a switching controller system for a wheeled mobile robot

Corresponding author: Masanori Sato E-mail: m-sato@brain.kyutech.ac.jp

Journal of Bionic Engineering 4 (2007) 281−289

A Switching Controller System for a Wheeled Mobile Robot

Masanori Sato, Atushi Kanda, Kazuo Ishii Department of Brain Science and Engineering, Kyushu Institute of Technology, Kitakyushu 808– 0196, Japan

Abstract A wheeled mobile mechanism with a passive and/or active linkage mechanism for rough terrain environment is developed

and evaluated. The wheeled mobile mechanism which has high mobility in rough terrain needs sophisticated system to adapt various environments.

We focus on the development of a switching controller system for wheeled mobile robots in rough terrain. This system consists of two sub-systems: an environment recognition system using link angles and an adaptive control system. In the en-vironment recognition system, we introduce a Self-Organizing Map (SOM) for clustering link angles. In the adaptive control-lers, we introduce neural networks to calculate the inverse model of the wheeled mobile robot.

The environment recognition system can recognize the environment in which the robot travels, and the adjustable con-trollers are tuned by experimental results for each environment. The dual sub-system switching controller system is experi-mentally evaluated. The system recognizes its environment and adapts by switching the adjustable controllers. This system demonstrates superior performance to a well-tuned single PID controller. Keywords: mobile robot, rough terrain, neural network, Self-Organizing Map

Copyright © 2007, Jilin University. Published by Elsevier Limited and Science Press. All rights reserved.

1 Introduction

Recently, various mobile mechanisms have been developed combining wheels and passive and/or active linkage mechanisms. This work concerns one of the most important issues for mobile robots: effective mo-bility. Compared to other mobile systems (e.g. legged robots), wheeled systems have advantages of high en-ergy efficiency, simple mechanics and well investigated control systems.

On the other hand, the height of a bump such ve-hicles are able to climb over without inertial force is generally 1/3 or less of the wheel diameter. Wheeled mobile robots have difficulties traveling on rough terrain. Until now, various wheeled mobile robots with high mobility have been proposed. Famous mechanisms for high mobility in rough terrain include the Rocker-Bogie mechanism developed by NASA/JPL and installed on Sojourner[1,2]. Kuroda, et al. developed the PEGASUS mechanism and installed on Micro 5[3,4]. EPFL devel-

oped passive linkage mechanisms and installed on Shrimp[5] and CRAB[6]. Chugo et al. developed a pro-totype vehicle with a Rocker-Bogie mechanism and omni-wheels[7]. The common features of these robots are small diameter wheels, passive linkage mechanisms and high mobility on rough terrain without reducing the mobility on flat surface.

In previous research, we developed a wheeled mo-bile robot “Zaurus”, with six wheels and a linkage mechanism, and its maneuverability was experimentally verified. The ability to climb over a 0.20 m high bump, which is twice of the wheel diameter 0.10 m, was achieved and the newest Zaurus can climb over the 0.15 m high stairs[8]. Following this, control systems for the Zaurus were developed and evaluated. While many controller design methods have been proposed, we fo-cused on a nonlinear control system using a neural network[9,10]. We have already applied neural networks to controllers for underwater vehicles with nonlinear dynamics, and these have shown good performance in

Journal of Bionic Engineering (2007) Vol.4 No.4 282 spite of disturbances[11,12].

Here, control systems using neural networks were designed so that the neural networks express the inverse model/dynamics of the Zaurus. The control systems were evaluated in simulations[13,14], and experiments using Zaurus[15]. Our proposed control systems, based on neu-ral networks, show almost the same performance as a well-tuned PID controller. The neural network learns from the numerical simulation results of climbing over bumps using a proportional controller (initial controller).

To increase adaptiveness, that can recognize dif-ferent environments in which the robot travels and select the optimal controller for each environment is needed because a single control system is limited in terms of number of applicable environments.

In this paper, a switching controller system for a wheeled mobile robot in a rough terrain environment with an environment recognition system using a Self-Organizing Map (SOM)[16] with adjustable control-lers using neural networks is developed and evaluated.

2 Wheeled mobile robot

A wheeled mobile robot for rough terrain move-ment, Zaurus, has been developed using six small wheels and linkage structures. Fig. 1 shows an overview and the linkage mechanisms of Zaurus. Wheel diameter is 0.10 m and each wheel can be driven independently. The front wheel is connected to the body through the front fork, the rear wheel is fixed to the body and two pairs of two side wheels are connected to the body through side links. Zaurus can adapt its shape to the terrain conditions as the front fork and the side links are connected to the body with passive joints.

