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Procedia CIRP 29 (2015) 354 - 359

The 22nd CIRP conference on Life Cycle Engineering

Minimization of the energy consumption in motion planning for single-robot tasks

Stefania Pellegrinellia'*, Stefano Borgiaa, Nicola Pedrocchia, Enrico Villagrossia. Giacomo Bianchia, Lorenzo Molinari Tosattia

"Institute oflndustrial Technologies and Automation, NationalResearch Council, ITIA-CNR, Via Bassini 15, Milan, 20133, Italy * Corresponding author. Tel.: +390223699954; fax: +390223999915. E-mail address: stefania.pellegrinelli@itia.cnr.it

Abstract

Recently, the importance of sustainable manufacturing has been widely discussed. The optimization of energy consumption in product manufacture has been deeply analyzed, mainly focusing on the energy directly absorbed by the manufacturing process. On the contrary, this paper focuses on the analysis and optimization of the energy consumption related to auxiliary robotic assembly processes, contributing to the identification of sustainable manufacturing strategies for pick and place robots. It proposes a methodology for the automatic generation of robot trajectories and the sequencing of the robot task, while minimizing the energy consumption. A probabilistic roadmap is created to identify a collision-free and minimum energy consumption trajectory for each couple of feasible tasks. Trajectory power consumption is evaluated exploiting dynamic information coming from the real robot motion planner using a model that takes into account the energy behavior of motors and drives and their operative conditions. A set of generated trajectories is selected, defining the task sequence and minimizing the robot cycle time. The differences between the results deriving by employment of the energy consumption minimization criterion versus time minimization criterion are presented through a simplified case.

© 2015 The Authors. Published by Elsevier B.V.This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

Peer-reviewunder responsibility of the scientific committee of The 22nd CIRP conference on Life Cycle Engineering

Keywords: Motion planning; Energy consumption; Optimization

1. Introduction

During the last years, the rapid increase of the energy price together with strictly international and national policies has pointed out the problem of energy efficiency [1], moving companies' awareness from the reduction of the production time to the identification of an optimal trade-off between production time and energy consumption.

Since 1998, the energy consumption in the industrial sector has been reducing. For instance, in the US the manufacturing energy consumption decreased by 17% from 2002 to 2010 [2]. However, an unnecessary use of energy equal to 20-40% may still be found. This percentage is impressive considering a total EU-27 industrial energy use of 324 Mtoe (2004-2005) [3].

According to [4], for many industrial processes, e.g. the robotized spot-welding assembly, the consumption can be catalogued as "process energy" or "auxiliary energy". The process energy, generally representing the majority of the

consumption, is the energy directly used in the manufacturing of the products, e.g. the assembly welding energy. The auxiliary energy is the energy required by the operations that allow the execution of the process, e.g. robotic energy consumption. Even if several papers cope with the reduction of the process energy [3], auxiliary energy plays a relevant role and deserves to be studied.

In [5], the relevance of the energy consumption reduction in robotic operations is underlined. The paper deals with the optimal placement of a path in the robot workspace so that the energy consumption is minimized coping with geometric, kinematic and dynamic constraints. [6] provides a methodology able to determine robot velocity and acceleration in order to minimize the energy consumption when moving from a starting point to a target point in a predetermined amount of time. Similarly, in [7], the influence of robot movement parameters on energy consumption is presented, focusing on robot optimal speed, acceleration and

2212-8271 © 2015 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.Org/licenses/by-nc-nd/4.0/).

Peer-review under responsibility of the scientific committee of The 22nd CIRP conference on Life Cycle Engineering doi: 10.1016/j .procir.2015.02.174

jerk. A more comprehensive approach can be found in [8] with reference to the automobile industry, where the electrical energy consumed by robotic application is about 8%. In this approach, several strategies to save energy for medium and high payload robot are presented: speed and acceleration variation along the robot path, fly-by trajectories and intelligent management of robot breaks. The same attention to energy saving is presented in [9], where an approach for reducing energy consumption of pick-and-place industrial robot is described. As in the previous approaches, the idea is to reduce the total energy consumption by means of constant time scaling, staring from pre-scheduled trajectories. An evolution of this paper can be found in [10], where the modeling and optimization of energy consumption in cooperative multi-robot is proposed. Specifically, the robots are coordinated through the variation of the velocities and acceleration along predefined path. The task execution sequence changes accordingly to the minimization criterion.

