Workspace determination of planar parallel robots via progressive growing neural gas network

This paper is a revival for the so-called Growing Neural Gas Network (GNGN) approach in the context of kinematic analysis of parallel robots, more precisely workspace determination. Generally, in parallel robots, solving the forward kinematic problem (FKP) is much harder than finding the inverse kinematic solution (IKP), thus, workspace determination using FKP is a demanding task in most cases. Therefore, in this paper, a progressive growing neural gas network algorithm (PGNGN) is proposed, which is a systematic and general approach to obtain the topology of the workspace based on IKP equations. After establishing a preliminary network with few initial data points, the network starts to develop itself by considering new data points around its border neurons through a boundary data generation procedure. The proposed algorithm is able to continue learning, adding units and connections, until a performance criterion has been met which leads to a clear workspace topology with minimal errors. Finally, as case studies, the workspace of two planar 3-DOF parallel robots with 3-RPR and 3-PRR structures are studied. Results reveal the applicability and reliability of this method.