A Review on Energy-Saving Optimization Methods for Robotic and Automatic Systems <s> 0θ (t)τ(t)dt; <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> 0θ (t)τ(t)dt; <s> This paper proposes a technique of iterative dynamic programming to plan minimum energy consumption trajectories for robotic manipulators. The dynamic programming method is modified to perform a series of dynamic programming passes over a small reconfigurable grid covering only a portion of the solution space at any one pass. Although strictly no longer a global optimization process, this iterative approach retains the ability to avoid some poor local minima while avoiding the curse of dimensionality associated with a pure dynamic programming approach. The algorithm has an inherent parallel structure, allowing for reduced computation time on parallel architecture computers. No limiting assumptions are made about the performance index, or function to be optimized. As such, extremely complex functions and constraints are easily handled. Joint actuator and time constraints are considered in this work. The modified dynamic programming approach is verified experimentally by planning and executing a minimum energy consumption path for a Reis V15 industrial manipulator. <s> BIB002 </s> A Review on Energy-Saving Optimization Methods for Robotic and Automatic Systems <s> 0θ (t)τ(t)dt; <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> BIB003 </s> A Review on Energy-Saving Optimization Methods for Robotic and Automatic Systems <s> 0θ (t)τ(t)dt; <s> An optimized path-planning approach is presented for flexible dynamic systems. Feedforward command profiles are determined for rest-to-rest large angle maneuvers that keep vibrations to a minimum. The performance index included both minimum energy and minimum time optimization problems. The feedfoward command profiles were generated by solving a discrete-time optimal control problem via discrete dynamic programming (DDP). A simple planar two-link flexible robot arm was utilized to demonstrate the DDP path-planning scheme. Numerical simulation results included: 1) minimum effort, 2) minimum effort with bounds, 3) minimum time, and 4) minimum torque-rate or power, respectively. The DDP approach demonstrated an effective alternative for numerical optimization, to generate optimal feedforward trajectory profiles. <s> BIB004 </s> A Review on Energy-Saving Optimization Methods for Robotic and Automatic Systems <s> 0θ (t)τ(t)dt; <s> Optimal trajectory planning for robot manipulators is a very important issue in the research field of robotics. Many applications require smooth trajectories and the minimization of a performance index, usually the traveling time or the mechanical energy of the actuators. This paper presents a novel method that uses eighth-degree polynomial functions to generate smooth trajectories for the parametric representation of a given path. The optimization algorithm presented in this paper minimizes the mechanical energy consumed in the robot manipulator. To solve the optimization model, a genetic algorithm is implemented. A software platform has been developed to test this optimal trajectory-planning algorithm. The software includes modules to solve the direct kinematics, the inverse kinematics, and the dynamics of the robot manipulator. <s> BIB005 </s> A Review on Energy-Saving Optimization Methods for Robotic and Automatic Systems <s> 0θ (t)τ(t)dt; <s> The industrial sector is the largest users of energy around the world. Industrial motor uses a major fraction of total industrial energy uses. This paper describes a comprehensive literature review about electric motor energy analysis. This paper compiles latest literatures in terms of thesis (MS and PhD), journal articles, conference proceedings, web materials, reports, books, handbooks on electrical motor energy use, losses, efficiency, energy savings strategies. Different types of losses that occur in a motor have been identified and ways to overcome these losses explained. An energy audit that helps to identify motor energy wastages have been discussed extensively. As motors are the major energy users, different energy savings strategies such as use of high-efficient motor, variable speed drive (VSD), and capacitor bank to improve the power factor to reduce their energy uses have reviewed. Different policy measures (i.e. regulatory, voluntary and incentives based) to save motor energy use have been reviewed and presented in this paper. In this review, computer tools that can be used to analyze electric motors energy used has been discussed. Cost parameters to carry out economic analysis have been shown as well. Moreover, payback period for different energy savings strategies have been identified. <s> BIB006 </s> A Review on Energy-Saving Optimization Methods for Robotic and Automatic Systems <s> 0θ (t)τ(t)dt; <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> BIB007 </s> A Review on Energy-Saving Optimization Methods for Robotic and Automatic Systems <s> 0θ (t)τ(t)dt; <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> BIB008 </s> A Review on Energy-Saving Optimization Methods for Robotic and Automatic Systems <s> 0θ (t)τ(t)dt; <s> In this paper, we propose a novel trajectory planning method for a 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 motion. In this method, we design a high-degree polynomial to compute minimum-energy trajectories, and consider the problem of initial and final constraints 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 adaptive control (AC) are developed based on mathematical knowledge of the precision positioning table and the PMSM. The proposed adaptive control is robust not only to parametric uncertainties of mass variations but also to external disturbances. The effectiveness of the proposed trajectory planning and adaptive control are demonstrated by numerical simulations in the point to point motion processes for the precision positioning table. <s> BIB009 </s> A Review on Energy-Saving Optimization Methods for Robotic and Automatic Systems <s> 0θ (t)τ(t)dt; <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> BIB010 </s> A Review on Energy-Saving Optimization Methods for Robotic and Automatic Systems <s> 0θ (t)τ(t)dt; <s> This paper proposes a novel cost function formulation for minimization of the energy consumption of industrial robots by trajectory optimization. Besides the dynamics of the robot including friction losses, the model especially takes into account the losses of servo drives and inverters. Furthermore, the ability of energy exchange between the robot axes via the coupled DC-bus is included, since