Trajectory planning of kinematically redundant parallel manipulators by using multiple working modes

Abstract

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.

Numerical and experimental evaluation of the dynamic performance of kinematically redundant parallel manipulators

“…Both prepositioning and the ongoing approaches were described by multiobjective problems, defined by Eqs. (26) and (31), respectively. Both optimization problems were solved using the same weighting factors, w 1 ¼ w 2 ¼ 1.…”

“…The second cost function, that penalizes motion near singular regions can be related to the Condition Number of the Jacobian matrix A as proposed in Alba-Gomez et al [25] and Reveles et al [26]. In fact, this number can be interpreted as a measurement of the closeness of the endeffector and singular regions.…”

“…Due to this, the performance indexes derived from this matrix can be misleading [27]. An alternative to treat this issue is to homogenize it using the manipulator's characteristic length L c ¼ ffiffi ffi 2 p h as proposed in Alba-Gomez et al [25] and Reveles et al [26]:…”

“…The optimization problems defined by Eqs. (26) and (31) can be solved using evolutionary or deterministic methods that can solve constrained multivariable non-convex optimization problems [24]. In this work, starting values have been found using genetic algorithm and the optimum values by using sequential quadratic programming [24].…”

Full-Rotation Singularity-Safe Workspace for Kinematically Redundant Parallel Robots

“…A problem for parallel robots is that in addition to the the failure of the system when the mechanism is directly in a singularity, the performance of the robot also deteriorates as such a configuration is neared [8]. Therefore, as well as defining the geometric conditions where the robot is directly in a singularity, it is useful to define a region around this condition where the performance of the robot is likely to deteriorate.…”