Some aspects of robot motion in Cartesian space

Paper describes of the steps required in planning the desired motion. Namely, in many robot applications as spot welding etc. desired path is defined by critical points. Operator has to specify these points, usually, in system in which he can visualise and measure, in other words in operational space. Sometimes it' need to define and velocity of end effector in operational space, too. But, robot understands only variable in joint space. Critical path points can be transformed in suitable values in joint space using inverse kinematics while velocity in operational space may be transformed by inverse of Jacobian matrix or by time derivative of joint variables whose can be parameterised with cubic spline, as done in this paper.