# Robust and Energy Efficient Scheduling

[Doktorsavhandling]

Scheduling can generally be described as the act of allocating resources to tasks over time such that a given performance measure is optimized. Traditionally, disturbances are not considered while developing schedules. A rescheduling framework has thus emerged, aiming to minimize the impact of unforeseen disruptions. In this thesis, different rescheduling methods are proposed, where the obtained schedule is compared with the runtime schedule to evaluate the quality in terms of robustness and stability. The robustness is measured by the final time delay, whereas deviations in execution order or start time deviations act as stability measures.

A method is suggested, where the order in which tasks start in a time-optimal schedule is formulated as an event-based description. This results in a preserved execution order if delays are present. Logical restrictions are examined, and possibly relaxed, to avoid unnecessary delays. Another modeling approach presented, shows that an already established rescheduling method performed partly offline and partly online, called Affected Operations Rescheduling, can be performed completely offline.

From the aforementioned methods, stable schedules subject to sequence deviation are obtained. To generate both stable and robust schedules, a strategy is studied where idle time, so called slack, is inserted to schedules with the intention to absorb possible delays. Schedules are consequently protected against both start time deviations and makespan delay. In the literature on energy optimization, slack is diminished and often eliminated on behalf of reduced accelerations and velocities for robots, resulting in reduced energy consumption as well as extended execution times. The conflict between slack-based rescheduling techniques and energy optimization is highlighted in this thesis. The trade-off is evaluated by posing an optimization problem with measures of energy consumption, robustness and stability as criteria. %combining methods from the two research fields. %A mixed integer quadratically constrained quadratic program formulation is posed with makespan, energy, robustness and stability as criteria.

A challenge in production systems nowadays, especially with the increase in automation, is multiple resources sharing a restricted space. Much effort has been devoted to handle collision avoidance in such systems. A method is proposed in this work, where robustness is incorporated into trajectory planning for robots. When disruptions are present, the time at which a common workspace is expected to become available can differ. In the suggested approach, a clearance point is introduced, where the availability of the common workspace is evaluated. If the robot reaches this point and the shared space is not yet available, the robot has to be able to stop outside the shared space to avoid potential collisions. This requirement restricts the velocity at the clearance point. The impact on final time and energy consumption with respect to the position and timing related to the clearance point is studied. Results show the optimal clearance point position for different amount of slack available.

**Nyckelord: **Energy optimization, Trajectory planning, Discrete Event Systems, Common workspace, Robust Scheduling

Denna post skapades 2017-11-09. Senast ändrad 2017-11-14.

CPL Pubid: 253041