## 3 Task Scheduling with Mixed-Integer Programming
### Task Scheduling with the Kinematic Constraints
The red dashed line indicates the time at which the command was given. The result shows the change of planning result when the situation changes in the middle of planning. In all cases, planning was conducted well without any violation of the constraints. (**a**) The case of dish 4 being added in the middle of execution. (**b**) The case of dish 4 being removed in the middle of execution. (**c**) The case of dish 4 restarting after failure. situation that needs to be optimized, such as the scheduling of work in a warehouse using multiple mobile robots, where more than one robot is used and the workspace is shared. Future work includes cooking in a real environment with a vision-recognition system that can detect tasks that fail. Conceptualization, J.-s.Y., T.A.L. and M.S.A. ; methodology, J.-s.Y. and T.A.L. ; software, J.-s.Y. and T.A.L. ; validation, J.-s.Y. and T.A.L. ; formal analysis, J.-s.Y. and T.A.L. ; investigation, J.-s.Y. and T.A.L. ; resources, J.-s.Y. ; data curation, J.-s.Y. ; writing--original draft preparation, J.-s.Y. and T.A.L. ; writing--review and editing, H.C., M.S.A., D.N., H.N.T., E.A., N.P. and F.Y. ; visualization, J.-s.Y., M.D. ; supervision, D.H. and H.M.; project administration, J.-s.Y. and H.M.; All authors have read and agreed to the published version of the manuscript. This research was supported by the MOTIE (Ministry of Trade, Industry, and Energy) in Korea, under the Fostering Global Talents for Innovative Growth Program (P0008746) supervised by the Korea Institute for Advancement of Technology (KIAT). Not applicable. The authors declare no conflict of interest. ## References

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