A Review on Energy-Saving Optimization Methods for Robotic and Automatic Systems <s> IGBT = Insulated Gate Bipolar Transistor; PLC = Programmable Logic Controller <s> The motion profile for point-to-point control under acceleration, which is applied to many applications in electro-mechanical systems, should be planned so as to maximize the energy conversion efficiency. Initially, a theoretically ideal profile was derived by adopting Pontryagin's minimum principle. The performance of this energy efficient motion profile is compared to those of three conventional profiles widely used in practice: trapezoidal, variable-rate transymmetric, and exponential. Finally, a selection guide for motion profile is presented for applications in which energy conversion efficiency and peak acceleration become critical, such as the material handling machine, copying machine, various dedicated purpose machines, electric motor cars, and space vehicles. <s> BIB001 </s> A Review on Energy-Saving Optimization Methods for Robotic and Automatic Systems <s> IGBT = Insulated Gate Bipolar Transistor; PLC = Programmable Logic Controller <s> This paper considers the control problem of a robotic manipulator with separately excited dc motor drives as actuators. An innovative method is proposed which achieves robot speed-control requirements, with simultaneous minimization of total electromechanical losses, while the drives follow the desired speed profiles of the robot joints under various loads and random load disturbances. If there is no demand for a specific speed profile, the optimal speed trajectory is determined by minimizing an electromechanical losses criterion. Controllable energy losses, such as armature copper losses, armature iron losses, field copper losses, stray load losses, brush load losses, friction and windage losses, can be expressed proportionally to the squares of the armature and the field (exciting) currents, the angular velocity and the magnetic field flux. The controllable energy loss term is also included in the optimal control integral quadratic performance index, defined for the whole operation period. Thus the appropriate control signals required for following the desired trajectory by simultaneous energy loss minimization for the whole operation interval are achieved. Two case studies of optimal robot control with and without minimization of actuator energy losses are presented and compared, showing the energy savings that can be achieved by the proposed methodology. <s> BIB002 </s> A Review on Energy-Saving Optimization Methods for Robotic and Automatic Systems <s> IGBT = Insulated Gate Bipolar Transistor; PLC = Programmable Logic Controller <s> In this paper, the optimal time-energy trajectory planning problem for a three degrees-of-freedom planar manipulator is considered using a multi-level fuzzy-neural system. First, a neural network is achieved to solve the inverse kinematics problem (IKP). After pre-processing steps characterizing the minimum time trajectory and the corresponding torques, a fuzzy-neuro controller is developed to deal with the minimum energy trajectory planning. The basic function of this controller is to select the minimum energy link actuator torques allowing the robot end-effector to move from a starting point S to a target point T. This optimization is performed under actuators and workspace constraints. It starts with a fuzzy clustering of input-output data, uses Tsukamoto fuzzy inference and back-propagation algorithm to train the resulting adaptive neural network. The premises parameters (antecedent membership functions parameters) as well as rule-consequence parameters are then learned and optimized, giving the optimal energy torques. Simulation results are provided to prove the efficiency of the proposal. <s> BIB003 </s> A Review on Energy-Saving Optimization Methods for Robotic and Automatic Systems <s> IGBT = Insulated Gate Bipolar Transistor; PLC = Programmable Logic Controller <s> A new method of minimum-energy point-to-point (PTP) trajectory planning is proposed for an LCD glass-handing robot, which is driven by a permanent magnet synchronous motor (PMSM). The variable structure controller (VSC) is designed to track the trajectories and compensate LuGre model of frictional torque effects. The robot system is described by a mechanical equation and an electrical equation. To generate the minimum-energy trajectory, we employ a high-degree polynomial with suitable end-point conditions. The real-coded genetic algorithm (RGA) is used to search for the coefficients of the polynomial with the fitness function of minimum-energy input. Finally, numerical simulations of the minimum-energy inputs are compared for various degrees of polynomials. It is concluded that the proposed methodology can effectively design the minimum-energy trajectory, and the nonlinear VSC can track the designed trajectories for the robot