Energetically optimal cruising motion of robots

A robot motion is cruising when one of the velocities (joint or Cartesian) is at its limit value. When the path of the motion is given (CPC problem) it can be proved that time-optimal motion is realized when at least one of the joint velocities is at its maximum value. Which joint's velocity should be at maximum depends on the position in working space, and the maximum velocity values of joints, and can be determined by simple general method. The authors consider the following problem: The robot end effector centre point should move between two points (PTP problem) for minimum time and also satisfying the conditions of energetical optimality. A motion is energetically optimal when there is no energy lost for not needed changes of kinetic energy of the robot mechanisms. A simple method is given for the determination of minimum time cruising PTP motion. All of the realizable trajectories inside the attainable domain of motion realize minimum time. From these trajectories the energetically optimal can be determined using the dynamic model of robots in Riemann space. As side results, the problem of when the motion on a straight line takes more time than on some other, and energetically optimal motion along a given path, is also solved.