Abstract
In a competitive industry, production lines must be efficient. In practice, this means an optimal task assignment between the robots and an optimal motion of the robots between their tasks. To be optimal, this motion must be collision-free and as fast as possible. It is obtained by solving an optimal control problem where the objective function is the time to reach the final position and the ordinary differential equations are the dynamics of the robot. The collision avoidance criterion is a consequence of Farkas’s lemma. The criterion is included in the optimal control problem as state constraints and allows us to initialize most of the control variables efficiently. The resulting model is solved by a sequential quadratic programming method where an active set strategy based on backface culling is added.
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This work has been supported by the DFG Research Center MATHEON Mathematics—for key technologies.
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Landry, C., Gerdts, M., Henrion, R., Hömberg, D., Welz, W. (2014). Collision-Free Path Planning of Welding Robots. In: Fontes, M., Günther, M., Marheineke, N. (eds) Progress in Industrial Mathematics at ECMI 2012. Mathematics in Industry(), vol 19. Springer, Cham. https://doi.org/10.1007/978-3-319-05365-3_34
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DOI: https://doi.org/10.1007/978-3-319-05365-3_34
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