This paper proposes a completely different approach. Indeed, the idea is to allow the selection of the collision-free paths to move from a starting point to a target point that minimizes the energy consumption, while considering technological and geometrical constraints. The modification of the robot velocity and acceleration along all the selected paths is not included in this paper, but represents a future work. Moreover, the paper also take into account the whole robot motion plan, i.e. all the trajectories for the execution of several robot tasks have to be defined. Thus, in this paper, a method able to provide a single-robot motion plan minimizing the comprehensive energy consumption is presented, while taking into account robot cycle time.

The paper is structured as follows: in Section 2 the industrial problem is described; Section 3 presents the methodology, while Section 3.1, 3.2 and 3.3 describe in details the three steps of the approach: trajectory generation, robot dynamic and energy assessment, and task sequencing; in Section 4 the test case is presented and discussed; finally, conclusions and future works are driven in Section 5.

2. Problem statement

The paper focuses on the robot energy consumption in pick-and-place tasks. A task consists in the grabbing or release of an object in a specific position, thus representing a constraint to the robot configuration during the task execution. In such a context, two main problems have to be faced: the definition of collision-free trajectories among the tasks (couples of tasks) and the task execution sequence.

These two problems are interconnected since the execution sequence, apart from existing precedence constraints among the tasks, depends on the trajectories definition. In other words, task sequence may not be completely predefined, i.e. the final task sequence has to be optimized taking into account the energy consumption, the required cycle time and possible precedence constraints among the tasks. This optimization may lead to different results, if different trajectories are considered. In such a context, the optimization of the energy consumption and the cycle time generally represent a trade-off [9].

1. Trajectory

generation

Am. HM, HM. T £

2A- Trajectory dynamic 4№ '/>• !M T 2B, Trajectory energy

assessment assessment

3. Trajectory selection and task sequencing_¡

Figure 1: The approach

Worthy, the energy optimization is of upmost importance for pick and place tasks, where only the start and goal configurations are constrained.

3. Methodology

The proposed approach is based on three steps (Fig. 1). The first step (Section 4 - Step 1) concerns the generation of the trajectories. Specifically, for each couple of tasks (two tasks that could be executed one after the other), a collisionfree trajectory minimizing the energy consumption is defined. The generation of the trajectories exploits the probabilistic roadmap technique [11] and the Open Robot Realistic Library (ORL) [12] provided by COMAU. The ORL library represents the virtualization of the real robot controller, according with the standard RCS [13], providing the robot interpolator and all the functionalities related to the robot dynamic model. The trajectories generated by the ORL are expressed in terms of motor positions qM, velocities q'M, and accelerations q'M . The minimization of the energy consumption is based on the employment of probabilistic roadmaps that allow the identification of the best geometrical path, along which the joint velocity and the acceleration are maximal.

The evaluation of the energy consumption derives from Step 2 where the dynamic and energy assessments of the robot trajectory occur. On the basis of the information coming from Step 1, together with the dynamic model of the specific robot and the embedded dynamic parameters, the ORL is responsible of the trajectory dynamic assessment (Section 3.2.1 - Step 2A). On the contrary, the trajectory energy consumption E (Section 3.2.2 - Step 2B) is provided by an ad-hoc developed model that is able to predict the energy consumption according to the trajectory duration T, velocities qM [rad/s], acceleration qM [rad/s2] and torque tm [Nm].

The last step of the approach (Section 3.3 - Step 3) concerns the definition of the task sequence, thus the selection of the trajectories. Since the cycle time is often a relevant factor, the idea is to define the final sequence selecting the trajectories so that the cycle time is minimized. In such a way, a trade-off between the energy consumption and the cycle time is reached.

3.1. Step 1: Trajectorygeneration

During trajectory generation, collision-free path has to be calculated within the robot family of tasks. In this activity, three factors have to be considered: the degrees of freedom

(DOF) characterizing the robot, the complexity of the environment and the criterion selected according to which the path is generated and optimized. Indeed, on the one hand, the robot DOF and the environmental complexity lead the technique to be employed; on the other hand, the quality of final trajectory depends by the optimization criterion.

Several methodology addressing the problem of robot motion planning can be found in literature [14], such as potential fields, roadmaps, cell decomposition, probabilistic potential fields, probabilistic roadmaps, probabilistic cell decomposition and simple-query sampling-based method. However, not all the presented methodologies can be successfully employed in high-complex environments with industrial anthropomorphic robot like assembly cells. In such an environment, probabilistic roadmaps seem to be the most promising methodologies [12]. Indeed, this methodology has been successfully exploited to define robot motion planning in body-in-white spot-welding cells [12,15,16].