system driven by a PMSM. <s> BIB004 </s> A Review on Energy-Saving Optimization Methods for Robotic and Automatic Systems <s> IGBT = Insulated Gate Bipolar Transistor; PLC = Programmable Logic Controller <s> The main objective of this paper is to propose a novel minimum-energy trajectory planning for an LCD glass-handing robot, which is driven by a permanent magnet synchronous motor (PMSM). The system is described by a mathematical model of the electromechanical system. To generate the minimum-energy trajectory, we employ a high-degree polynomial with suitable conditions of angular displacement, speed, acceleration and jerk at the start and end points. The real-coded genetic algorithm (RGA) is used to search for the minimum-energy point-to-point (PTP) trajectory for the motion profile. The coefficients of the polynomial are determined by the RGA with the fitness function of minimum-energy input. The results are compared for various degrees of polynomials and to obtain the minimum energy input. It is concluded that the proposed methodology with minimum-energy input can also be applied to any electromechanical system driven by a PMSM. <s> BIB005 </s> A Review on Energy-Saving Optimization Methods for Robotic and Automatic Systems <s> IGBT = Insulated Gate Bipolar Transistor; PLC = Programmable Logic Controller <s> In this paper, we propose a novel minimum-energy point-to-point (PTP) trajectory planning method for a simple mechatronic system, which is a one-dimensional precision positioning table driven by a permanent magnet synchronous motor (PMSM). To generate the mechatronic trajectory we develop a real-coded genetic algorithm (RGA) to search for the optimal trajectory for the PTP motion. In this method, we design a high-degree polynomial to compute minimum-energy point-to-point trajectories, and consider the problem of initial and final constraints (position, velocity, acceleration and jerk) in the algorithm. The RGA determines the parameters, which are to formulate the polynomial, and satisfy the desired fitness function of the minimum input energy. The algorithm is tested in numerical simulations results and yields good results for the comparisons between the seven-degree to twelve-degree polynomial during motion operations. <s> BIB006 </s> A Review on Energy-Saving Optimization Methods for Robotic and Automatic Systems <s> IGBT = Insulated Gate Bipolar Transistor; PLC = Programmable Logic Controller <s> In this paper, an minimum-energy point-to-point (PTP) trajectory is designed for a mechatronic system, which is a toggle mechanism driven by a permanent magnet synchronous motor (PMSM). To generate the PTP trajectory, we employ the real-coded genetic algorithm (RGA) to search for the minimum-absolute-energy trajectory for the mechatronic system. In this paper, a high-degree polynomial is used and the initial and final conditions (position, velocity, acceleration and jerk) are considered as the constraints for the trajectory. In the RGA method, the coefficients of the polynomial are determined by satisfying the desired fitness function of input absolute electric energy. The numerical simulations are compared between several degrees' polynomials during motion operation time for the toggle mechanism. <s> BIB007 </s> A Review on Energy-Saving Optimization Methods for Robotic and Automatic Systems <s> IGBT = Insulated Gate Bipolar Transistor; PLC = Programmable Logic Controller <s> In this paper, we propose a novel minimum-energy point-to-point (PTP) trajectory planning method for a motor-toggle servomechanism, which is described by the mathematical model of a mechatronic system. To generate the mechatronic trajectory, we employed the real-coded genetic algorithm (RGA) to search for the minimum-energy trajectory for the PTP motion profile, which is described by a polynomial with suitable conditions of position, velocity, and acceleration at the start and end points. The RGA algorithm determines the coefficients of polynomials with the fitness function of minimum-energy input, and is performed in numerical simulations and experiments. The results are compared with those of the S-curve by a traditional proportional-integral control. The proposed methodology can also be applied to any mechatronic system driven by a motor. <s> BIB008 </s> A Review on Energy-Saving Optimization Methods for Robotic and Automatic Systems <s> IGBT = Insulated Gate Bipolar Transistor; PLC = Programmable Logic Controller <s> Abstract The elevator system driven by a permanent magnet synchronous motor (PMSM) is studied in this paper. The mathematical model of the elevator system includes the electrical and mechanical equations, and the dimensionless forms are derived for the purpose of practicable upward and downward movement. In this paper, the trapezoidal, cycloidal, five-degree (5-D) and seven-degree (7-D) polynomial and industry trajectories are designed and compared