An improved Monte Carlo method based on Gaussian growth to calculate the workspace of robots

This paper presents a new Monte Carlo method to calculate the workspace of robot manipulators, which we called the Gaussian Growth method. In contrast to classical brute-force Monte Carlo methods, which rely on increasing the number of randomly generated points in the whole workspace to attain higher accuracy, the Gaussian Growth method focuses on populating and improving the precision of poorly defined regions of the workspace. For this purpose, the proposed method first generates an inaccurate seed workspace using a classical Monte Carlo method, and then it uses the Gaussian distribution to densify and grow this seed workspace until the boundaries of the workspace are attained. The proposed method is compared with previous Monte Carlo methods using a 10-degrees-of-freedom robot as a case study, and it is demonstrated that the Gaussian Growth method can generate more accurate workspaces than previous methods requiring the same or less computation time.