Concerning the criteria for path optimization, the most common criterion is based on the evolution of the area swept by the robot for reaching the second configuration being in the first configuration [17]. Indeed, the higher the area swept by the robot, the higher the probability to have a collision. In [18,19], different metrics such as the Euclidean, the scaled Euclidean, the Minkowski, the modified Minkowski and the Manhattan distances are evaluated. All the presented metrics are easy to be calculated but are purely geometrical and do not take into account the real industrial problem.

The proposed methodology aims at solving the motion planning for a single robot in a complex environment through the employment of probabilistic roadmaps and an energy consumption minimization criterion.

The idea is to uniformly sample to robot configuration space C(q), with q the vector of the robot joint coordinates, through Halton point technique [20] and to connect each sampled points to the nearest points. In order to identify the nearest points, the robot energy consumption required to move from the sampled point in analysis to all the other points through joint point-to-point trajectories is evaluated. The trajectories showing the lowest energy consumption determine the nearest points. All the connections are tested for possible collisions with the cell elements [21] to consider only collision-free paths. The generated map is exploited for the identification of the robot minimum energy trajectories between the reference positions of two assembly tasks. The identification of the optimal trajectory is based on the Dijkstra algorithm [22]. At the end, Step 1 provides a minimum-energy and collision-free trajectory for each couple of tasks.

It is important to underline that the generated trajectories are optimal from the energy point of view in relation the specific generated probabilistic roadmap. Thus, a better sampling of the space during roadmap generation will allow the definition of a better energy profile of the trajectories.

3.2. Step 2: Robot Dynamic and Energy Assessment

Commonly, industrial robot is actuated by Permanent Magnet Synchronous Motors PMSM and relative power converters (rectifiers, DC bus and inverter). The robot energy

assessment passes through the knowledge of the mechanical power consumption and, thus by the estimation of the motor torque for each robot motor. Section 3.2.1 describes the process leading to the estimation of the motor torque, while Section 3.2.2 present a model for the estimation of the energy consumption taking into account motor torque and losses.

3.2.1. Step 2A: Dynamic Assessment

The joints torques of a standard industrial robot can be calculated by considering the inverse dynamic model of the machine. Starting from the standard rigid multi-bodies dynamic equation, different formulation can be used (e.g. the recursive Newton-Euler formulation, or on the Lagrangian energy approach) to write the dynamic equations of the system [23]. By regrouping the analytical equations, the inverse dynamic model of the robot can be written as:

^dyn =v{<1M,<1M, '4MV (1)

where, for a manipulator with n DOF, zdyn is the nxl vector of motor torques which includes the contribution of dynamics of the link masses, the first and the second moments of inertia of the link, and the motor rotor inertia. y is the n x np regression matrix (i.e. containing all of the geometrical information of the mechanical structure) which is in linear relation with the npxl set of dynamic parameters of the machine it, with np representing the number of essential parameters obtained from the entire dynamic parameters set as in [24,25]. Finally, the qM, qM, qM are respectively the n x 1 joint motor positions, velocities and accelerations vectors.

The friction term contribution can be added as independent term to zdyn. Different models, with increasing complexity can be considered, but a simple linear model represents a good compromise between accuracy and complexity:

= K k + Fcsign(q) (2)

where Fv and the Fc are respectively the n x n diagonal matrices representing the viscous and the Coulomb friction parameters.

Thus, the total motor torque t can be obtained by adding:

~ ^dyn + ^fric! (3)

The actual values of the dynamics parameters are often not available to the end user, and identification techniques are necessary to extrapolate these values. However, the above-mentioned ORL library that has been used in this work provides directly the calculus of the motor torque. It is worth to underline that the accuracy of the torque estimation given by ORL is guaranteed by the fact the ORL provides the dynamic model integrated in the COMAU robot controller.

3.2.2. Step 2B: EnergyAssessment

The main energy consumption is due to the motor. Previous studies assert that PMSM electrical power in robot applications can be estimated by referring to the electrical machine models described in [9,26], which relates the PMSM behavior at a generic operating point with the PMSM behavior at rated (nominal) operation.

Robot-A2.axis - Power,

1200 1000

P = P„ + P., + P, = P„ + k, i

, ix + Rs V

Table 1. Identified parameters for each axis motor.

