina Benarab (1, 2, 3) , Csenge A Molnar (4) , Islam Boussaada (2, 3, 1) , Karim Trabelsi (2) , Tamás Insperger (4) , Silviu-Iulian Niculescu (3, 1)

1 L2S - Laboratoire des signaux et systèmes
2 IPSA - Institut Polytechnique des Sciences Avancées
3 DISCO - Dynamical Interconnected Systems in COmplex Environments
4 BME - Budapest University of Technology and Economics [Budapest]

This paper considers the stabilization of a rolling balance board by means of the multiplicity-induceddominancy property. A two degree-of-freedom mechanical model of a human balancing on a rolling balance board is analyzed in the sagittal plane. The human body is modeled by an inverted pendulum which connects to the balance board through the ankle joint. The system is stabilized by the ankle torque managed by the central nervous system (CNS). The action of the CNS is modeled by a delayed full state feedback: a pointwise delay stands for all latencies in the neuromechanical system (reaction time, neuromechanical lag, etc.). The aim of the paper is to achieve a good occurrence in terms of the decay rate, it shows the links with dominancy and with the exponential stability property of the solution.

Keywords: Human balance; exponential stability; Multiplicity-Induced-Dominancy

Domains: Mathematics [math]; Systems and Control [cs.SY]; General Mathematics [math.GM]; Nonlinear Sciences [physics]; Automatic

Amina Benarab, Csenge A Molnar, Islam Boussaada, Karim Trabelsi, Tamás Insperger, et al.. Rolling Balance Board Robust Stabilization: A MID-based Design. TDS 2022 - 17th IFAC Workshop on Time Delay Systems, Sep 2022, Montreal, Canada. ⟨hal-03765149⟩