A Genetic Algorithm as Support in the Movement Optimisation of a Redundant Serial Robot

The paper illustrates the application of a genetic algorithm as a methodology to choose and improve the motion law governing the movement of a redundant robot. The subject of this research is an innovative system developed to introduce the laser ray technology in the on-line tube cutting. This technique allows a quality improvement in the pipe-cutting sector, thanks to the various goals. Firstly we underline the improvement of the working environment due to the elimination of cutting noise taking off the tool changing and the steel shaving creation. Secondarily there is a drastic reduction of the cutting cycle time and an improvement of the productivity accomplished by the use of brushless drives and linear motors. In the robot design, particular attention was dedicated to the masses distributions allowing a good natural machine dynamics. The ability of the robot to avoid the cutting object, the demand to maintain the laser torch orthogonal to the cutting surfaces, as well the necessity to impose a velocity behaviour as constant as possible during the cutting operation, suggested the introduction of a redundant degree of freedom. This aspect gives a lot of opportunities in the choose of movements because there are thousands motion profiles for the joints whichever satisfying the conditions imposed to the end-effector path. In this context, we have proposed the idea to combine the procedure to solve the inverse kinematics problem with the contemporaneous optimization of the trajectory. Literature offers a series of algorithms to solve well-known inverse kinematics problem of redundant robot. These are based on the inversion of the matrix representing the link between the end-effector co-ordinates and the joints. The presence of redundancy makes this matrix rectangular and requires the use of the pseudo-inverse matrix to solve the problem in several points of the trajectory. The introduction of some weights, one for each joint co-ordinate, allows to obtain a different distribution of the joint movements computing the pseudo-inverse matrix. If we change these weights in a continuous way in time domain, we can supervise the dynamic behaviors of the machine. The new idea we propose here is the use of an adapted multi-objective genetic algorithm to define a several of particular motion laws reducing vibrations and realizing “special harmonies” in the robot motion. The procedure, that will be completely discussed in the full paper, is actually working on a laser pipe cutting machine. This robot awarded the first prize between two thousand competitor at the EMO MILANO 2003 exhibition.