numerically in various motion and the absolute input energies. From numerical simulations, it is found that the trapezoidal trajectory consumes the minimum energy; the 7-D polynomial trajectory consumes the maximum one. The less end-point constraints are required, the less energy is consumed. Finally, the proposed sliding mode controller (SMC) is employed to demonstrate the robustness and well tracking control performance numerically. <s> BIB009 </s> A Review on Energy-Saving Optimization Methods for Robotic and Automatic Systems <s> IGBT = Insulated Gate Bipolar Transistor; PLC = Programmable Logic Controller <s> The energy demand of applications using in- verter controlled electrical servo drives is considerably de- pendent on the applied trajectory profiles. In this paper, the improvement potential in supply energy consumption is an- alyzed with respect to the standard servo controller func- tionality. The optimal choice of trajectory profiles and ex- ecution times for point-to-point movements offers distinct energy savings. From the presented results, a number of general trajectory parametrization advices of even roughly known system characteristics can be derived. Even with lit- tle effort and without knowledge of exact system parameters, considerable energy savings are achievable. <s> BIB010 </s> A Review on Energy-Saving Optimization Methods for Robotic and Automatic Systems <s> IGBT = Insulated Gate Bipolar Transistor; PLC = Programmable Logic Controller <s> Analyzing the mechatronic behavior of a manufacturing cell used in a customized manufacturing process is a difficult task with numerous obstacles. Therefore, a method that can be easily used for developing and optimizing a customized manufacturing cell, i.e., universal contacting module (UCM) cell, for the in-circuit testing of electronic modules is desired. In this paper, we present a convenient method using multi-domain simulation tools for analyzing the mechatronic behavior of the UCM cell. The UCM cell, which consists of mechatronic components such as a six-axis industrial robot and conveyor systems, were successfully modeled, simulated, and validated under several payloads. This work also presents a modeling procedure that can be applied by system engineers with a basic background in control systems for analyzing the mechatronic behavior of manufacturing cell components. <s> BIB011 </s> A Review on Energy-Saving Optimization Methods for Robotic and Automatic Systems <s> IGBT = Insulated Gate Bipolar Transistor; PLC = Programmable Logic Controller <s> Abstract The main idea of this paper is to design a novel point-to-point (PTP) trajectory based on minimum absolute input energy (MAIE) for an LCD glass-handing robot, which is driven by a permanent magnet synchronous motor (PMSM). The mechatronic system is described by a mathematical model of electrical and mechanical coupling equations. To generate the MAIE PTP trajectory, we employ a high-degree polynomial and compare with the trapezoidal, cycloidal and zero-jerk trajectories for various constraint conditions, which satisfy their corresponding desired constraints of angular displacement, speed, acceleration and jerk at the start and end times. The real-coded genetic algorithm (RGA) is used to search for the coefficients of high-degree polynomials for the PTP trajectories, and the inverse of absolute input electrical energy is adopted as a fitness function. From numerical simulations, it is found that either increasing the degree number of polynomials or decreasing the constraints at the start and end times will decrease the absolute input electrical energy. The proposed methodology for designing the MAIE PTP trajectory can also be applied to any mechatronic system driven by a PMSM. <s> BIB012 </s> A Review on Energy-Saving Optimization Methods for Robotic and Automatic Systems <s> IGBT = Insulated Gate Bipolar Transistor; PLC = Programmable Logic Controller <s> Abstract In this paper, energy-saving trajectories are planned for a toggle mechanism driven by a permanent magnet synchronous motor (PMSM). The point-to-point (PTP) trajectory is described by a high-degree polynomial, which satisfies the end conditions of displacement, velocity, acceleration and jerk at the initial and final times. The real-coded genetic algorithm (RGA) method is employed to obtain the mechatronic system’s parameters, and to determine the coefficients of the polynomial, and its fitness function is the inverse of various input energies. The numerical simulations and experiments are compared among several degrees’ polynomials during the whole operation motion. Finally, it is found that the input absolute electrical energy (IAEE) occurs when the highest-degree polynomial is chosen. From the percentage of relative error with respect to the absolute input energy of a 7-degree polynomial, it is found that the percentage of relative error achieves 32% as