Time-optimal motion planning for robots

At the practical application of robots, the part processing time has a key role. The part processing time is an idea borrowed from manufacturing technology. In robotics it mostly means that the robots tool-centre point should go along some given path and the tool orientation in every point should also have the given values. These two requirements have to be satisfied at the same time. In the present paper we propose a method which provides the motion in every point of the path with the possible maximum velocity. In fact, we divide the path to transient and cruising parts and require the maximum velocities only for this second part. The given motion is called “Time-optimal cruising motion”. We demonstrate on an example the simplicity of the approach. Using the parametric method of motion planning, we give the equations for determining time-optimal motions. Not only the translation motions of tool-centre points but, also the orientation motions of tools may be optimally planned. The time-optimal motion planning is also possible for free paths (PTP motions). A general approach for this problem is proposed, too. In the paper, some parts are devoted to the deeper understanding of the optimization problems.