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It is well known that the twisting controller (TWC) is robust against perturbations but consumes large amounts of energy while the linear state feedback (LSF) is less robust but low energy consuming. This paper proposes a first step towards a trade-off between both algorithms (TWC and LSF) allowing to keep the robustness and to reduce the energy consumption. To achieve the trade-off, the exponent gain of the classical homogeneous controller introduced by Bhat and Bernstain in 1997 is switched between 0 (TWC) and 1 (LSF). The finite time convergence of the closed-loop system to a vicinity of the origin is established. Finally, some simulations that validate the effectiveness of the proposed controller are given. An additional result concerns the use of a dynamical law for the exponent gain.

A suspended Cable-Driven Parallel Robot (CDPR) composed of eight cables and a moving platform (MP) is used in a pick-and-place application of metal plates with different shapes, sizes and masses. In order to ensure robust control despite mass variation, several combinations of control schemes and control laws have been experimented on a prototype at IRT Jules Verne, France. The main objective of this paper is to provide recommendations on the selection of a control strategy depending on the available information on the carried mass, and the presence or absence of force sensors. Three scenarios are considered representing a degradation of the information on the carried mass to observe the impact on the performance of applicable control strategies. In a first case, force sensors are assumed available to measure cable tension, allowing the real-time estimation of the carried mass. In a second case, the mass of the MP is known, but not the mass of the carried metal plate whereas the third case considers no information at all on both the MP and the carried metal plate. The tested control laws include a standard proportional-derivative controller (PD), and a recently developed nonlinear controller balancing between sliding mode and linear algorithms (SML). The performances of each control strategy are analyzed along a test trajectory for several payloads, and a decision tree is proposed.