Fig. 2 shows Zaurus’ system configuration and Table 1 lists its specifications. Zaurus has two control modes, autonomous mode using the proposed control system, remote control mode using a host PC or an IR remote controller. In the mounted PC, visual program-ming software, ICONNECT, is introduced to develop the control system and graphical user interface. Two micro computers integrate the sensors such as the optical encoder for traveling speed, potentiometers for front fork and side link angles, the attitude sensor for pitch and current sensors to measure the drive currents of each motor. The motor driver controls the angular velocity of each motor. The battery is Ni-MH 14.4 V, 3300 mAh, and the operating duration is about 1.5 h.

(a) Overview of Zaurus

(b) 3D model of Zaurus (left), frame image of Zaurus (right)

Fig. 1 Wheeled mobile robot, Zaurus.

Fig. 2 System configuration of Zaurus.

Masanori Sato et al.: A Switching Controller System for a Wheeled Mobile Robot 283

Table 1 Specifications for Zaurus

Size (L × W × H) 0.66 m × 0.53 m × 0.31 m Weight 13 kg

Computer system Laptop PC (for robot) PIC18F8720, PIC18F252

Communication Wireless LAN IrDA remote control

Sensor

Optical sensor × 1 Potentiometer × 3 Attitude sensor × 1 Current sensor × 6

Battery Ni-MH 14.4 V, 3300 mAh Actuator DC maxon motor 12 V, 10 W × 6Wheel diameter 0.10 m

3 A switching controller system

3.1 Concept of a switching controller system In experiments of our previous research[8,13−15],

Zaurus climbed over 0.20 m high bumps and 0.15 m high stairs. To gain high maneuverability, Zaurus needs an adaptive controller for each environment. However, it is difficult to design a controller able to adapt to every environments.

When a mobile robot travels around various envi-ronments, a controller system that recognizes the envi-ronment and selects the suitable controller for the envi-ronment to improve the maneuverability and usefulness of the robot. Here, we propose a switching controller system that consists of two sub-systems: an environment recognition system that switches controllers depending on the environment, and a set of adjustable controllers for each environment.

Fig. 3 shows the concept of the switching controller system for a mobile robot. The robot traverses various environments, and passive linkage data is used as input to the environment recognition system. The environment recognition system selects the adjustable controllers for each environment. The adaptive controller calculates the manipulate values (e.g. angular velocity) for the robot in each situation.

Zaurus can change its link mechanism passively depending on the environment situation. Link angle data can express the unevenness of ground. In other words, the whole passive linkage mechanism can be used as an environment recognition sensor. The more environment conditions are introduced, the more link data describing these environment conditions and classification analysis

can be performed. We define environmental recognition as “Classi-

fying environments by bump height using link angle data, obtaining basic environmental data, and identifying the environment”. Typical multiple classification analy-sis, PCA, k-means method and SOM are compared against this definition and finally SOM is selected as the environment recognition system.

Fig. 3 Concept of the control system for a mobile robot

on rough terrain.

The system consists of two subsystems. The first is the en-vironment recognition system using the SOM. This system rec-ognizes its environment using linkage data from a wheeled mobile robot and switches adaptive controllers for each environment. The second is the adaptive controller system using a neural network adjusts for each environment. 3.2 Environment recognition system 3.2.1 Basic environment data

The proposed control system recognizes various environments using passive link joint angles. The input data to the system includes the joint angle data with several time steps to express the dynamics of the robot.

Experiments are carried out to obtain the basic dataset for several time series climbing over bumps, including front fork angle (θf), side link angle (θs) and attitude pitch angle (θp). The basic environments contain one-step bumps whose heights are 0.00, 0.06, 0.12 and 0.18 m respectively. A PID controller is employed for data sampling[13].

The process of obtaining environmental data for multiple classification analysis is described as follows. Basic state variables consist of the three angles men-tioned above and their angular velocities. The sampling step, ∆t is 0.25 s for the state variables during 1.0 s, that

Journal of Bionic Engineering (2007) Vol.4 No.4 284 is, the 4 sets of state variables that compose a ( )t∗θ .