Parameter A1 A2 A3 A4 A5 A6

PB [W] 16.6818 31.2933 16.0939 8.0305 7.8799 8.0009

kt [Nm/A] 0.5343 0.6083 0.5351 0.2606 0.2451 0.2217

7.1216 2.689 7.1324 2.2807 2.3631 2.8327

ComauRobotNS16.A2-Axis.Motor-power [spectral content model V-I]

The selection of the motor model has been led by preliminary experimental investigation using the COMAU NS16-165 [12] robot, which is the robot employed in the test case presented in the Section 4. The experiments have shown that the motors of the robot work always in no flux weakening operative region. Thus, despite many detailed models are presented in literature, e.g. based on motor equivalent circuits and on experimental identification of parameters and losses [27,28], a simple model for the motor power losses has been identified. Thus, the motor power absorption P has been modelled as sum of constant power PB, mechanical power PM and motor copper losses PR:

5 4 3 2 1

0123456789 10 [Hz] x 104 Figure 3: A2-axis motor power spectral analysis.

where DFT is the discrete Fourier transform and ~ is the complex conjugate operator. Power analysis shows at high frequencies the presence of power dissipations due to the pulse with modulation (PWM), represented in the model by the estimated constant power coefficient PB [W] (Fig. 3). Hence, the analysis results indicate that the below constant current-torque relation is adequate for the application scenario of the here presented work.

where kt is the motor torque constant [Nm/Arms], and iq are the effective and peak values of the current [A], qM is motor velocity [rad/s], and Rs is the stator resistance [A], So, energy can be obtained as integral of the power along the time.

The estimation of the motor model parameters has been performed through a test campaign consisting of clockwise (CW) and counter clockwise (CCW) motions of each axis of the robot at different velocities and accelerations. Unknown coefficients PB, kt and Rs have been estimated using least mean square (LMS) fitting technique (Table 1). The results show a good representation of the power behavior of the axes motors taking as input kinematic and current data provided by robot control (e.g. Fig. 2, power absorption of A2-axis motor). Noteworthy, the validity of the model expressed by Eq. 8 is confirmed by the extremely low values attained by the estimation standard error. Thus, a possible additional term expressing the velocity-dependent losses (i.e. iron losses) is not significant in such application scenario and would not improve the power estimation for the considered motors.

As a matter of further validation of this consideration, a spectral analysis has been executed taking into exam 3-phases currents i1, i2, i3 and voltages v1, v2, v3 measured at a sample frequency of 200kHz. For each frequency, the motor power P has been computed as follows: P = Re{DFT(vj )• ~ (DFT(i1)) + DFT(v2 )• ~ (DFT(i2)) + DFT~ (DFT(/3))}

3.3. Step 3: Trajectoryselection and task sequencing

Step 3 of the methodology aims at selecting the trajectories and fining out the best task sequence so that the robot cycle time is minimized. This can be reduced to the travelling salesman problem (TSP) [29], where the tasks, the trajectories and the trajectories time represent respectively the nodes, the arcs and the arc weights.

The problem is solved through a mixed-integer linear mathematical model, whose indexes, parameters and variables are presented in Table 2, Table 3 and Table 4.

Table 2. Model indexes.

Indexes Definition

t, tl, t2 Tasks {1,.. executed . ,NT}, where NT is the number of tasks to be

Table 3. Model Input.

Input Type Definition

FMPftiit2 Bool Feasible motion plan. Equal to 1 if the robot can execute task tl immediately after task t2

MTilt2 Double Motion time [s]. Time required by the robot for the execution task tl immediately after task t2

MEtlit2 Double Motion energy [J]. Energy required by the robot for the execution task tl immediately after task t2

TTt Double Time required for the execution of the task t

Table 4. Model Variable.

Variable Definition

MPtlit2 Bool Selected motion plan. Equal to 1 if the robot can execute task tl immediately after task t2

MPStl,t2 Integer Task execution sequence. Equal to k if the robot can execute task tl immediately after task t2 as Kh task.

Stl,t2 Double Instant time in which the robot leaves task tl after its execution and approaches task t2

Ftl,t2 Double Instant time in which the robot approaches the task t2 after the completion of task tl

Tt Double Time lap in which the robot moves from task tl to task t2, and executes t2

FEC Double Final energy consumption

FCT Double Final robot cycle time

The objective function (Eq. 7) aims at minimizing the robot cycle time (FCT), while selecting the energy-based previously defined trajectories. Eq. 8 and Eq. 9 impose that from each task tl, a single task t2 is reachable, and each task t2 is reachable from the task t2. Because of the contemporary application of Eq. 8 and Eq. 9, each task can be executed only once. Eq. 10 is necessary to correctly define the optimal task sequence. Eq. 11 assures that, at time step k, task tl is left for the execution of task t2 at time step k+1. Eq. 12 establishes a relation between the MP and MPS matrices. Eq. 13-Eq. 16 lead to the definition of the motion plan in terms of initial time and completion time: Eq. 13 defines the initial time of the motion plan, Eq. 14 imposes the equality among the initial time of a trajectory and the completion time that considers the trajectory duration and the task duration (Eq. 15 and Eq. 16). Eq. 17 determines the equality between FCT and the biggest completion time. Finally, Eq. 18 provides the energy consumption related to the motion plan.

