Passivity-based control for haptic teleoperation of a legged manipulator in presence of time-delays

The paper’s continuous-time passivity identity for the tank-based teleoperator is correct and explicitly stated (Ḣmt + Ḣc + Ḣst = −uTmc ym − uTsc ys) with the tank dynamics and power-preserving interconnection defined in eqs. (6)–(8) . However, the discrete-time section relies on enforcing tank-positivity by design (master update (11), steering law (12), slave constraint (14)) without a rigorous proof that the master tank cannot reach negative energy within a sampling interval when wm = Fc (i.e., Hmt ≥ ζ regime) . The candidate solution correctly derives the continuous-time identity and the slave-side positivity under the inequality (14), but its master-side argument has a flaw: in the wm = Fc regime, it incorrectly invokes a boundary forward-invariance at Hmt = 0 that ignores the non-vanishing term −wT m ym in Ḣmt; the “send-only-if-present” rule applies to inter-tank exchange P±, not to this work term. Without an a priori per-step energy budget, Hmt can still decrease below zero in that regime. Hence both are incomplete: the paper lacks a full discrete-time proof for the master tank, and the model’s discrete-time master argument is incorrect in case (ii).