Optimum drive-train design of an industrial robot family.

Komenda, Titanilla Vanessa ; Feng, Xiaolong ; Katalinic, Branko 等

1. INTRODUCTION

This thesis focuses on the development of a tool frame to verify the feasibility of optimum drive-train design of an industrial robot family of a modular type (Fig. 1.). According to Olvander et al. (2008) product family design based on a modular architecture is a good method to meet the demands of mass customization. The objective is to obtain the best possible sharing strategy of drive-train components within the robot family considering performance and cost of all family members simultaneously and to understand the trade-off between these issues. The key is to find the "most profitable balance between quality, performance, and cost" (Pettersson, 2008).

[FIGURE 1 OMITTED]

2. PROBLEM- AND TASK FORMULATION

The state-of-the-art of robot development is to develop and release a robot family simultaneously. The common strategy is to develop members of the robot family (variants) based on one prestigious master robot by changing either upper or lower arm length of this master robot while adjusting appropriate payload. The advantage of this methodology is that, normally, the actuators used in the master robot may be re-used in its variants which may significantly reduce design and simulation complexity. This development strategy ensures the design synergy for robots in the family and results in reduced development efforts per robot and time-to-market. Therefore, an increasing need for optimum design of an industrial robot platform has been evident. A robot platform is a robot family in a broader sense that can consist of a number of master robots and their associated variants. The ultimate challenges are:

* How to determine the actuator modules and the arm structural modules in the platform so that a large number of robots may be optimally constructed based on pre-defined product specifications.

* How drive-train of each robot in the family under study may be optimized to ensure requested time performance, when available actuators and structural modules are given.

3. BASIC PRINCIPLE

A highly challenging demand in the design process of industrial robots is the determination of appropriate gearboxes while considering critical trade-offs between conflicting objectives. Trade-off information can be generated on consecutive optimizations and is valuable when negotiating between different design alternatives. Traditionally the generation of these trade-offs is a time consuming process, but by introducing optimization the process can be partly automated. The design variables concerning these issues are composed of "continuous and discrete parameters, where the latter are associated with different gearbox alternatives and the continuous variables with the speed-torque limitations of the gearboxes" (Pettersson et al., 2005). In general, a non-gradient based optimization algorithm which can handle mixed variable problems is used to solve the highly non-linear issues (Krus & Andersson, 2003). The outcomes are minimization of cost by simultaneously balancing the trade-off between lifetime and performance. The design optimization involves the following matters (Papalambros & Wilde, 2000):

* Selection of a set of design variables to describe the design alternatives.

* Formulation of an objective function (criterion) based on the design variables, which should be minimized or maximized.

* Determination of a set of constraints, which must be satisfied by an acceptable design.

* Determination of a set of values for the design variables, which minimizes or maximizes the objective, while satisfying the constraints.

4. IMPLEMENTATION

Drive-train components normally including motors and gearboxes are large contributors to the overall costs of industrial robots. Understanding the optimal choice of gearboxes and motors for individual members of the robot family and identification of a possible sharing strategy among the members are essential for the optimal drive-train design of industrial robot families. In this thesis, only an integrated type of gearbox and motor including even brake and position sensor is considered. The size, i.e. the weight of the actuators, is held constant during the optimization. That is to say, the design parameters are the torque levels that may be delivered by the actuators. These parameters affect the system characteristics maximum Tool Center Point (TCP) linear acceleration and cycle time. Therefore, the objective function is formulated as the sum of maximum TCP linear acceleration, cycle time and cost, which correspond to sum of scaling factors for adjusting gearbox torques. The maximum TCP linear acceleration is a good robot performance reference value to determine the performance of a robot when there is no pre-defined cycle time requirement available. Furthermore, specific weighting factors have been included.

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

In the case of this thesis, MATLAB is used as a tool frame for drive-train optimization of the robot family. This is done based on the following two facts:

* The motion simulations of individual robots needs to be repeatable for all robot members in the family and the results need to be kept for computing an overall objective function.

* Optimizers are readily available in MATLAB.

Fig.2. shows the family optimization tool architecture for multiple robot drive-train optimization of a robot family. The design variables defined for each robot respectively influence the motion simulation results and are created by the optimizer again and again for new optimal search attempts. The optimization loop ends, if the objectives are achieved or after a predefined certain number of function calls is reached. That is to say, that the scaling factors for adjusting gearbox torques are created as long as the optimizer finds an optimized set of design variables considering the trade-offs between the conflicting objectives. Furthermore, the optimized needed maximum motor torques and the maximum torques that may be delivered by the specified actuators can be compared in order to find an optimum sharing strategy among family members. The identification and comparison of needed and achieved torque levels and the required replacement of actuators lead to an iteration in the design process in regard to lower costs while not sacrificing too much of the performance of individual members. However, it has to be considered that in some parts of the solution space a large increase in performance could correspond to a small increase in cost and vice versa.

[FIGURE 2 OMITTED]

[FIGURE 3 OMITTED]

Fig.3. shows the convergence curve of a MultiRobot drive-train optimization with the target of 3g maximum TCP linear acceleration. This figure indicates that the simultaneous optimization of a number of robots works.

6. CONCLUSION AND PROSPECT

This thesis has succeeded some of the essential steps towards an automatic and optimum design of an industrial robot platform for a modular type robot. This thesis has accomplished the following:

* Development of a tool frame in MATLAB to verify the feasibility of optimum drive-train design of an industrial robot family.

* Proposal and verification of an overall objective function, based on maximum TCP linear acceleration, cycle time, and required gearbox torques.

* Usage of the SolidWorks-API for efficient mass data extraction into the configuration file of a robot.

Due to the enormous simulation efforts for the optimization of a robot family of four robots, future improvement in the simulation efficiency is evident. Advancements can be achieved with:

* Usage of parallel computing.

* Usage of a more efficient optimizer or software tool.

* Integration of the CAD modelling tool in the optimization loop, for automatically updating the actuators in the CAD model and extracting mass data in the robot configuration file.

7. REFERENCES

Krus, P. & Andersson, J. (2003). Optimizing Optimization for Design Optimization, Proceedings of ASME 2003 Design Automation Conference, pp 1-10, ASME

Olvander, J.; Holmgren, B. & Feng, X. (2008). Optimal Kinematics Design of an Industrial Robot Family, Proceedings of ASME 2008 International Design and Engineering Technical Conference & Computers and Information in Engineering Conference, pp 1-11, New York, August 2008, ASME, New York

Papalambros, P. & Wilde, D. (2000). Principles of Optimal Design, Cambridge University Press, 0-521-62727-3, Cambridge

Pettersson, M. (2008). Design Optimization in Industrial Robotics: Methods and Algorithms for Drive Train Design, Linkoping University, Linkoping

Pettersson, M.; Krus, P. & Andersson, J. (2005). On optimal Drive-Train Design in Industrial Robots, Proceedings of IEEE International Conference on Volume, pp 254-259, Linkoping, December 2005, 0-7803-9484-4, Linkoping University, Linkoping