Introduction
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Unit direct production cost (€/part), i.e. the ratio of the hourly costs of the workcell and the average throughput;
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Mix flexibility, i.e. the ability to handle a wide variety of parts, and manage a wide variety of parts and products;
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Volume flexibility, i.e. the ability to change the productivity of the system without reducing its efficiency.
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The identification of the characteristics that influences the performance of a multi-resources CAS;
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To provide a model that allows to estimate the cycle time given the product characteristics, the number of feeding devices and resources and the degree of collaboration without the need of a simulation environment.
Related work
Performance evaluation model for multi-robot multi-operator CAS
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To obtain a suitable collaboration between the resources;
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To estimate the achievable makespan \(T_{tot}\) with the considered task allocation.
Nomenclature
Hypotheses
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The considered assembly system does not distinguish between different feeding typologies, since this work supposes that all the devices can provide each part when required.
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Between each change in assembly tasks the payload difference is minimal, therefore retooling is not needed and each resource can move every parts.
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The considered assembly process does not take into account any precedence constraint.
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The number of resource \(N_r\) is defined as:where \(T_k\) is the time needed to carry out task k and \(T_c\) is the desired cycle time. In this work we will focus only on the scenarios with \(N_r > 2\).$$\begin{aligned} N_r = \frac{\sum _{k}^{N_p} T_k}{T_c} \end{aligned}$$(2)
Model description
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picking, i.e. when a resource moves from the feeding point to an assembly point and returns to the feeder or from a point to the following one in the case of a pure assembly process;
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placing, i.e. when a resource places the picked part in the proper position;
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fastening, i.e. when a resource attaches the part to another or to the product base.
Definition of \(T_{c0}\)
Definition of f
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Resources
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Resource type and number, i.e. the distribution of human operators and cobots composing the CAS. Since the resources present greatly different task times (\(t_a\) and \(t_{pp}\)) between each other, an asymmetrical resource distribution, e.g. n cobots and m operators, results in a more critical layout, increasing f. Moreover, considering n type 1 resources and m type 2 resources, with \(m < n\), the considered layout will be more critical if the type 1 resources have higher task times since they will occupy the shared workspace for a longer time, thus increasing the risk of spatial interferences.
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Resource task time, i.e. the difference between \(t_a\) and \(t_{pp}\) of the resources. As shown previously, different times between the resources increase f, since higher differences reduce the possibility of synchronization between the resources, i.e. they cannot enter and leave the shared workspace at the same time. Moreover, in the hypothesis of an assembly process without any precedence, the resources time and distribution influence the task distribution r which in turn further influences f.
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Feeding devices
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The ratio \(r_f\) between the number of feeding device \(N_f\) and \(N_r\). Under the hypothesis that each bulk can provide every part required for the process assembly, each bulk can serve every resource, thus lowering \(r_f\) to values inferior to 1 increases the chances of interferences, and as a consequence f. It should be noted that due to the hypothesis set on the feeding devices, values of \(r_f\) greater than 1 does not imply a further reduction of f since the resources will reach the nearest unoccupied feeding device.
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Feeding device position, since an increase of the minimum distance of each resource from the feeding devices, decreases the possibility of interferences, and therefore f.
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Simulation environment
Model application: assumptions and input values
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The pick-and-place time is evaluated as the time needed to move from the completed point to the feeder and then to the placing point, considering also the time required for grasping the object. Regarding the cobot(s), we considered a gripper with a closing/opening time of 0.7 s.
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The human operator(s) is allowed to move his/her base, representing the shoulder, around the workspace in order too reach bulks/placing points too far from the base. This motion is outside the workspace in order to reduce the risk of interferences, but it is simulated to better compute the expended time.
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Besides the motion time component, the assembly and picking time of each task are equal.
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The space occupied by the cobot(s) and by the human operator(s) is represented by a two-dimensional sphere-swept line (SSL) with corresponding radius.
Product parameter | Value | Unit |
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\(N_p\) | >16 & <40 | – |
L | >150 & <600 | mm |
Manual parameter | Value | Unit |
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\(t_{a}\) | \(1.04\cdot 10^{-3}\) | h/part |
\(t_{pp}\) | \(3 \cdot 10^{-4}\) | h/part |
s | \(7.2 \cdot 10^5\) | mm/h |
\(L_{min}\) | 0 | mm |
\(L_{max}\) | 600 | mm |
R | 95 | mm |
Robot parameter | Value | Unit |
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\(t_{a}\) | \(2.1 \cdot 10^{-3}\) | h/part |
\(t_{pp}\) | \(1.94 \cdot 10^{-4}\) | h/part |
s | \(9 \cdot 10^5\) | mm/h |
\(L_{min}\) | 65 | mm |
\(L_{max}\) | 1300 | mm |
R | 95 | mm |
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shared tasks allows each agent to perform picking and assembly tasks, i.e. every resource fasten each part they picked.
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human p/p separates the placing from the assembly tasks, thus the human operators pick and place every part so that the robots can fasten it; this choice was driven by the assembly considered, which showed a manual picking faster than the robotic one.
Validation test
Std. deviation \(\sigma \) | Estimated \(T_{c0}\) | Mean \(T_{c0}\) | Unit |
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0.1\(\mu \) | \(1.7\cdot 10^{-3}\) | \(1.62\cdot 10^{-3}\) | h/mm |
0.3\(\mu \) | \(1.7\cdot 10^{-3}\) | \(1.61\cdot 10^{-3}\) | h/mm |
Std. deviation \(\sigma \) | Estimated f | Mean f | Unit |
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0.1\(\mu \) | 1.95 | 1.97 | – |
0.3\(\mu \) | 1.95 | 2.00 | – |
Results and discussion
Process characteristics
Process characteristic | Scenarios |
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\(N_r\) | 3,4 |
Resource distribution | 2 cobots 1 operator |
1 cobot 3 operators | |
2 cobots 2 operators | |
3 cobots 1 operator | |
\(r_f\) | 1/2 |
2/2 | |
3/4 | |
4/4 | |
2/3 | |
3/3 | |
Layouts for \(N_r = 3\) | a,b,c |
Task allocation method | Shared tasks |
Human p/p |
Shared tasks method
Resources distribution
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1 cobot and 3 human operators;
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2 cobots and 2 human operators;
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3 cobots and 1 human operator.
Number of resources
Layout
Number of feeding devices
Human p/p method
Resource distribution
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2 cobots and 2 human operators;
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3 cobots and 1 human operator.
Number of resources
Layout
Number of feeding devices
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2 cobots and 2 operators, \(r_f\) equal to 1;
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2 cobots and 2 operators, \(r_f\) equal to 0.5;
Conclusion
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An exponential model for determining the \(T_{norm}\) of a CAS is provided;
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A method for evaluating \(T_{c0}\), the coefficient of the exponential model, is provided; moreover the difference between the estimation and the simulated result is up to 5%.
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The influence of different process characteristics, e.g. the layout, on the exponent f is presented along with their effect.