Corresponding author: Masanori Sato E-mail: m.sato@astec.kyushu-u.ac.jp

Journal of Bionic Engineering 7 Suppl. (2010) S185–S190

Simultaneous Optimization of Robot Structure and Control System Using Evolutionary Algorithm

Masanori Sato1, Kazuo Ishii2

1. Kyushu University, Fukuoka, 819-0385, Japan 2. Kyushu Institute of Technology, Fukuoka, 808-0196, Japan

Abstract The simultaneous optimization of a robot structure and control system to realize effective mobility in an outdoor envi-

ronment is investigated. Recently, various wheeled mechanisms with passive and/or active linkages for outdoor environments have been developed and evaluated. We developed a mobile robot having six active wheels and passive linkage mechanisms,and experimentally verified its maneuverability in an indoor environment. However, there are various obstacles in outdoor environment and the travel ability of a robot thus depends on its mechanical structure and control system.

We proposed a method of simultaneously optimizing mobile robot structure and control system using an evolutionary al-gorithm. Here, a gene expresses the parameters of the structure and control system. A simulated mobile robot and controller are based on these parameters and the behavior of the mobile robot is evaluated for three typical obstacles. From the evaluation results, new genes are created and evaluated repeatedly. The evaluation items are travel distance, travel time, energy consump-tion, control accuracy, and attitude of the robot.

Effective outdoor travel is achieved around the 80th generation, after which, other parameters are optimized until the 300th generation. The optimized gene is able to pass through the three obstacles with low energy consumption, accurate control, and stable attitude.

Keywords: simultaneous optimization, evolutionary algorithm, mobile robot, rough terrain Copyright © 2010, Jilin University. Published by Elsevier Limited and Science Press. All rights reserved. doi: 10.1016/S1672-6529(09)60234-1

1 Introduction

Wheeled mobile robots with a passive and/or active linkage mechanism for operation in an outdoor envi-ronment have recently been developed and evaluated; for example, NASA/JPL developed the rocker-bogie mechanism installed in Sojourner[1,2], Kuroda et al. de-veloped the PEGSUS mechanism installed in Micro 5[3,4], Siegwart et al. developed the original passive linkage mechanism installed in Shrimp[5] and CRAB[6]. Chugo et al. developed a prototype vehicle with a rocker-bogie mechanism and omni-wheel[7]. The common features of these wheeled mobile robots are small wheels, a passive linkage mechanism, and high mobility on rough terrain without the reduction of mobility on a flat landscape.

We developed a wheeled mobile robot that has six active wheels and a passive linkage mechanism, and its maneuverability was experimentally verified in an in-door environment. To extend its maneuverability, we

proposed a control system design method, environment recognition system, and adaptive control system[8–12]. However, there are various obstacles and road condi-tions in outdoor environments, such as bumps, gaps, stairs, dirt roads, grass roads, and paved roads. The ability of mobile robots to travel on such surfaces strongly depends on their mechanical structures and control systems.

We have proposed the intelligent mechanical de-sign method[13,14] and applied the method to develop a mobile robot that inspects sewer pipes[15]. The present paper addresses one of the most important issues for mobile robots: the simultaneous optimization of the robot structure and control system to realize effective mobility employing an evolutionary algorithm and dy-namics simulation. In our previous research, the opti-mized mobile robot could handle three typical envi-ronments in dynamics simulations[16,17]. However, the benchmark environments were independent, the mobile

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robot attitude was not evaluated, and only a single con-trol parameter, the proportional gain, was optimized. Therefore, the optimized mobile robot could not main-tain stable attitude, especially when climbing down ob-stacles, and thus, could not overcome continuously un-even surfaces.

The aim of this paper is to achieve stable travel on continuously uneven surfaces by applying our proposed simultaneous optimization method. In dynamics simu-lations, the optimization method evaluates the travel ability, travel time, energy consumption, control accu-racy, and robot attitude. The optimized parameters in-clude not only those of the mechanical structure but also the PID control gain for each wheel.

