| The direct optimization codes recently developed at the University of Heidelberg, have made it possible to numerically solve the optimal control problem, including state inequality constraints, for realistic robot models in a few minutes on a work station. This suggests that it is within reach to routinely use time optimal trajectory planning in industrial robot applications, employing realistic dynamic robot models. This thesis is part of research currently directed toward application and demonstration of the approach on a robot in a press chain on the Mercedes Benz automobile manufacturing facility. This robot takes the longest to do its job, and hence determines the cycle time of the press chain. By speeding up this robot the whole chain can be operated faster, with increased productivity.; It is the purpose of the research reported here to take a major step toward this goal, by developing appropriate approaches to handle a series of practical issues, and by developing the needed information to use realistic as opposed to idealized robot models. Typical optimal control solutions give you an open loop optimal answer. We choose to use the feedback controllers built into the industrial robot, so that the optimal control results can be applied easily in hardware. This raises the issue of how does one get the feedback controller to execute the optimal trajectory, since simply commanding this trajectory is insufficient. Among these approaches are back calculation and learning control. The vibrations present in robot hardware must be addressed. Here we do the optimization on a robot model without vibrations, motivated by the expected difficulty of having a good vibration model and the sensitivity of the open loop optimal solutions to the model parameters. We must then find ways to constrain the optimization to produce trajectories that do not excite the vibrations excessively. And then, the optimization must be realistic in terms of the hardware limitations. In addition to pointwise limits on the torque output of the motor, we include limits on average torque, address lifetime constraints on the gearing, speed limitations for the bearings, contact stress issues and ratcheting in the drives, overheating, etc. A consistent set of constraints is developed, that include pointwise and average constraints, on the control variable or on state variables. And finally, practical approaches are suggested to handle the effects of imperfect robot modeling, and how one causes the robot to correct the associated endpoint errors. |
