Optimal Motion Planning



In many applications, especially for spot welding tasks, industrial robots should move as fast as possible in order to minimize cycle time and production cost. This problem can only be solved with efficient Optimal Motion Planning algorithms. Constraints, such as maximum motor and gear box torques or maximum motor speeds, should be automatically taken into account by means of suitable model based real-time algorithms.

We have developed algorithms which enable KUKA robots to move in point-to-point applications as fast as possible under all essential constraints. Furthermore, the vibrations of the robot are significantly reduced. With this change of the path planning software, KUKA robots move up to 30% faster, the amplitudes of the vibrations at the end effector are up to 5 times smaller, and the teaching time is reduced considerably.

The algorithms use ideas from many published articles in this area. The difficult part was to get the solution of a constrained trajectory optimization problem in a short time (= real-time algorithms) and in all situations (= very robust). These unpublished mathematical algorithms use very fast dynamic robot models, including a 6-degree of freedom mechanical model of the robot. Furthermore, the exact minimum time path is not suited for industrial robots because the non-differentiable points in the velocity profile induce vibrations into the robot movement. Algorithmic modifications reduce induced vibrations while deviating not too much from the optimal solution. Hence we also developed the proper measurement procedure, including the evaluation software, for the friction characteristic and for validation of the overall model.

Typical curves of the joint velocities of a high-speed path


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