2 Simultaneous optimization

In this section, we describe the optimization method including a presentation of the dynamics simu-lator, genetic algorithm, and evaluation functions. Fig. 1 is a diagram of the simultaneous optimization method. In this method, a gene of a genetic algorithm expresses parameters of the mobile robot structure and control system. The mobile robot and controller are designed on the basis of these parameters, and the behavior of a mobile robot is evaluated in dynamics simulation. From the evaluation results, new genes are created in a genetic algorithm operation and evaluated repeatedly.

Fig. 1 Diagram of simultaneous optimization using a dynamics simulator and genetic algorithm. 2.1 Open dynamics engine

The Open Dynamics Engine (ODE) has been in development by Russell Smith since 2001[18]. The ODE is a library for simulating articulated rigid body dy-namics. It is fast, flexible, and robust and has built-in collision detection. In our research, the ODE is used as the dynamics simulator to model the mobile robot and the benchmark environment because of its high calcula-tion speed.

Fig. 2 shows our wheeled mobile robot, which has six active wheels and a passive linkage mechanism. The mobile robot structure consists of four passive linkage

mechanisms: a front link, side link, middle link, and rear link. In this work, the front link, side link, and rear link are optimized. Fig. 3 is an overview of our wheeled mobile robot using the ODE.

Fig. 2 Overview of the wheeled mobile robot and a 3D-CAD design image.

Fig. 3 Overview of the wheeled mobile robot using ODE.

2.2 Genetic algorithm

The optimization parameters of the mechanical structure are the height of the mobile robot, rear link length, side link length, front link length, front link angle, wheel diameter, mass of weight, and position of weight. The control system parameters are the PID control gain for each wheel. One parameter is expressed in 8 bits, and a gene expresses 24 parameters of the wheeled mobile robot. Therefore, this optimization problem is to find solutions in [0–272] search space. Fig. 4 shows genes in the creation of various wheeled mobile robots.

Sato and Ishii: Simultaneous Optimization of Robot Structures and Control Systems Using Evolutionary Algorithm S187

Fig. 4 Genes creating various wheeled mobile robots.

2.3 Evaluation function

Outdoor environments have various obstacles and road conditions. In this research, we select three benchmark environments for evaluation: a bump and two sets of stairs. The bump height is 0.2 m. The two sets of stairs each have three steps with 0.3 m tread and 0.15 m rise. The tread face and rise face are perpendicular for one set of stairs and form an acute angle for the other set of stairs as shown in Fig. 5.

Fig. 5 Benchmark environments having three kinds of obstacles.

The genes are evaluated to achieve effective out-door travel. In this paper, the evaluation items are travel ability, travel time, energy consumption, control accu-racy, and attitude of the robot. The evaluation items are expressed below.

(i) travel ability: D d− , (1)

(ii) travel time: t, (2)

(iii) energy consumption: 6

0 1

1 | ( ) |,N

in i

nN

τ= =

(3)

(iv) control accuracy: 6

0 1

1 | ( ) |,N

r in i

v v nN = =

− (4)

(v) attitude of robot: 0

1 | ( ) |.N

nn

Nθ

=

(5)

Here, d is the travel distance and D is the maximum travel distance (15 m), t is the simulation time, i is the driving torque of the i-th wheel after n steps, N is the maximum number of simulation steps, vr is the target velocity and vi (n) is the travel velocity of the i-th wheel after n steps, (n) is the pitch angle of the robot after n steps.

The evaluation functions are as follows. (i) travel ability:

1

1

1( ) ,100 1

f x xN

=× +

(6)

(ii) other evaluation items:

1 –( ) , ( 2 5).1

j

j

f x jxN

= =+

(7)

Here, j is the index of the evaluation items, Nj is the normalized parameters for each evaluation item; N1 = 15, N2 = 300, N3 = 5, N4 = 0.2, and N5 = 0.5. The travel ability conflicts with other evaluation items. In this re-search, the travel ability is emphasized because we suppose that the mobile robot must be able to travel in the outdoor environments.

The fitness of one gene is expressed as Eqs. (8) and (9) on the basis of Eqs. (1)–(7). Eq. (8) is used for the first 80 generations and Eq. (9) from the 81st generation to the final generation.

