Abstract— Multi objectives optimization in Robotics is one of the most difficult problem to be solved. In the paper will be shown the matrix form of the resistive and active forces and the proper algorithm to establish the best case between all studied cases. The mathematical matrix form of the active forces equations was transposed to the virtual LabVIEW instrumentation with the goals to obtain some characteristics of the active forces in each joints of the robot variation vs. time in the case when were changed some functional or constructive parameters. By using proper algorithm was choose the best solution between the studied cases for down movements of the robot’s arm. The applied method, the algorithm and the proper virtual instrumentation solve one small part of the complex problems of the optimisation in robotics. Index Terms—Assisted research, multi objective optimization, virtual instrumentation, robot’s joints forces. I. INTRODUCTION The optimizing of the force variation vs. time in Robotics is one of the most important problem to be solved. Without the assisted research isn't possible to study the dynamic behavior because will be necessary to show the variation of the forces and moments vs. time to identify and establishing the better solution of the movements, or dimensions of the bodies and the relative velocities. In the paper authors [1]-[17] by using the special software RoboAnalyzer, Robotech, V- Rep, RoKiSim, Ros,show some characteristics and solve direct and inverse kinematics problem and also the direct and inverse dynamic problem, but without show the mathematical matrix model and how could be influenced the force variation by different velocity characteristics or to obtain the minimum variation of the forces. Robotect [5] and V-REP [6] are robotics learning and simulation software. A user could simulate robot manipulators and mobile robots in various environments by introducing virtual sensors and actuators. RoKiSim [7] and RoboDK, Webots [8] are a development environment which focuses on modeling, programming, and simulation of robots. In the papers [18]-[37] are shown some Manuscript received September 20, 2019; revised March 1, 2020. This work was realized together with University Politehnica of Bucharest, Romania, ACTTM national agency, Romania, Techno Accord Quebec, Canada and Kosice University of Technology, Slovakia. A. D. Olaru is with the University Politehnica of Bucharest, Romania (e- mail: aolaru_51@ymail.com). S. A. Olaru was with ACTTM agency, Bucharest, Romania (e-mail: serban1978@yahoo.com). N. C. Mihai is with the Techno Accord SA, Quebec, Canada (e-mail: mniculae@gmail.ca). N. M. Smidova is with Kosice University of Technology, Slovakia. applications, simulation, and visualization based on the Gazebo [15] simulator. The proper assisted research was made by using the proper virtual LabVIEW instrumentation. In the literature about the research of the robot’s forces don’t show the mathematical matrix model, don’t show how will be the variation of these forces when will be changed the successive or simultaneously movements of the robot’s bodies. In the last research [38]-[47] we solved some problem from the dynamic behavior of the robots. II. THE FORCES MATHEMATICAL MATRIX MODEL The mathematical model of the robot’s forces analyze contents the following matrix equations, see Fig.1: () 0 = [ ]{() 0 −/+[ ]( ,0 ) 0 } (1) [ ]=| … … … … , … … … … | , =( −1 − ℎ 1 − ℎ 0 − ′ ℎ ℎ ) (2) ( 0 )= ( [ 1 0 ]( 1 1 ) [ 2 0 ]( 2 2 ) [ 3 0 ]( 3 3 ) [ 4 0 ]( 4 4 ) …… ) (3) [ 4 0 ] = [ 1 0 ][ 2 1 ][ 3 2 ][ 4 3 ] [ ]=[ 1 0 0 0 − 0 ] [ 0 − 0 1 0 0 ] [ − 0 0 0 0 1 ] (4) [ 1 1 ]=[ 0 0 − 1 ] [ ]= [ 1 [ 1 0 0 0 1 0 0 0 1 ] 0 0… 0 2 [ 1 0 0 0 1 0 0 0 1 ] 0… 0 0 … ] (5) Fig. 1. Arm type studied robot. Assisted Multi Objectives Research Optimization of the Arm Type Robot’s Forces Adrian D. Olaru, Serban A. Olaru, Niculae C. Mihai, and Natalia M. Smidova International Journal of Modeling and Optimization, Vol. 10, No. 2, April 2020 61 DOI: 10.7763/IJMO.2020.V10.748