On the Optimal Singularity-Free Trajectory Planning of Parallel Robot Manipulators

Parallel robot manipulators comprise a mobile platform connected to a fixed base through three or more articulated links and are used extensively throughout industry for such diverse applications as high-precision positioning systems, fiber alignment, welding, robotic manipulators, automatic inspection systems, and so forth. Therefore, planning a trajectory to perform a specific task is one of the most important class of problems in the applications of the parallel robot manipulators. However, while moving along a specified trajectory, due to the limits on the workspace and existence of the force singularities, the parallel robot manipulators may not oppose forces or moments at some configurations. As a consequence, the manipulator gains some degrees of reedom, and becomes uncontrollable. Even the manipulator is very near to a singular manifold, the leg forces will increase violently to reach their allowable limits. Therefore, it is meaningful to plan a path without crossing a singular manifold on any operation for the parallel robot manipulators. Compared to the vast researches on the path-programming of serial manipulators, studies on the singularity-free path programming of the parallel robot manipulators are relatively few. (Bhattacharya et al., 1998) developed an exact and an approximate on-line singularity avoidance method to restructure a path in the vicinity of a singular manifold for platform type parallel manipulators. (Dasgupta & Mruthyunjaya, 1998) proposed an algorithm to obtain a singularity-free trajectory for given two end-poses. The continuous paths are constructed through well-conditioned via points by examining the condition number at discrete steps on the corresponding straight line segment. (Sen et al., 2003) used a variational approach based on a Lagrangian to plan singularity-free paths with the actuators lengths remaining within their allowable limits. (Dash et al., 2005) used local routing method based on Grassmann’s line geometry to avoid isolated singularities inside the reachable workspace of parallel manipulators. However, at present, most researches on the singularity-free path programming only deal with the kinemetics of the parallel robot manipulators. When repetitive tasks in industrial applications are considered, some of physical operating costs, such as actuating forces or energy consumption, will become significantly important. Consequently, these effects should be further taken into account for a singularity-free path programming. 23