(i) fitness (first 80 generations):

1,fitness f= (8)

(ii) fitness (from the 81st generation):

1 2 3 4 5( ).fitness f f f f f= + + + (9)

3 Simulation

An initial generation is created randomly and one generation has 200 genes. In the genetic algorithm op-eration, two genes are selected by elite selection, and the others are selected by roulette selection and created by two-point crossover. The probability of crossover is 80% and the probability of mutation is 0.1%.

Initially, only the travel ability fitness is considered because the mobile robot must have sufficient ability to

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travel outdoors. After the mobile robot has sufficient ability for outdoor travel, the other evaluation items are optimized for effective travel.

Figs. 6 and 7 show the dynamics simulation results. The horizontal axis shows the generation of the dy-namics simulation and the vertical axis shows the fitness. In this work, the mobile robot has sufficient travel ability in the benchmark environments around the 80th gen-eration. After the 80th generation, all evaluation items are evaluated in a simultaneous optimization. At the 80th generation, the top 20 genes in the 79th generation are selected, and the other 180 genes are created randomly.

In Fig. 6, the fitness of the best genes improves incrementally after the 80th generation. The fitness is shown in detail in Fig. 7. The travel time is almost con-stant after the 80th generation. The energy consumption improved after the 200th generation. The control accu-racy and attitude of the robot were constant from the 80th generation to the 300th generation. The graphs show that the mobile robot is optimized for effective travel in an outdoor environment.

Fig. 6 Transition of the fitness. The bold line shows the fitness of the best gene in each generation and the dashed line shows the average fitness of each generation.

Fig. 7 Transition of the evaluation items. The bold line shows the travel ability, the thin line shows the travel time, the dashed line shows energy consumption, the dotted line shows control accu-racy, and the gray line shows the attitude of the robot.

In Fig. 8, top figure is an overview of the optimized wheeled mobile robot and bottom figure is a previously designed mobile robot, respectively. Comparing the optimized linkage mechanism with the previous one, the height of the robot and rear link length are almost the same. On the other hand, the side link is longer, the front link has a long linkage structure, the wheel diameters are greater by a factor of 1.6, and the mass of the weight is around 5 kg greater. In addition, the optimized parame-ters show that the front link mechanism of the mobile robot requires a spring mechanism with a spring con-stant of 16 Nm·rad 1, whereas the previously designed mobile robot does not have such a spring mechanism for the front link.

Fig. 8 Overview of the optimized wheeled mobile robot and a previously designed wheeled mobile robot.

Table 1 shows the optimized control system pa-rameters. It seems reasonable to suppose that the pro-portional gain and integral gain are more important for outdoor travel than the derivative gain.

Table 1 Optimized control parameters

Wheel Proportional gain Integral gain Derivative gainFront wheel 474.51 101.96 0.0 Rear wheel 584.31 899.67 11.76

Side front wheel 952.94 403.92 0.0 Side rear wheel 27.45 364.71 0.0

Sato and Ishii: Simultaneous Optimization of Robot Structures and Control Systems Using Evolutionary Algorithm S189

Fig. 9 shows the dynamics simulation results. It is seen that the optimized mobile robot could climb over/down the three surfaces. In particular, the mobile robot maintained stable attitude when climbing down. Therefore, the mobile robot could handle continuously uneven environments.

Fig. 9 Dynamics simulation results for the optimized linkage mechanism and control system.

4 Conclusion

In this paper, we propose a method of simultane-ously determining the structure and control system of a wheeled mobile robot using an evolutionary algorithm and dynamics simulations. The aim of the optimization method is for the wheeled mobile robot to travel in outdoor environments effectively. To achieve effective outdoor travel, five evaluation items are considered:

travel ability, travel time, energy consumption, control accuracy, and attitude of the robot.

The experiment results show that the optimized mobile robot could effectively overcome three bench-mark environments. In addition, the results suggest that the front link requires a spring mechanism for effective outdoor travel. It is likely that the spring mechanism assists in maintaining the attitude of the robot. Conse-quently, our proposed method achieved simultaneous optimization and was found to be effective.

Acknowledgements

This work was partly supported by a grant of Re-gional Innovation Cluster Program implemented by Ministry of Education, Cluster, Sports, Science and Technology (MEXT).

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