( ) ( ) ( ) ( )( ) , , 2 , 3

( , , ).

t t t t t t t t

f s p

θ θ θ θ∗ ∗ ∗ ∗ ∗= − Δ − Δ − Δ⎡ ⎤⎣ ⎦∗ =

θ

(1)

Finally, the environmental data x(t) is expressed as follows:

[ ])()()()()()()( ttttttt psfpsf θθθθθθx = (2)

3.2.2 Environment recognition methods (1) Principle Component Analysis Principal Component Analysis (PCA) is a feature

extraction algorithm for reducing multidimensional data sets to lower dimensions. The advantage of PCA is its data contraction and the feature extraction, the principle components contain the important aspects of data.

Fig. 4 shows the results of analysis using PCA, for bumps heights of 0.06, 0.12 and 0.18 m respectively. The horizontal axis shows the first principle component and the vertical axis shows the second. In Fig. 4, the data for climbing over/down do not produce a predictive model, therefore PCA is proved difficult for use in the environment recognition system.

(2) k-means method With regard to multiple classification analysis,

the k-means method is one of the most popular non- hierarchical cluster analysis methods. The number of clusters, k, is assumed at first, and each input is classified into a cluster on similarity. Then, a new center of the cluster is calculated and all data are re-classified into new clusters. Finally, the procedure described above is repeated until the error between all points and the centers of clustered data becomes sufficiently small.

Fig. 5 shows the results of analysis using the k-means method. In this analysis, we set the cluster number, k, as 9 and 27. The number of clusters is set to nine as it is assumed that Zaurus has nine phases when climbing a bump: it travels on a flat surface, the front wheel climbs over the bump, the side front wheels climb over the bump, the side rear wheels climb over the bump and the rear wheel climbs over the bump. Twenty seven clusters are assumed as the above nine situations can occur for each bump height. The number of clusters, k, is 9 on the top and 27 on the bottom. The horizontal axis shows the sampling step (0.25 s) and the vertical axis shows the index of classification.

As shown in Fig. 5, the data sets are clustered for the attitude where Zaurus is climbing over/down the bump. However, the height of the bumps is not clustered because the results for 9 and 27 clusters are almost the same.

Fig. 4 Analysis using PCA.

The solid line shows the data set for climbing up the bump and dotted line shows the data set for climb down.

Masanori Sato et al.: A Switching Controller System for a Wheeled Mobile Robot 285

(a) The number of clusters is 9

(b) The number of clusters is 27

Fig. 5 Analysis using the k-means method. The solid line shows the data set for 0.06 m, the broken line

shows the data set for 0.12 m and the dotted line shows the data set for 0.18 m climbing over/down.

(3) Self-Organizing Map The SOM proposed by T. Kohonen[16] is introduced

as a clustering method of the principle data. A SOM is trained using unsupervised learning to produce a low resolution representation of training data. Also, SOM can recognize unknown environments using its interpo-lation capability.

The SOM algorithm is described in Eqs. (3) to (7). 2

minarg ik

kik xw −=∗ (3)

( ) ( )τσσσσ t−−+= expminmaxmin (4) ( )( )22,exp σφ ∗−= i

ki kkd (5)

∑=i

ki

ki

ki φφψ (6)

∑=i

iki

k xw ψ (7)

where wk is the reference vector of the k-th unit in the competitive layer and xi is i-th input. k* is the indication number of the “winner” unit. The neighborhood function, φi

k is expressed employing a neighborhood radius σ in Eqs. (4) and (5), is the learning coefficient ψi

k is nor-malized using Eq. (6) and the reference vector of the units in the competitive layer is updated using Eq. (7).

Fig. 6a shows the generated feature map, the brightness of each unit shows the Euclidean distance between the reference and neighbor units. A white unit is distant and black shows that similar units are close to neighborhood units. The map is classified based on the Zaurus’ attitude. The movement of climbing up and down is shown on opposite sides of the diagram (ex. circles 5 and 9). Traveling on flat floor is shown in the center of the map. The sequence of climbing over/down a bump is numbered from 1 to 9. We can see from this that the SOM feature map also includes information of the dynamics of the robot.

We also evaluate the interpolation function using experiment results using test data sets. In this research, the SOM learned from 0.06 and 0.12 m data sets, while

(a) Circled numbers show the sequence for climbing over/down a bump

Fig. 6 Database of the environment recognition system. Map size is 30 × 30, learning time is tmax = 1000, neighbor

radius σmax = 45, σmin = 1 and time constant τ = 50. The dotted line shows the 0.06 m data, solid line shows the 0.10 m data and broken line shows the 0.12 m data. The 0.10 m data is unlearned data and is placed between 0.06 and 0.12 m learned data.

