This work is devoted to prove that the nonlinear control scheme previously proposed by Zavala-Río, Fantoni and Lozano for the global stabilisation of the planar vertical take-off and landing (PVTOL) aircraft with bounded inputs neglecting the lateral force coupling is robust with respect to the parameter characterising such a lateral force coupling, ϵ, as long as such a parameter takes small enough values. In other words, global stabilisation is achieved even if ϵ > 0, provided that such a parameter be sufficiently small. As far as the authors are aware, such a property has not been proved in other existing control schemes when the value of ϵ is not known. The presented methodology is based on the use of embedded saturation functions. Furthermore, experimental results of the control algorithm implemented on a real prototype are presented.

Saturating‐proportional‐derivative‐type global continuous control for the finite‐time or (local) exponential stabilisation of mechanical systems with bounded inputs is achieved involving the desired conservative‐force compensation. Far from what one could expect, the proposed controller is not a simple extension of the on‐line compensation case but it rather proves to entail a closed‐loop analysis with a considerably higher degree of complexity. This gives rise to more involved requirements to guarantee its successful performance and implementability. Interesting enough, the proposal even shows that actuators with higher power‐supply capabilities than in the on‐line compensation case are required. Other important analytical limitations are further overcome through the developed algorithm. Experimental tests on a two‐degree‐of‐freedom robotic arm corroborate the efficiency of the proposed scheme.

SUMMARY: In this work, a generalized adaptive control scheme for the global position stabilization of robot manipulators with bounded inputs is proposed. It gives rise to various families of bounded controllers with adaptive gravity compensation. Compared with the adaptive approaches previously developed in a bounded-input context, the proposed scheme guarantees the adaptive regulation objective: globally, avoiding discontinuities in the control expression as well as in the adaptation auxiliary dynamics, preventing the inputs to reach their natural saturation bounds, and imposing nosaturation-avoidancerestriction on the control gains. Experimental results corroborate the efficiency of the proposed adaptive scheme.