Implementation of Time-Optimal Path-Tracking Control on Palletizing Robots Leon ˇ Zlajpah and Bojan Nemec Department for Automatics, Biocybernetics and Robotics Joˇ zef Stefan Institute Jamova 39, 1000 Ljubljana, Slovenia leon.zlajpah@ijs.si Abstract — It is not easy to apply the algorithms for time-optimal trajectory planning in practice because they rely on the exact dynamic models of the system. In this paper we propose a simplification of the time- optimal path-tracking control algorithms. The proposed algorithms are based only on the kinematic constraints. Such simplifications can be justified in cases when the ac- tuators are never pushed to their torque limits and when the task gives the constraints for the optimal trajectory. One of the practical applications of these simplified algo- rithms are palletizing robots. For these robots the grip- ping force is one of the key factors. If the dynamic forces are to high the gripper may loose the load. Assuming that the payload is constant during the motion the dy- namic properties in the task space are not changing, and the maximal allowable accelerations can be determined from maximal gripping force. The acceleration and ve- locity bounds are then used in the trajectory planning algorithm. Although the the simplifications reduce the computational complexity the trajectory has still to be precalculated off-line. The proposed algorithm has been implemented in our PC-based robot controller which is used to control the palletizing robot. Experimental re- sults confirm that the proposed algorithms assure the end-effector motion in the prescribed bounds. I. Introduction Interest in time-optimal motion of industrial robots is motivated by the desire to reduce cycle times. In practice, a variety of tasks require sophisticated mo- tion. Usually, this is a motion along a predefined path and the path accuracy is vital. Typical industrial ap- plications in this category are arc welding, cutting, and gluing. The technology may pose some motion require- ments like constant path velocity or bounded path ac- celeration, but also a fast production is required. So, it is of general interest to perform the path motion as fast as possible. In such cases, the manipulator perfor- mance is the limiting factor. Consequently, we have to minimize the path travelling time, i.e. to find the max- imal feasible path velocity profile concerning the task requirements and manipulator limitations. In some ap- plications such as palletizing the actual path is not so important, but the task should be performed in mini- mal time. Although in these applications the tracking accuracy is not so vital (important is only the posi- tion accuracy at the pick and place positions) the robot should move close to the prescribed path because of the obstacles in the neighbourhood. The control process of the manipulator is usually di- vided into more levels. The lowest level is the close-loop control and the next higher is the motion planning. The motion planning can be divided into the path planning and the trajectory planning. In contrast to many indus- trial applications where the path is completely defined by the task and only the trajectory planning is the issue, the motion planning for palletizing (or other pick-and- place) applications has to be done in two steps: path planning and trajectory generation. In the first step, a collision-free path is planned between the pick position and the place position. In most cases this is a combina- tion of linear and circular segments, or a spline based on some intermediate points. In the second step the trajectory (i.e. the time evolution) along the path is generated. Several authors studied the minimum-time control in robotics. Khan and Roth [1], assumed constant torque limits and non-constraint path. Different aspects of the problem are presented in [2], [3], [4]. The optimal tra- jectory planning in the form we use was first introduced by Bobrow [5] and then further developed by by others [6], [7], [8], [9], [10]. In order to utilize the manipulator capabilities with maximal efficiency, the dynamics of the manipulator should be taken into account in opti- mal trajectory planning. For the optimization different constraints have to be considered like actuator satura- tion limits, path constraints, gripper and payload con- straints, etc. Since the bounds vary with position, pay- load mass, etc., and to avoid the “worst case” design method, an accurate model should be used in the tra- jectory planner. Some authors address the application of these methods and the problems caused by model uncertainties. Dahl and Nielsen[11], [12] use a feedback scheme for path following scheme with on-line trajec- tory scaling to solve the problem of saturation of the control output (torque). Kieffer et. al [13] proposes robust algorithms where the modelling errors are iden- tified as disturbances to tracking errors and are used to prevent the actuator saturation. In the paper we present a simplification of the well- known time-optimal path-tracking algorithms and their application to the palletizing robots. Namely, for pal- letizing the constraints are posed primary by the grip- per and the objects to be manipulated; the actuators usually do not reach their saturating limits in torques. Hence, the optimizing algorithms can be based only on kinematic constraints. Such simplifications can be jus- tified in cases when the actuators are never pushed to their torque limits. For palletizing robots the gripping force is one of the key factors because if the dynamic forces are to high the gripper may loose the load. In the following first the time-optimal trajectory problem is reviewed. Then the simplifications of the standard al- gorithms are proposed. Next the algorithms are applied to the palletizing robot and in the end some experimen-