Journal of Bionic Engineering (2007) Vol.4 No.4 286

(b) Comparison of the trajectories using a sequence

Fig. 6 Continued.

the 0.10 m data set was left aside. Fig. 6b shows a com-parison of robot trajectories using time series data for bump heights of 0.10 m, 0.06 m and 0.12 m respectively. The trajectory of 0.10 m height bump is similar to those of 0.06 m and 0.12 m. The unlearned data set is placed between these lines. We can see that the map can esti-mate the Zaurus’ attitude and the height of bump. The areas where the trajectories overlap are where the envi-ronmental differences are not clear. 3.3 Adjustable controllers 3.3.1 Inverse model

Neural network controllers are used to set adjust-able controllers for each environment. Neural networks are used as they can express nonlinear systems and in this case learn unknown environments. The controllers are adjusted by the neural network trained in various previous environments.

System identification plays an important role in control theory, obtaining learning data is the central. In previous work[11,12], learning data was obtained from experimental results using the robot, and the neural network expresses the inverse model of the robot.

In this research, the learning data is obtained from simulations using mechanical analysis software, DADS.

Various kinds of learning data are obtained from simu-lations carried out on various situations without risk of damaging the robot[13–15].

The design flow of the neural network for the con-trol system is described as follows.

(1) Simulations using the initial controller are car-ried out on flat floor, one-step bumps and slopes. The heights of the bumps are 0.05, 0.10, 0.15 and 0.20 m, and slope obliquities are 10˚, 20˚ and 30˚.

(2) Learning data is obtained from the simulations, and the neural network is trained.

(3) The trained neural network becomes the basic controller.

(4) Finally, the basic neural network controller trained in the simulations is applied to Zaurus in the real world. The neural network controller is tuned with each experimental result in real environments. 3.3.2 Initial controller and PID controller

The initial controller consists of a proportional controller, Eq. (8), and PID controller, Eq. (9).

( )d

P ru K v v

u u t

⎧ = −⎪⎨ =⎪⎩ ∫

(8)

1 d

d

P DI

r

u K e e t T eT

e v v

u u t

⎧ ⎛ ⎞= + +⎪ ⎜ ⎟

⎝ ⎠⎪⎪ = −⎨⎪ =⎪⎪⎩

∫

∫ (9)

where, vr is the reference velocity, v is the traveling velocity and u is target angular velocity of each wheel to a motor driver. The parameters of the controllers are KP = 30, TI = 50 and TD = 0.01 obtained by the Ziegler- Nichols Ultimate Method. 3.3.3 Adjusted controller

Fig. 7 shows the structure of the neural network. The neural network controller input consists of PID controller inputs and state values of Zaurus:

,p p f s

r

e e e v

e v v

θ θ θ θ⎧⎡ ⎤⎪⎣ ⎦⎨= −⎪⎩

∫ (10)

where, vr is the reference velocity, v is the travelling velocity, θp is the pitch, θf is the front fork angle, θs is the side link angle, e is the difference between vr and v. The

Masanori Sato et al.: A Switching Controller System for a Wheeled Mobile Robot 287

Fig. 7 Structure of the neural network controller.

The inputs of the neural network consist of the inputs for the PID controller and state values of Zaurus. The output is u which is the target angular velocity of the motor driver. output of the neural network controller u is the target angular velocity of each wheel to the motor driver.

Table 2 shows the average of five trial experiment results. The basic neural network controller shows al-most the same results as the PID controller in the simu-lation. The adjusted neural network controller shows slightly better performance than the PID controller. Es-pecially, for climbing bumps, where the mean square of the difference between vr and v is almost 58% lower. Fig. 8 shows a comparison of the experiment results for climbing over a 0.18 m bump using a PID controller with an adjusted neural network controller. Fig. 8a shows the traveling velocity of Zaurus, and Fig. 8b shows the outputs of each controller. The circled numbers form the same sequence as climbing over the bump in Fig. 6.

In each situation, the adjusted neural network con-troller decreases the traveling velocity and output for the motor drivers in comparison with the PID controller.

Table 2 Comparison of the mean square of the difference between reference velocity and traveling velocity

for PID and neural network controllers.

