Planning the Trajectory of a Collaborative Robot for Bioprinting

Abstract

In situ bioprinting is an automated process of direct application of biomaterials to a defective area of living tissue during a medical operation. To perform such bioprinting, it is advisable to use robotic manipulators with five or more degrees of mobility, which can give the end effector the desired orientation. The actual task is to plan the trajectory of the robot for in situ bioprinting on a real curved surface. A brief analysis of solutions allowing to plan the trajectory of bioprinting is carried out. A mathematical description of the surface used as a defect model is given, which is necessary for constructing the trajectory. Additional restrictions were introduced in order to reduce the complexity of the scheduling algorithm. To localize a defect on a curved surface, information about a given contour covering this defect is used. An algorithm has been developed for forming a flat trajectory of the robot’s end effector to fill in the defect, followed by projecting it onto a real curved surface. The importance of preprocessing data on the scanned surface using the developed filtering algorithm based on the moving average method is noted. The trajectory of the robot’s end effector is formed by layers first in the plane. It is then projected onto a curved surface. For each point of the trajectory, such a homogeneous transformation matrix is calculated so that the robot’s end effector is perpendicular to the curved surface. The calculation of the orientation angles of the working body of the KUKA robot is presented on the basis of data obtained from a homogeneous transformation matrix. The operability of the proposed trajectory planning algorithm for in situ bioprinting is confirmed by the results of computer modeling using the software developed by the authors and the results of an experimental study of bioprinting performed by the KUKA LBR R820 collaborative robot on three samples with different surface curvature and defect contour