Minimal representation for the control of Gough-Stewart platforms via leg observation considering a hidden robot model

This paper presents new insights about the sensor-based control of Gough-Stewart (GS) platforms. Previous works have shown that it was possible to control the GS platform by observing its legs directions instead of using the encoders values or the measurement of the platform pose. It was demonstrated that observing only three legs directions was enough for the control but no physical explanations were given. Moreover, sometimes, the GS platform was not converging to the desired pose and the reasons of these divergences were not disclosed. This paper aims at answering to this two opened problems. It is shown that observing three leg directions involves controlling the displacement of a hidden robot whose models differs from those of the usual GS platform. This robot has assembly modes and singular configurations different from those of the GS platform. This involves that the legs to observe should be chosen carefully in order to avoid inaccuracy problems. In this sense, the accuracy analysis of the new robot is performed to show the importance of the leg selection. All these results are validated on a GS platform simulator created using ADAMS/Controls and interfaced with Matlab/Simulink.