The modeling of humanoid robots with many degrees-of-freedom (DoF) can be done via the complete dynamic model. However, the complexity of the model can hide the essential factor of the walking, i.e. the equilibrium of the robot.

A method for joint trajectory planning of kinematically redundant parallel manipulators is presented in this paper. The method is based on the use of feasibility maps that allow the graphical assessment of postures related to the different working modes of the manipulator. Thus, in such maps suitable trajectories are found in order to improve the performance of the manipulator and to avoid parallel singularities. When the desired path cannot be achieved by using only one working mode of the manipulator without crossing parallel singularities then, by applying the approach proposed here, a number of working modes could be chosen and combined to complete the whole path. The method can be applied to parallel manipulators with one degree of kinematic redundancy, whose legs allow the changing of working modes. The efficiency of this method is shown in a case study with a 3-RRR parallel manipulator (note that this manipulator becomes kinematically redundant if the orientation of the mobile platform is not specified for a desired task), in which postures associated to four working modes are employed in such a way that parallel singularities can be avoided. The obtained joint trajectories are applied to an experimental prototype to successfully execute the desired task.

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