Optimization of Timed Automata Models Using Mixed-Integer Programming

Panek, Sebastian; Stursberg, Olaf; Engell, Sebastian

doi:10.1007/978-3-540-40903-8_7

Cited by 9 publications

(16 citation statements)

References 11 publications

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“…In other words, it is not always convenient, from an energy consumption point of view, to slow down an operation as much as allowed by the schedule. This behaviour is due to coefficient C 1 in (12), which in turn depends on torques due to gravity g i (q(T f )), as explained in (10) and (13). Its physical explanation is that the torques components due to accelerations and velocities (10) are reduced by increasing the operation execution time, while the torques component due to gravity loads still must be supplied.…”

Section: B Generation Of the Parametric Energy Signaturesmentioning

confidence: 94%

“…The two most important differences between this approach and [12], [13] and [14], are that a nonlinear objective function for minimizing the energy is used and that the robots are allowed to idle when not executing the operations. The idle time is defined as the time a robot waits before it starts executing the first operation, the time between completing an operation and starting the next and the time after the completion of the last operation in the sequence until the total cycle time is reached.…”

Section: Scheduling Of Energy Consumptionmentioning

confidence: 99%

“…The nonlinear objective function is formulated as the sum of the energy consumptions for every operation in the system, including the idle energy consumption, as defined in (14). Due to (12), the nonlinearity of the objective function forces the need to use a mixed-integer nonlinear programming solver to compute the optimal schedule. The variables are the starting and stopping times for every operation and the total cycle time.…”

Section: Scheduling Of Energy Consumptionmentioning

confidence: 99%

“…Looking at high-level supervisors, optimization in scheduling has mostly been done considering a system's cycle time, as in [12] and [13], where a discrete event system is modelled with timed deterministic finite automata and the time-optimal schedule is derived using mixed-integer linear programming (MILP). In scheduling problems, it is often assumed that a robot performs the operations at its maximal speed, starting when allowed by the schedule and stands idle otherwise.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Embedding detailed robot energy optimization into high-level scheduling

Vergnano

Thorstensson

Lennartson

et al. 2010

2010 IEEE International Conference on Automation Science and Engineering

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Reduction of energy consumption is important for reaching a sustainable future. This paper presents a novel method for optimizing the energy consumption of robotic manufacturing systems. The method embeds detailed evaluations of robots' energy consumptions into a scheduling model of the overall system. The energy consumption for each operation is modelled and parameterized as function of the operation execution time, and the energy-optimal schedule is derived by solving a mixed-integer nonlinear programming problem. The objective function for the optimization problem is then the total energy consumption for the overall system. A case study of a sample robotic manufacturing system is presented. It shows that there exists a possibility for a significant reduction of the energy consumption, in comparison to state-of-the-art scheduling approaches.

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Section: B Generation Of the Parametric Energy Signaturesmentioning

confidence: 94%

Section: Scheduling Of Energy Consumptionmentioning

confidence: 99%

Section: Scheduling Of Energy Consumptionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Embedding detailed robot energy optimization into high-level scheduling

Vergnano

Thorstensson

Lennartson

et al. 2010

2010 IEEE International Conference on Automation Science and Engineering

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“…In particular, we encode the optimum bounded reachability problem up to depth k for MPTA as a Mixed Integer Linear Program (MILP). In the remainder of this section, we provide a corresponding algorithm, which is based upon reducing Problem 1 for cost-charging MPTA to a Mixed Integer Linear Program, along the lines of [16] illustrating BMC for acyclic LPTA.…”

Section: Viable Canonical Path and Letmentioning

confidence: 99%

Revisiting Decidability and Optimum Reachability for Multi-Priced Timed Automata

Fränzle

Swaminathan

2009

Lecture Notes in Computer Science

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Abstract. We investigate the optimum reachability problem for MultiPriced Timed Automata (MPTA) that admit both positive and negative costs on edges and locations, thus bridging the gap between the results of Bouyer et al. (2007) and of Larsen and Rasmussen (2008). Our contributions are the following: (1) We show that even the location reachability problem is undecidable for MPTA equipped with both positive and negative costs, provided the costs are subject to a bounded budget, in the sense that paths of the underlying Multi-Priced Transition System (MPTS) that operationally exceed the budget are considered as not being viable. This undecidability result follows from an encoding of StopWatch Automata using such MPTA, and applies to MPTA with as few as two cost variables, and even when no costs are incurred upon taking edges. (2) We then restrict the MPTA such that each viable quasi-cyclic path of the underlying MPTS incurs a minimum absolute cost. Under such a condition, the location reachability problem is shown to be decidable and the optimum cost is shown to be computable for MPTA with positive and negative costs and a bounded budget. These results follow from a reduction of the optimum reachability problem to the solution of a linear constraint system representing the path conditions over a finite number of viable paths of bounded length.

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