A Passive Recursive Newton Euler Algorithm and Its Application to Inverse Dynamics under Passivity-based Controller

This paper proposes a passivity-based Recursive Newton-Euler algorithm, abbreviated pRNE. The proposed pRNE algorithm solves the inverse dynamics under a passivity-based controller, which requires calculating the product term of the Coriolis matrix $C(q,\dot q)$ and the reference velocity ${\dot q^{{\text{ref}}}}$, that is, $C(q,\dot q){\dot q^{{\text{ref}}}}$. Two major parts are modified compared to the standard RNE algorithm: 1) matrix-vector factorization in single rigid body dynamics satisfying the skew-symmetric property, and 2) propagation for reference velocity and acceleration in recursive computation. Through simulation, the proposed pRNE algorithm combined with the passivity-based inverse dynamic controller (P-IDC) validates an accurate tracking performance under model uncertainty and disturbance compared to the standard inverse dynamic controller (IDC).