A Review on Energy-Saving Optimization Methods for Robotic and Automatic Systems <s> Multi-Point Trajectory Optimization <s> In this paper a method to solve the trajectory generation problem in redundant degree of freedom manipulator has been proposed, and the variational approach within the B-spline function are introduced for minimization of the consumed electrical energy of a robot manipulator system. In the proposed method, the inverse matrix of Jacobian calculation is not required, and the minimal trajectory error is guaranteed while minimizing the consumed electrical energy. The theory, simulation, and experiments are presented in the paper. <s> BIB001 </s> A Review on Energy-Saving Optimization Methods for Robotic and Automatic Systems <s> Multi-Point Trajectory Optimization <s> In this paper we propose an energy efficient method for path planning by a robot arm. First we have developed a cost function that provides a set of via points determining a suitable path according to the obstacles present in the surroundings and other restrictions in its motion. Then we fit a suitable polynomial to this set of interior points to ensure that the journey is smooth and takes place with the consumption of minimum energy. The set of via-points as well as the minimum energy path have been determined using IWO (Invasive Weed Optimization) which is a new search heuristic based on the colonizing property of weeds. Application of such evolutionary algorithms in trajectory planning is advantageous because the exact solution to the path planning problem is not always available beforehand and must be determined dynamically. The entire procedure has been demonstrated through simulations. The above formulation is very simple and versatile and can be effectively applied to a variety of situations. <s> BIB002 </s> A Review on Energy-Saving Optimization Methods for Robotic and Automatic Systems <s> Multi-Point Trajectory Optimization <s> Abstract This paper presents a systematic methodology for on-site identification and energy-optimal path planning of an industrial robot. The identification experiments are carried out on-site, in a quick, non-invasive way using a CA8335 Qualistar three-phase electrical networks analyser. Next, the collected data is compared with a parametrised dynamic robot model in an optimisation routine. This routine results in the specification of a parametric dynamic robot model. The model is used as a dynamic constraint for a model predictive control problem, where other physical constraints are added i.e. the limited workspace and the constraints on the joint velocities and accelerations. A sequential quadratic programming solver is used to minimise a mechanical energy based cost function. The resulting energy-optimal path is translated into custom robot commands executable on an industrial robot. The systematic methodology is validated on an IRB1600 industrial ABB robot performing a custom pick-and- place operation. The obtained dynamic robot model is given and compared to the collected measurements. To demonstrate the possibility of energy saving by ‘intelligently’ programming a robot trajectory the energy and time-optimal paths are generated taking all physical constraints into account. Simulation results show a significant time and energy improvement (up to 5%) compared to most trajectories generated by the ABB software. The most remarkable result is that the fastest energy-optimal trajectory turns out to be 4% more energy efficient and 3% faster then the commercially available fastest trajectory. Additional stand-still experiments show that activation of the brakes is favoured over an actuated stand-still from an energy point of view, assuming that the start-up time when releasing the brakes is limited. <s> BIB003 </s> A Review on Energy-Saving Optimization Methods for Robotic and Automatic Systems <s> Multi-Point Trajectory Optimization <s> The paper proposes an off-line robot motion planning approach, aimed at the reduction of the energy consumption, for any trajectory defined on a set of target points including some “fly” ones, i.e., points that must not be exactly reached by the robot. The proposed solution is based on the search for alternative paths close to the fly target points originally defined by the operator, and on the computation of the mechanical and total energy associated to each single possible motion defined for the generated alternative paths. A branch and bound algorithm is employed to scan all the possible motions and find the complete trajectory that corresponds to the minimum energy consumption. The approach has been implemented in a software architecture that exploits some COMAU software modules, but it could be easily adapted to generic, similar modules. The results that have been experimentally obtained for two typical industrial cycles, performed by a COMAU Racer robot, can be considered as very satisfying. <s> BIB004 </s> A Review on Energy-Saving Optimization Methods for Robotic and Automatic Systems <s> Multi-Point Trajectory Optimization <s> Optimal trajectory planning for robot manipulators is always a hot spot in research fields of robotics. This paper presents a Constraint Immune Multi-objective Optimization Algorithm (CIMOA) for computing optimal trajectory of an industrial robot manipulator. The problem has a multi-criterion character in which two objectives, the minimum traveling time objective and minimum mechanical energy consumption objective are considered. In this paper, a model of trajectory planning for six-DOF manipulator based on CIMOA is established. With robot's mechanism system constraints, taking minimum traveling time and minimum energy as criterion, the robot trajectories are planned using CIMOA. Compared the results with single objective algorithm by genetic algorithm (GA) and weighted objective genetic algorithm (WGA), it is shown that, the travelling time and consuming energy by multiple objective method CIMOA are much less, and the trajectory in joint space is much smoother. <s> BIB005 </s> A Review on Energy-Saving Optimization Methods for Robotic and Automatic Systems <s> Multi-Point Trajectory Optimization <s> Minimizing the computational complexity of torque optimization and the ability to calculate the magnitude of the joint torque accurately will result in a safe operation without overloading the joint actuators. Reduced torque will lead to lighter robotic arm and easier control. The main objective of this work is to design a robotic arm with all the motors located at the base so that the arm becomes lighter than the conventional arms. The main advantage from this development is to decrease the torque required to control the arm. The motion of motors is transferred to links via aluminum pulleys, bearings, and timing belts which yields to the need of lighter motors and hence a lighter manipulator. The maximum torque of each joint has been calculated then compared with the torque needed using conventional design to show the effectiveness of the proposed design for decreasing the weight of the manipulator and minimizing driving joint torques. <s> BIB006
In MP trajectory optimization, the energy consumption of a mechatronic system is achieved by both optimizing the path and the timing BIB001 BIB003 BIB002 BIB004 BIB005  . In literature, the studied systems are usually multi-degrees-of-freedom systems. If planar motion is to be achieved, both planar (e.g., two-degrees-of-freedom BIB002 and three-degrees-of-freedom BIB001 redundant manipulators) and spatial kinematics (e.g., six-degrees-of-freedom anthropomorphic industrial manipulators BIB003 BIB004 BIB005  ) are exploited. The system dynamics are usually modeled by means of a classical formulation, Equations (1) and BIB006 . Generally, parameters are retrieved by datasheet, by CAD, or are estimated on the basis of some assumptions BIB001 BIB002 BIB004 BIB005  . Rarely are the dynamic parameters obtained through an identification procedure such as that in BIB003 , for which the robot performs a specific excitation trajectory and data about torque, speed and acceleration are collected directly or indirectly before the dynamic parameters are extrapolated. Different techniques can be found in literature for the applied methodology and the trajectory representation. In BIB004 , a path of at least three points (either "no-fly" or "fly" points), connected through straight lines and circular arcs in the proximity of a fly point is planned. The method searches among alternative paths, close to the fly points, so as to reduce the energy consumption during the execution of the trajectory, without worsening the cycle time. In BIB005 , a similar approach is followed, that is, initial and final points and a series of intermediate points are considered, but in this case, the joint-space path is interpolated through a non-uniform cubic B-spline. In BIB001 , a variational approach within the B-spline function is implemented. In BIB003  , the searching methods are used in combination with a commercial robotic programming studio. This provides a set of trajectories in the form of the "time history" of each joint and, by evaluating these, the trajectory that allows for the minimum consumption is chosen. Finally, in BIB002 , a set of via-points in between the initial and final position, also taking into account the presence of obstacles, is searched by using an invasive weed optimization (IWO) method; then the computed points are connected with a cubic polynomial to form a continuous and relatively smooth trajectory. This approach considers several cost functions to be minimized in the optimization process in order to retrieve the less-energy-hungry trajectory profile: • minimum effort (i.e., sum of squared torque) BIB005 ; • minimum electrical energy BIB001 , expressed as T 0 e(t)i(t)dt; • minimum mechanical energy BIB002  , expressed as • minimum grid energy BIB004 ; • minimum of squared velocity BIB003 ; • minimum of acceleration average value BIB005 . The algorithms utilized for the searching phase are the following: • invasive weed optimization (IWO) BIB002 ; • artificial immune system (AIS) BIB005 ; • steepest gradient method (SGM) BIB001 ; • genetic algorithm (GA) BIB005 ; • weighted objective genetic algorithm (WGA) BIB005 . The MP trajectory optimization method allows for optimizing the energy consumption without detrimental effects on the cycle time. In some cases, the cycle time can even be shortened. A comparison between different methods in terms of energy saved is not straightforward. Indeed, this highly depends on several parameters, such as the system type and the considered task. Some authors BIB001 BIB003 BIB004  compare the results of their optimization algorithm with that provided by a commercial integrated development environment for robotics. Paes et al. BIB003 claim savings of energy of up to 4%, compared to the fastest trajectory obtained with ABB RobotStudio, in a pick-and-place movement. Furthermore, the cycle time results are 3% shorter. Mohammed et al.  achieve an energy reduction of up to 30% with their module compared to ABB RobotStudio in a pick-and-place task, both with and without a payload. In BIB004 , savings of up to 18% of the energy, compared to the fastest trajectory obtained with ABB RobotStudio in a pick-and-place operation, are achieved, while the cycle time is shortened by 11%. Hirakawa et al. BIB001 consider three kinds of operations: a linear trajectory in which up to 30% of energy is saved, a top-to-bottom linear trajectory in which up to 70% of energy is saved, and a circular trajectory that consumes 42% less energy.