A Physics-Based Safety Recovery Approach for Fault-Resilient Multi-Quadcopter Coordination

The paper’s control-layer derivation is sound and matches the model’s use of input–output feedback linearization: after dynamic extension, the position output appears in its fourth derivative; a state transformation yields an external linear system ż = Az + Bs with yaw as a 2D internal subsystem, and choosing uψ and s places the fourth-order characteristic polynomial (31)–(36) for exponential tracking, exactly as the model states . The high-level guidance also aligns: the desired planar velocity ṙd = v(Ψy, −Ψx) keeps Ψ invariant along trajectories (cf. (1)–(2), (9)–(10)), which the model explicitly verifies by d/dt Ψ = 0 . However, the paper does not rigorously justify the existence or computation of the maximum admissible sliding speed v*: it proposes to “assign” v* by bisection and gives Algorithm 1 that increases translation speed until a rotor-speed limit is approached, but it neither proves continuity/monotonicity of the rotor-speed margin in v nor shows that the feasible set is nonempty and bounded—points the model carefully supplies (openness/nonemptiness at v = 0, boundedness from hardware, continuity-based bracketing) . The paper’s multiple-failure case also relies on a finite-difference Laplace solver (instead of the closed-form complex potential), which the model abstracts correctly at the level of Ψ-invariance but does not note this numerical replacement . Net: the paper’s qualitative claims and control design are correct, but key theoretical guarantees for v* are incomplete; the model fills those gaps with a defensible argument.