Robot trajectory optimization for the relaxed end-effector path

In this paper we consider the trajectory optimization problem for the effective tasks performed by industrial robots, e.g., welding, cutting or camera inspection. The distinctive feature of such tasks is that a robot has to follow a certain end-effector path with its motion law. For example, welding a line with a certain velocity has an even influence on the surface. The end-effector path and its motion law depend on the industrial process requirements. They are calculated without considering robot kinematics, hence, are often “awkward” for the robot execution, e.g., cause high jerks in the robot's joints. In this paper we present the trajectory optimization problem where the end-effector path is allowed to have a certain deviation. Such path is referred to as relaxed path. The goal of the paper is to make use of this freedom and construct the minimal-cost robot trajectory. To demonstrate the potential of the problem, jerk of the robot joint trajectory was minimized.