A Novel Method for the Localization of Convex Workpieces in Robot Workspace Using Gauss Map

Workpiece localization is the process of obtaining the location of a workpiece in a robot workspace. The location (position and orientation) is represented by the transformation between the workpiece (local) coordinate frame and the reference (world) frame. In this work, we propose a workpiece localization strategy to automate the localization process by collecting data sequentially and efficiently without the two common restrictive assumptions: the data used to calculate the transformation is readily available and the correspondence between the features used for calculation is known. Correspondingly, two subproblems are involved: (1) determining the correspondence between the measured data and the CAD model data, and (2) determining the next-best-views (NBVs) in case of limited measurement data. We assume the workpiece is convex and has at least three flat surfaces. We use the extended Gaussian images (EGIs) from the Gauss map of both the CAD model point clouds and measured point clouds to find the flat surfaces on the workpiece. A mixed integer convex optimization problem is solved to estimate the correspondence and the rotation between the flat surfaces in the CAD model and the measured point clouds. The translation part of the homogeneous transformation is obtained by solving a least-squares problem using the estimated correspondence. Potential views for further measuring the workpiece are generated by evaluating a defined search region to find the NBVs based on a specified criterion. The workpiece is considered to be fully localized when the distances in the estimated homogeneous transformation matrices are within a predefined threshold. Simulation results are provided to show the effectiveness of the proposed localization method.