Generation of the global workspace roadmap of the 3-R R using rotary disk search

Abstract

Path planning for parallel manipulators in the configuration space can be a challenging task due to the existence of multiple direct kinematic solutions. Hence the aim of this paper is to define a generalised hierarchical path planning scheme for trajectory generation between two configurations in the configuration space for manipulators that exhibit more than one solution in their direct kinematics. This process is applied to the 3-RPR mechanism, constrained to a 2-DOF system by setting active joint parameter ρ 1 to a constant. The overall reachable workspace is discretised and deconstructed into smaller patches, which are then stitched together creating a global workspace roadmap. Using the roadmap, path feasibility is obtained and local path planning is used to generate a complete trajectory. This method can determine a singularity-free path between any two connectible points in the configuration space, including assembly mode changes.

Path planning and assembly mode-changes of 6-DOF Stewart-Gough-type parallel manipulators

“…In previous works [38], the rotary disk search was used for sorting and stitching multiple kinematic solutions together via a simple continuity function. This was a weighted depth-first search that favoured traversing away from the known boundaries of workspaces to improve the accuracy of solution-tracking.…”

“…A minimum of two sets of connected cells was expected, one for each aspect in positive and negative. It was also anticipated that there will be multiple connected sets of smaller workspaces for the positive and negative aspects as seen for other parallel mechanisms such as the 3-RPR and 3-RRR [38,39]. However for the parameters given for the 3-3 SGP, there seem to be only two connected workspaces.…”

“…Particularly for high-DOF parallel manipulators, it is more time-efficient to generate the reduced C-space, then utilise efficient path planning techniques for overcoming the problems with using this space. This has been widely studied, where different path planning methods to achieve this were explored [35,36,37,38,39]. In previous works [38,41], the path planning problem was simplified on this type of manipulator using the global workspace roadmap, which is a graphical representation of the reduced C-space.…”

“…This has been widely studied, where different path planning methods to achieve this were explored [35,36,37,38,39]. In previous works [38,41], the path planning problem was simplified on this type of manipulator using the global workspace roadmap, which is a graphical representation of the reduced C-space. This resulted in efficient path planning in that the existence of a singularity-free path can be pre-determined before path planning algorithms are applied.…”

Planning algorithms for complex manipulation tasks

“…While planning closed-chain motions in this so-called component level is relatively well-understood, the planning in the global level, i.e., across di erent connected components, remains a major hurdle when deploying a bimanual system to address practical tasks. Most results on the global-level planning exist only for planar parallel mechanisms (see, e.g., Au, Chen, and Chung 2012;Au, Chung, and Chen 2014). Motion planning presented in these works relied on discretization of the conguration space, the complexity of which escalates exponentially with respect to the number of DOFs.…”