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The method em- beds detailed evaluations of robots’ energy consumptions into a scheduling model of the overall system. The energy consumption for each operation is modeled and parameterized as function of the operation execution time, and the energy-optimal schedule is derived by solving a mixed-integer non- linear 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 and an experiment on an industrial robot are presented. They show that there exists a real possi- bility for a significant reduction of the energy consumption in comparison to state-of-the-art scheduling approaches. Manuscript received June 13, 2011; revised September 28, 2011; accepted November 06, 2011. Date of publication January 27, 2012; date of current ver- sion April 03, 2012. This paper was recommended for publication by Associate Editor T. Murphey and Editor V. Kumar upon evaluation of the reviewers’ com- ments. A. Vergnano carried this work as a Visiting Researcher at the Department of Signals and Systems, Chalmers Universityof Technology, SE-412 96 Gothen- burg, Sweden. A. Vergnano, M. Pellicciari, and F. Leali are with the Laboratory of Integrated Design and Simulation, Department of Mechanical and Civil Engineering, Uni- versity of Modena and Reggio Emilia, 41125 Modena, Italy (e-mail: alberto. vergnano@unimore.it). C. Thorstensson, B. Lennartson, and P. Falkman are with the Au- tomation Research Group, Department of Signals and Systems, Chalmers University of Technology, SE-412 96 Gothenburg, Sweden (e-mail: bengt.lennartson@chalmers.se). S. Biller is with the Research and Development General Motors Technology Center, Warren, MI 48090 USA. Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TASE.2011.2182509 Note to Practitioners—The motivation for this work is the great interest of companies on energy consumption optimization, looking for cost reduction and sustainability in manufacturing. Existing optimization methods focus on different levels of details. A high-level model would be able to optimize the overall system. Unfortunately, due to the high computational cost, it can hardly consider the deep level of mechanical and electrical parame- ters, which determine the real energy consumption. This paper presents a novel method to embed detailed energy consumption models into a sched- uling optimization problem. An effective parameterization of the time vari- ables reduces the model complexity, allowing the optimizer to reschedule the complete sequence of operations for minimizing the total energy con- sumption, while keeping a fixed cycle time. The method has been integrated into a commercial tool for robot programming. The optimization is appli- cable both on new and existing robotic systems, since the required modifi- cations are limited to the operations rescheduling, and no investments on new hardware are expected. Index Terms—Energy optimization, mathematical programming, robot cells, scheduling and coordination, system modeling and simulation. I. INTRODUCTION The reduction of energy consumption has become a major area of interest in manufacturing automation, as part of a global trend, where society is putting a growing effort, [1], [2], for reaching an environ- mentally sustainable future. The energy losses during the manufacturing processes can be re- duced by developing new equipment or processes. However, energy consumption can also be reduced by rethinking how it is used by al- ready existing manufacturing systems, which is the focus of this paper. A large potential for energy savings is within robotic manufacturing systems, [3]–[5]. Those systems are complex, with the final perfor- mances, including energy consumption, resulting from a deep interac- tion of mechanical, control and software engineering, [6], [7]. An ef- fective energy optimization method should therefore exploit more than one of the research areas. Optimization of the energy consumption for electromechanical hard- ware is well investigated in, e.g., [8] and [9]. In [10], a selection of off-the-shelf robots is made regarding their energy consumptions for a specified operation. Much research on low-level software program- ming concerns energy-optimal paths and motion profiles, considering the robots’ dynamics and control, see, e.g., [11] and [12]. At a higher level perspective, scheduling optimization mostly consider a system’s cycle time, as in [13]. In scheduling problems, it is often assumed that the robots perform the operations at their maximal speed, starting when allowed by the schedule, and standing idle otherwise. This could lead to unnecessarily high energy consuming accelerations and longer idle times, in which the robots still use energy to compensate gravity forces. In [14], two methods are proposed to balance the robots’ velocities and accelerations, but the schedules are derived without concerning the en- ergy consumption. This paper presents a novel method for deriving the schedule that minimizes the total energy consumption of robotic manufacturing sys- tems. The first step of the method, explained in Section II, associates a nonlinear energy consumption law to each robot operation, parame- terized by its execution time. Two examples of such laws are reported in Fig. 1. Following an integrated approach, this law is uniquely asso- ciated to a single operation and the selected robot, and is referred to as an energy consumption signature. This concept is used, as in [15], to find a parametric description of the energy consumption of a system, by integrating its general mathematical model with data of its specific usage. In the second step, presented in Section III, the system scheduling problem is modeled by mixed-integer linear constraints, including all 1545-5955/$31.00 © 2012 IEEE