the servo drives support generator mode during deceleration. The utilized energy-based robot model is applicable to different manipulator types. For the energy-efficient motion planning, point-to-point trajectories are defined by B-spline functions. The given nonlinear optimization problem is solved using gradient-based methods, considering kinematic and dynamic constraints. Several simulation results are presented, demonstrating the intense effect of energy exchange in the robot controller's power electronics. Furthermore, a comparative study is given showing that the proposed method is able to outperform existing torque-based approaches. <s> BIB011 </s> A Review on Energy-Saving Optimization Methods for Robotic and Automatic Systems <s> 0θ (t)τ(t)dt; <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> BIB012 </s> A Review on Energy-Saving Optimization Methods for Robotic and Automatic Systems <s> 0θ (t)τ(t)dt; <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> BIB013 </s> A Review on Energy-Saving Optimization Methods for Robotic and Automatic Systems <s> 0θ (t)τ(t)dt; <s> The improvement of energy efficiency in automation and robotic systems still has high significance in engineering research. This paper presents experimental results of minimum energy trajectory optimization for multi-axis manipulators using electrical energy exchange via the shared inverter DC link. Thus, existing simulation findings demonstrating the potential of the proposed minimum energy optimization approach are validated. In this context, a global optimization method is applied utilizing an advanced cost function formulation that is based on an energy flow model including all servo drive components. After the validation of the utilized system model, increased efficiency improvements are proven and compared to established methods. The presented approach as well as the experimental results are fully transferable to any kind of multi-axis system comprising DC link energy supply. <s> BIB014 </s> A Review on Energy-Saving Optimization Methods for Robotic and Automatic Systems <s> 0θ (t)τ(t)dt; <s> This paper proposes a minimum energy trajectory planning method with residual vibration reduction for a robot manipulator mounted on flexible base, in which a point-to-point motion task of the manipulator is considered. In the proposed method, the joint angle of the robot manipulator is generated by radial basis function networks (RBFNs). The maximum residual vibration amplitude and operating energy are adopted as the objective functions, and then, the RBFNs are tuned by an elitist non-dominated sorting genetic algorithm (NSGA-II). The trajectory obtained using the proposed method can suppress the residual vibration of the flexible base in energy conservation. Results obtained from simulations reveal a trade-off relationship between the residual vibration amplitude and the operating energy. Furthermore, the validity of the proposed method is confirmed experimentally. <s> BIB015 </s> A Review on Energy-Saving Optimization Methods for Robotic and Automatic Systems <s> 0θ (t)τ(t)dt; <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> BIB016 </s> A Review on Energy-Saving Optimization Methods for Robotic and Automatic Systems <s> 0θ (t)τ(t)dt; <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> BIB017 </s> A Review on Energy-Saving Optimization Methods for Robotic and Automatic Systems <s> 0θ (t)τ(t)dt; <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> BIB018 </s> A Review on Energy-Saving Optimization Methods for Robotic and Automatic Systems <s> 0θ (t)τ(t)dt; <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> BIB019 </s> A Review on Energy-Saving Optimization Methods for Robotic and Automatic Systems <s> 0θ (t)τ(t)dt; <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> BIB020 </s> A Review on Energy-Saving Optimization Methods for Robotic and Automatic Systems <s> 0θ (t)τ(t)dt; <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> BIB021 </s> A Review on Energy-Saving Optimization Methods for Robotic and Automatic Systems <s> 0θ (t)τ(t)dt; <s> Abstract This paper presents a proposal for a minimum energy feedforward control technique for flexible structures to suppress residual vibrations in point-to-point (PTP) motion. In the proposed method, the trajectory profile of the PTP motion is generated through a cycloidal function whose input is the output of a polynomial function. The obtained trajectory is dependent upon the coefficients of the polynomial function. To achieve the suppression of the residual vibration as well as the operating energy of this PTP motion, the coefficients are tuned by metaheuristic algorithms. In the numerical simulations, we investigated the PTP motions of a single-link flexible manipulator and a robotic arm attached to a flexible link. The simulation results were compared with those of previous studies, revealing the effectiveness of the proposed method. <s> BIB022 </s> A Review on Energy-Saving Optimization Methods for Robotic and Automatic Systems <s> 0θ (t)τ(t)dt; <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> BIB023
• minimum of grid energy (i.e., considers the energy exchanged between axes due to recovery process) BIB014 ; • minimum of losses in a robot DC motor drive BIB003 . In addition to the energy expenditure, other quantities can be minimized, such as the residual vibration amplitude BIB015 BIB022 . A wide range of optimization algorithms are used to find the optimum trajectory. These include the following: • gradient-based optimization algorithms BIB011 , and more specifically, sequential quadratic programming (SQP) BIB003 ; • genetic algorithms (GA) BIB005  ; • real-coded genetic algorithms (RGA) BIB007 BIB008 BIB012 BIB016 BIB017 BIB009 BIB010 BIB013 ; • radial-basis function networks and genetic algorithms (RBF-GA) BIB015 ; • Pontryagin's minimum algorithm (PMP) BIB001 BIB020 ; • metaheuristic algorithms (MA) BIB022 ; • discrete dynamic programming (DDP) BIB004 ; • iterative dynamic programming (DP) BIB002 . In the direct approach, the electromechanical model of the system is more complex compared to the previous system; in fact, in this case, the non-linearities and secondary losses contributions are taken into account. The model, besides the dynamics of the system, has to include several energy losses due to the mechanical parts, the motor and the drive system. In Table 3 , a qualitative categorization of energy losses by proportionality to the speedθ and torque τ is reported BIB006 BIB018 BIB023 BIB021 BIB019 . Table 3 . Qualitative categorization of energy losses BIB006 BIB018 BIB023 BIB021 .