A method for simplifying the analysis of leg-based visual servoing of parallel robots

As the end-effector pose is an external property of a parallel robot, it is natural to use exteroceptive sensors to measure it in order to suppress inaccuracies coming from modelling errors. Cameras offer this possibility. So, it is possible to obtain higher accuracy than in the case of classic control schemes (based on geometrical model). In some cases, it is impossible to directly observe the end-effector, but the leg directions can instead be used. In this case, however, unusual results were recorded, namely: (i) the possibility of controlling the robot by observing a number of legs less than the total number of legs, and that (ii) in some cases, the robot does not converge to the desired end-effector pose, even if the observed leg directions did. These results can be explained through the use of the hidden robot concept, which is a tangible visualisation of the mapping between the observed leg direction space (internal property) and Cartesian space (external property). This hidden robot has different assembly modes and singular configurations from the real robot, and it is a powerful tool to simplify the analysis of the aforementioned mapping. In this paper, the concept of hidden robot model is generalised for any type of parallel robot controlled through visual servoing based on observation of the leg directions. Validation has been accomplished through experiments on a Quattro robot with 4 dof.