Application of MARS to robotic assembly

Optimization of a robotic assembly process

V.L. Markine

Railway Engineering Group, Faculty of Civil Engineering, Delft University of Technology, Stevinveg 1, NL-2628, CN Delft, The Netherlands

Email: V.Markine@ct.tudelft.nl

Colaboration:

TU Delft
burgeon

As an example of application of the MARS method (Toropov et al. 1993, 1996, van Keulen and Toropov 1998) to a system with geometrically and physically nonlinear behaviour, an optimization of an automated assembly process performed by a manipulator has been considered. The determination of the position and elastic properties of the remote centre of the ARCC (Adjustable Remote Centre Compliance) mechanism (Figure 1), which is used to avoid failure of error-corrupted assembly, has been formulated as an optimization problem. The production speed should be as high as possible while imposing restrictions on the values of contact forces and initial errors. The vector of the design variables comprises the parameters of the ARCC and the velocity of insertion (Figure 2).

Figure 1. ARCC mechanism (TU Delft, Netherlands)

Figure 2. Design variables of optimization of ARCC

It has been observed that for some set of the design variables the constraints (contact forces) cannot be evaluated because of the failure of a numerical integration procedure in the response analysis software. Physically, such a situation corresponds to a failure of the assembly process. The problem is solved in (Markine 1999) using a multilevel approach. Due to a difficulty of finding a feasible initial design for a manipulator with flexible links, the problem for a manipulator with rigid links is solved first. The optimal design is then used as a starting point for the optimization of a flexible link manipulator. Here, a straightforward optimization of a flexible link manipulator has been performed using the modified plan of experiments suggested above. The optimum design has been obtained in 18 iterations. The results are collected in Table 1.

Design variable	Lower bound	Upper bound	Optimum design (Markine 1999)	New optimum design	Units
L_C	0	250	34.57	34.01	mm
V_ins	5	30	18.3	18.2	mm/s
K_X	10	900	114	116	KN/m
K_G	0.02	2	1.11	1.2	Nm/rad
F₁			10.3	10	N
F₂			10.9	10	N

Table 1. Optimization of an assembly process

References

van Keulen, F.; Toropov, V.V. (1998). New Developments in Structural Optimization using Adaptive Mesh Refinement and Multi-Point Approximations. Engineering Optimization, 29, 217-234.
Markine V.L. (1999). Optimization of the Dynamic Behaviour of Mechanical Stystems. PhD Thesis, Delft University of Technology, The Netherlands. Shaker Publishing B.V. ISBN 90-423-0069-8
Toropov, V.V., Filatov, A.A. and Polynkin, A.A. (1993). Multiparameter Structural Optimization Using FEM and Multipoint Explicit Approximations. Structural Optimization 6, 7-14.
Toropov, V.V., Keulen, F. van, Markine, V.L., de Boer H. (1996). Refinements in the Multi-Point Approximation Method to Reduce the Effects of Noisy Structural Response. Proceedings of the 6-th AIAA/USAF/NASA/ISSMO Symposium on Multidisciplinary Analysis and Optimization, 2, 941-951.