Previous works on parallel robots have shown that their visual servoing using the observation of their leg directions was possible. There were however found two main results for which no answer was given. These results were that (i) the observed robot which is composed of n legs could be controlled in most cases using the observation of only m leg directions (m < n), and that (ii) in some cases, the robot did not converge to the desired end-effector pose, even if the observed leg directions did (i.e. there was not a global diffeomorphism between the observation space and the robot space). Recently, it was shown that the visual servoing of the leg directions of the Gough-Stewart platform and the Adept Quattro was equivalent to controlling other virtual robots that have assembly modes and singular configurations different from those of the real ones. These hidden robot models are tangible visualizations of the mapping between the observation space and the real robots Cartesian space. Thanks to this concept, all the aforementioned points pertaining to the studied robots were answered. In this paper, the concept of the hidden robot model is generalized for any type of parallel robots controlled using visual servos based on the observation of elements other than the endeffector, such as the robot legs into motion. It is shown that the concept of the hidden robot model is a powerful tool that gives useful insights about the visual servoing of robots and that it helps define the necessary features to observe in order to ensure the controllability of the robot in its whole workspace. All theoretical concepts are validated through simulations with an Adams mockup linked to Simulink.

Previous works on the Gough-Stewart (GS) platform have shown that its visual servoing using the observation of its leg directions was possible by observing only three of its six legs but that the convergence to the desired pose was not guarantied. This can be explained by considering that the visual servoing of the leg direction of the GS platform was equivalent to controlling another robot, the 3-UPS that has assembly modes and singular configurations different from those of the GS platform. Considering this hidden robot model allowed the simplification of the singularity analysis of the mapping between the leg direction space and the Cartesian space.In this paper, the work on the definition of the hidden robot models involved in the visual servoing using the observation of the robot leg directions is extended to another robot, the Adept Quattro. It will be shown that the hidden robot model is completely different from the model involved in the control of the GS platform. Therefore, the results obtained for the GS platform are not valuable for this robot. The hidden robot has assembly modes and singular configurations different from those of the Quattro. An accuracy analysis is performed to show the importance of the leg selection. All these results are validated on a Quattro simulator created using ADAMS/Controls and interfaced with Matlab/Simulink.

Previous works on the visual servoing of parallel robots using the observation of their leg directions validated the feasibility of the approach but they have enlighten two main surprising results for which no answer was given: (i) the observed robot which is composed of n legs could be controlled in most cases using the observation of only m leg directions (m < n), and that (ii) in some cases, the robot did not converge to the desired end-effector pose, even if the observed leg directions did (i.e. there was not a global diffeomorphism between the observation space and the robot space). Recently, it was shown that the visual servoing of the leg directions of the Gough-Stewart platform and the Adept Quattro with 3 translational degrees of freedom was equivalent to controlling other virtual robots that have assembly modes and singular configurations different from those of the real ones. These hidden robot models are tangible visualizations of the mapping between the observation space and the real robots Cartesian space. Thanks to this concept, all the aforementioned points were answered for the mentioned robots. In this paper, the concept of hidden robot model is generalized for any type of parallel robots controlled using visual servos based on the observation of the leg directions. It is shown that the concept of hidden robot model is a powerful tool that gives useful insights about the visual servoing of robots using leg direction observation. With the concept of hidden robot model, the singularity problem of the controller can be addressed and the convergence issues of the controller can be explained, understood and solved. All these results are validated in simulations and through experiments on a Quattro robot.

Previous works on parallel robots have shown that their visual servoing using the observation of their leg directions was possible. There were however found two main results for which no answer was given. These results were that (i) the observed robot which is composed of n legs can be controlled using the observation of only m leg directions (m < n) arbitrarily chosen among its n 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. Recently, it has been shown that the visual servoing of the leg directions of the Gough-Stewart platform and the Adept Quattro with 3 translational degrees of freedom was equivalent to controlling other virtual hidden robots that have assembly modes and singular configurations different from those of the real ones. In this paper, the concept of hidden robot model is generalized for any type of parallel robots controlled using visual servos based on the observation of the leg directions. It is shown that the concept of hidden robot model is a powerful tool that gives useful insights about the visual servoing of robots using leg direction observation. With the concept of hidden robot model, the singularity problem of the mapping between the space of the observed robot links and the Cartesian space (including the analysis of the local minima and of the diffeomorphism between the observation space and the robot space) can be addressed. And above all, it is possible to give and certify the information about the controllability of the observed robots using the proposed controller. All these results are validated through experiments on a Quattro robot.