Minimize: FCT

Subject to:

X MPtlt2 =1 W2 ti

X MPIII2 =1 Vi7

X MPsm = 1

X MPSlt2 -X MPStll = 1 V? * 0

MPSIU NT

Vtl,t2

X A* = X Q, V? * 0

C,l,2 = 1,1,2 + T,l.,2

T = MP MT + MP TT

FEC = £ MPi1i2MEi1i2 Vtl,t2

Vtl,t2

(8) (9)

(10) (11) (12)

Figure 4: Simplified case

Table 5. Robot position and orientation in the cell.

COMAU NS16-165

Rototranslation - position [mm] [1 0 0 -2000; 0 1 0 0; 0 0 1 0; 0 0 0 1]

Home joint position [°] - HP

0 0 -90 0 0 0

Table 6. Robot tasks

Task Position [mm] ZY'Z'' orientation [°]

T1 -800 -700 1000 30 5 30

T2 -1300 0 600 10 30 10

T3 -450 250 1300 50 40 10

T4 -600 -700 1300 20 10 0

T5 -500 -500 1200 -40 -10 -10

4. Test Case

A pick-and-place test case is hereafter presented and analysed. An anthropomorphic COMAU NS16-165 robot (R1) is employed for the execution of 5 assembly tasks (Fig. 4). The robot position and orientation, its home position (called HP) as well as the task position respect to the cell reference system are described in Table 5 and Table 6. Precedence constraints among the tasks are not considered.

The proposed case is solved according to the paper presented in this approach. The results (S1) are compared with the results obtained by the same approach substituting the energy consumption criterion with the time criterion (S2).

The first experiment (S1) based on the proposed approach led to the identification of a work cycle characterized by a cycle time of 22.7s and an energy consumption of 22.27kJ with the task sequence HP^T4^T5^T3^T2^T1^HP. On the contrary, the experiment S2 provided a cycle time of 17.98s with and energy consumption of 25.19&/ and the task sequence HP^T5^T4^T3^T1^T2^HP. Thus, an improvement of 12% on the total energy consumption is reached. Two trajectories can be found in Fig. 5.

A detailed analysis of the most significant results is presented in Table 7. An initial comparison between the results provided by S1 and S2 revels a medium improvement of the energy consumption in S1 by 8% (0.35fc/) against a time increase of 38% (0.85.s). The overall mean is calculated considering all the generated trajectories and not only the subgroup presented in the table. In the majority of the cases, the trajectory energy consumption obtained by S1 is lower that the energy consumption provided by S2. The remaining cases may be explained through the under sampling of the robot joint space during the generation of the probabilistic roadmap. In the best case (trajectory HP-T1), the energy consumption reduction is equal to 59%, i.e. 2.661kJ.

(b) Time minimization S2 - T3-T5

Figure 5: Example of the same trajectory (at the end effector) generated in S1 and S2

Table 7. Detailed results

Energy min - S1 Time min - S2

Trajectory -

Time[s] Energy[kJ] Time[s] Energy[kJ]

HP-T1 2.72 1.847 2.76 4.508

HP-T2 2.96 2.957 2.55 5.1877

HP-T3 3.26 3.339 2.90 5.509

T1-T2 2.43 2.175 1.39 2.087

T4-T5 3.14 4.836 2.77 5.851

Overall 3.11 4.093 2.26 4.441

The results presented in this section are derived by simulation through the use of a developed software tool. This software tool exploits the experimental parameters of Table 1 for trajectory energy estimation.

5. Conclusions and future work

In this paper, the reduction of the energy consumption related to auxiliary process and specifically to robot energy consumption in pick-and-place operations has been investigated. An approach for the automatic generation of collision-free trajectories minimizing the energy consumption and looking at the robot cycle time has been provided. The developed approach led in the proposed case to the reduction of the work cycle energy by 12%, in comparison to an approach only minimizing the cycle time.

Future work will be related to the analysis of the approach response in a complex and real environment. Moreover, multi-robot motion planning will be taken into account.

Acknowledgements

This paper has been partially funded by Regione Lombardia under the project "Fabbrica intelligente per la deproduzione avanzata sostenibile" (FIDEAS).

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