the degree is 24 with enough for minimum input energy degree. The proposed methodology described in this research has the contribution. It can be applied to any mechatronic system which is required to design a minimum-energy point to point trajectory. <s> BIB013 </s> A Review on Energy-Saving Optimization Methods for Robotic and Automatic Systems <s> IGBT = Insulated Gate Bipolar Transistor; PLC = Programmable Logic Controller <s> Reducing the energy consumption of industrial robots (IR) that are used in manufacturing systems has become a main focus in the development of green production systems. This is due to the reality that almost all automated manufacturing processes are using IR as the main component. Thus, reducing the energy consumption of IR will automatically reduce operating costs and CO2 emissions. Therefore, a method for reducing the energy consumption of IR in manufacturing systems is desired. Firstly, this paper presents a literature survey of the research in energy consumption analysis of IR that is used in manufacturing processes. The survey found that current research in this field is focused on the development of simulation models of IR that are able to be used to predict its energy consumption. Secondly, a modular model to analyze power consumption and dynamic behavior of IR is developed. Afterward, an experimental investigation is carried out to validate and estimate the accuracy of the model developed. The investigation shows that the developed modular model can be conveniently used to optimize the industrial robot’s operating parameters, which are commonly needed for production planning and at the process optimization stage. In addition, the investigation shows that the process constraints, environment layout, productivity requirement, as well as the robot payload and operating speed are the key factors that must be considered for optimizing the productivity and efficiency of IR. <s> BIB014 </s> A Review on Energy-Saving Optimization Methods for Robotic and Automatic Systems <s> IGBT = Insulated Gate Bipolar Transistor; PLC = Programmable Logic Controller <s> This paper considers real-time energy-optimal trajectory generation for a servomotor system that performs a single-axis point-to-point positioning task for a fixed time interval. The servomotor system is subject to acceleration and speed constraints. The trajectory generation is formulated as a linear-constrained optimal control problem (LCOCP), and the Pontryagin's maximum principle is applied to derive necessary optimality conditions. Instead of solving multipoint boundary value problems directly, this paper proposes a novel real-time algorithm based on two realizations: solving the LCOCP is equivalent to determining an optimal time interval of the speed-constrained arc and solving a specific acceleration-constrained optimal control problem (ACOCP), and solving an ACOCP is equivalent to determining optimal switch times of acceleration-constrained arcs and solving a specific two-point boundary value problem (TBVP). The proposed algorithm constructs sequences of time intervals, ACOCPs, switch times, and TBVPs, such that all sequences converge to their counterparts of an optimal solution of the LCOCP. Numerical simulation verifies that the proposed algorithm is capable of generating energy-optimal trajectories in real time. Experiments validate that the use of energy-optimal trajectories as references in a servomotor system does not compromise tracking performance but leads to considerable less energy consumption. <s> BIB015 </s> A Review on Energy-Saving Optimization Methods for Robotic and Automatic Systems <s> IGBT = Insulated Gate Bipolar Transistor; PLC = Programmable Logic Controller <s> Abstract Among the techniques to improve energy efficiency of mechatronic systems, the synthesis of optimized motion profiles has been proved to be an effective and almost costless method. In order to boost the use of this approach, this paper proposes an analytical method for improving energy efficiency in rest-to-rest motion through optimal planning, by selecting both the optimal motion law and the optimal motion time (duration). The proposed technique is suitable for constant inertia systems. As a matter of fact, this kind of mechatronic systems covers a wide range of applications in production, packaging or logistic plants. The method practical application is straightforward, since it just relies on the knowledge of the task specifications and of some system parameters to compute the optimal motion time for each selected trajectory and to compare analytically different motion profiles. The limitations due the servo-actuator (torque, speed, bandwidth), to machine throughput requirements, as well as the smoothness specifications (acceleration and jerk limitations, degree of continuity) are explicitly accounted for through bounds, to ensure the feasibility of the motion profiles developed. Since the proposed method proposes an analytical algebraic equation, it does not require either time-consuming simulations and trial-and-error evaluations, or numerical optimizations. Hence, it is well suited for industrial mechatronic applications. <s> BIB016
