Abstract
A basic task in the design of an industrial robot application is the relative placement of robot and workpiece. Process points are defined in Cartesian coordinates relative to the workpiece coordinate system, and the workpiece has to be located such that the robot can reach all points. Finding such a location is still an iterative procedure based on the developers’ intuition. One difficulty is the choice of one of the several solutions of the backward transform of a typical 6R robot. We present a novel algorithm that simultaneously optimizes the workpiece location and the robot configuration at all process points using higher order optimization algorithms. A key ingredient is the extension of the robot with a virtual prismatic axis. The practical feasibility of the approach is shown with an example using a commercial industrial robot.
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References
Corke, P.: Robotics, Vision and Control: Fundamental Algorithms in MATLAB. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-20144-8
Eiselt, H.A., Sandblom, C.L.: Linear Programming and Its Applications. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-73671-4
Geu Flores, F., Röttgermann, S., Weber, B., Kecskeméthy, A.: Generalization of the virtual redundant axis method to multiple serial-robot singularities. In: Arakelian, V., Wenger, P. (eds.) ROMANSY 22 – Robot Design, Dynamics and Control. CICMS, vol. 584, pp. 499–506. Springer, Cham (2019). https://doi.org/10.1007/978-3-319-78963-7_62
Glockner, G.: How to covert min min problem to linear programming problem? (2016). https://math.stackexchange.com/questions/1858740/how-to-covert-min-min-problem-to-linear-programming-problem
KUKA Roboter GmbH: KR AGILUS sixx Specification (2013)
KUKA Roboter GmbH: KUKA System Software 8.3: Operating and Programming Instructions for System Integrators (2015)
Laporte, G., Nobert, Y.: Generalized travelling salesman problem through n sets of nodes: an integer programming approach. INFOR: Inf. Syst. Oper. Res. 21(1), 61–75 (1983)
Léger, J., Angeles, J.: Off-line programming of six-axis robots for optimum five-dimensional tasks. Mech. Mach. Theory 100, 155–169 (2016)
Luenberger, D.G., Ye, Y.: Linear and Nonlinear Programming. International Series in Operations Research & Management Science, vol. 228, 4th edn. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-18842-3
Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, New York (2006). https://doi.org/10.1007/978-0-387-40065-5
Pellegrino, F.A., Vanzella, W.: Virtual redundancy and barrier functions for collision avoidance in robotic manufacturing. In: 2020 7th International Conference on Control, Decision and Information Technologies (CoDIT), pp. 957–962 (2020)
Weiß, M.: Optimal object placement using a virtual axis. In: Lenarcic, J., Parenti-Castelli, V. (eds.) ARK 2018. SPAR, vol. 8, pp. 116–123. Springer, Cham (2019). https://doi.org/10.1007/978-3-319-93188-3_14
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Weiß, M.G. (2022). Optimization of Cartesian Tasks with Configuration Selection. In: Holderbaum, W., Selig, J.M. (eds) 2nd IMA Conference on Mathematics of Robotics. IMA 2020. Springer Proceedings in Advanced Robotics, vol 21. Springer, Cham. https://doi.org/10.1007/978-3-030-91352-6_16
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DOI: https://doi.org/10.1007/978-3-030-91352-6_16
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