Distributed Finite-Time Formation Control for Multi-Parafoil Swarms Under Actuator Saturation Constraints

Rapid formation control of multi-parafoil swarms under gust disturbances and steering-line stroke limits is challenging because three-dimensional virtual commands must be realized through only two control channels and post-allocation saturation causes command mismatch. To address these problems, this paper proposes a distributed integral nonsingular fast terminal sliding-mode (INFTSM) controller based on a nonlinear six-degree-of-freedom model under the rigid-composite canopy–payload assumption, with gusts and steering-line saturation explicitly represented. Using information from neighboring parafoils, a controller maps virtual commands to symmetric and asymmetric steering inputs; the saturation residuals, gusts, and bounded modeling uncertainties form a lumped disturbance. An adaptive variable-gain power reaching law (AVPRL) adjusts the reaching gain according to the magnitude of the sliding variable, causing the gain to approach a prescribed minimum near the sliding manifold. Under bounded disturbances and sufficient residual control capability, Lyapunov and homogeneity analyses establish nominal finite-time convergence and local finite-time error bounds. Finally, 200 paired Monte Carlo trials are conducted on a software-in-the-loop (SIL) simulation platform based on MATLAB/Simulink and RflySim. The results show that the proposed method achieves a final 100 s formation-error RMSE of 58.706 ± 31.984 m, a conditional settling time of 629.29 ± 38.16 s, and an actuator saturation percentage of 1.046 ± 0.191%. These results demonstrate that, under the considered simulation conditions, the proposed method achieves multi-parafoil swarm formation control while satisfying the steering-line constraints and provides a favorable overall balance among tracking accuracy, convergence speed, and actuator-constraint handling.