In this case, the trajectory is not synthesized by an optimization process, but instead, different standard pre-defined industrial motion laws are considered in order to evaluate their impact on the energy consumption: • triangular velocity BIB009 BIB010 BIB016 ; • harmonic BIB016 ; • cycloidal BIB009 BIB010 BIB016 ; • third-degree polynomial BIB016 ; • fifth-degree polynomial BIB009 BIB010 BIB016 ; • seventh-degree polynomial BIB009 BIB010 BIB016 ; • modified trapezoidal BIB016   ; • modified sinusoidal BIB016 ; • Gutman 1-3 BIB016 ; • Freudenstein 1-3 BIB016 ; • Freudenstein 1-3-5 BIB016 . The trajectories are defined following three different approaches: In  BIB009 BIB010   BIB014 BIB011 , they are defined numerically with a time discretization. In BIB003 , an analytic approach is exploited. Finally in BIB016 , it is demonstrated that the energy losses in a PTP motion depend only on the root-mean-square (RMS) value of the speed or acceleration. The RMS values are obtained by multiplying some characteristic coefficients (i.e., c V RMS , and c A RMS ) that describe the "geometry" of the profile by the parameters of the PTP motion (i.e., displacement ϑ, and inverse of the cycle time T), as follows: The direct method involves the comparison of different planning strategies on the basis of some metric related to the energy consumption. In BIB009 , the electrical energy is considered, while in BIB010   , the grid energy is chosen. This is done also in BIB016 , but there it is purged from the terms that do not depend on the motion. Finally, in BIB003 , the sum of the squared torque is used. Because the direct method is numerical, it allows for analyzing the impact that every factor has on the energy consumption through a sensitivity analysis. In BIB016 , the impact of both constant force (i.e., relevant increase of the Coulomb friction) and inertia (i.e., counterweight mass) are considered. In BIB010 , a sensitivity analysis is performed considering a variation of the Coulomb and viscous friction coefficients of the mechanical inertia and of the axis displacement. The works of Paryanto et al.  BIB014 BIB011 focus on the development of a modular model for industrial robots, able to analyse the power consumption and the dynamic behavior. They exploit the model to perform a sensitive analysis to investigate the effects of the robot operating parameter (i.e., payload, operating speed, and trajectory smoothness) on the energy consumption. Finally in   , the trajectory optimization of a storage and retrieval vehicle is considered. The impact of kinematic parameters (i.e., speeds and accelerations) on the energy consumption and on the lift times is analyzed. In addition, in  , a method to calculate the optimal lifting starting point and the optimal velocity is presented. The results show that the trapezoidal trajectory profile is a good trade-off for increasing the saved energy without affecting the cycle time. Indeed, the energy consumption is related to the constraints at the initial and final times: less constraints imply less energy consumption BIB012 BIB009 . In this way, a five-degree polynomial trajectory consumes less than a cycloidal and a seven-degree polynomial BIB009 BIB016 . Richiedei et al. BIB016 and Hansen et al. BIB010 show that a large constraint on the cycle time (i.e., a longer cycle time) gives a significant chance to obtain energy savings. If a constant cycle time is considered, a different behavior is achieved BIB004 BIB005 BIB007 BIB012 BIB013 BIB006 BIB008 ; it can be demonstrated that increasing the degree number of the polynomial trajectory profile leads to a decreasing of the absolute input energy. However, the use of a high-degree polynomial becomes counterproductive after a convergence point: the rate of saved-energy becomes smaller, while a more intensive computational effort is needed BIB012 BIB013 . Sergaki et al. BIB002 declares that 3-8% can be achieved in industrial robot motor drives. Wang et al. BIB015 show an improvement of the 16% with respect to a conventional system. Richiedei et al. BIB016 show it is possible to obtain energy savings greater than 30% of the maximum possible consumption (within the feasible domain) in a non-fixed cycle time. The modified parabolic velocity profile suggested by Park et al. BIB001 allows savings of up to 12.5% in each repetition of the PTP motion and furthermore, up to 33% of input energy under the same peak acceleration. A comparison of methods in terms of achievable energy savings is not available and, as a result of the various and different ranges of applications, this would be hard to perform.