Fractional-Order Dynamics Modeling for Continuum Robots

This paper proposes a fractional-order dynamics modeling approach for a multiple-backbone continuum robot, which is driven by superelastic Nickel-Titanium (NiTi) alloy wires and the NiTi wires behave a stress-strain hysteresis signature due to the viscoelasticity. Based on the basic knowledge of fractional calculus, the fractional-order Euler-Lagrange equation is derived, which extends the integral-order Euler-Lagrange equation. Then, fractional-order Euler-Lagrange equation is applied to Lagrange dynamics model and the continuum robot is modeled by fractional-order Lagrange dynamics. Simulation illustration is performed to demonstrate that there is hysteresis loop in the results of fractional-order dynamic model but not in the results of integral-order dynamic model, which shows that the fractional-order Lagrange dynamic model of continuum robots driven by NiTi wires has higher modeling accuracy.