1/N Σ (vr – v)2

Simulation Experiment

PID Ctrl. NN Ctrl. (basic)

PID Ctrl. NN Ctrl.

(adjusted)

Flat 0.00010 0.00010 0.00003 0.00003

Climb over 0.00063 0.00067 0.00503 0.00208

Climb bown 0.00030 0.00034 0.00108 0.00127

4 Experiment results for a switching controller system

To verify the effectiveness of the environment recognition system and neural network controllers, ex-periments were executed in an environment that consists of a flat surface and 0.18 m bump.

Fig. 9 and Table 3 show the experiment results us-ing the proposed control system. Fig. 9a shows the ref-erence velocity, traveling velocity and adjusted neural network controller’s outputs from Zaurus. Fig. 9b shows the output of the environment recognition system. Table 3 shows a comparison of the mean square of the difference between the reference and traveling velocities, and variance of the derivative controller output.

(a) Travelling velocity of Zaurus

(b) Output of controllers

Fig. 8 Comparison of the experiment results of PID

controller with neural network controller.

Broken line shows the reference velocity, thin solid line shows the PID controller results and thick solid line shows the adjusted neural network controller results. Circled numbers show the sequence of climbing over the bump.

Journal of Bionic Engineering (2007) Vol.4 No.4 288

(a) Traveling velocity of Zaurus and output of the adjusted neural

network controller

(b) Output of environment recognition system

Fig. 9 Experiment results for traversing rough terrain using neural networks and SOM.

In Fig. 9a, the broken line shows the reference velocity, a thick solid line shows the travelling velocity and thin solid line shows the output of the adjusted neural network controllers. In Fig. 9b, the solid line shows the output of SOM.

Table 3 Comparison of single PID controller with proposed

control system

( )21 rN v v−∑ ( )21 N u∑

PID control system 0.00267 2.512

NN controls. with SOM control system 0.00237 2.133

As shown in Fig. 9, Zaurus started to move from 2 s

and kept the reference velocity until 12 s while on the flat surface. After 12 s, the environment recognition system switched to the controller for climbing, and Zaurus climbed the 0.18 m bump. Finally, the environ-ment recognition system switched the controller from

climbing up the bump to climbing down the bump. On top of the bump, the environment recognition

system did not switch the controller for a flat surface, though we assumed the environment recognition system would detect the flat surface and switch accordingly. One possible reason is that the length of the top of the bump is too short to detect as a flat surface. At 26 s in Fig. 9a, the traveling velocity of Zaurus was almost 0.25 m·s−1, when Zaurus reached the edge and climbed down the bump.

As shown in Table 3, the proposed control system reduced the mean square of error and variance of de-rivative output of the controller, that is, the proposed control system showed better performance than a well-tuned single PID controller.

5 Conclusions

In this research, we proposed a switching controller system for a wheeled mobile robot in a rough terrain environment. The system consists of two components, an environment recognition system using a Self-Orga-nizing Map and an adjustable controller using neural networks.

First, we discussed the environment recognition methods, Principle Component Analysis (PCA), k-means method and Self-Organizing Map (SOM). The SOM method was selected as the environment recogni-tion system.

Second, to adjust the controllers, we introduced neural networks which express the inverse model of wheeled mobile robot, Zaurus. In experimental scenarios the neural network controller shows better performance than a well-tuned PID controller, though the learning data for the neural network is obtained only from simple initial controllers consisting of proportional controllers.

In the experiments, the proposed controller system recognized its environment and switched controllers to match, producing better performance than a well-tuned single PID controller.

Acknowledgement

This work was partly supported by a grant of Knowledge Cluster Initiative implemented by Ministry

Masanori Sato et al.: A Switching Controller System for a Wheeled Mobile Robot 289of Education, Culture, Sports, Science and Technology (MEXT). References [1] Volpe R, Balaram J, Ohm T, Ivlev R. The Rocky 7 Mars

rover prototype. Proceedings of the 1996 IEEE/RSJ Inter-national Conference on Intelligent Robots and Systems, Osaka, Japan, 1996, 3, 1558−1564.

[2] Hayati S, Volpe R, Backes P, Balaram J, Welch R, Ivlev R, Tharp G, Peters S, Ohm T, Petras R, Laubach S. The Rocky 7 rover: A Mars sciencecraft prototype. Proceedings of the 1997 IEEE International Conference on Robotics and Automation, New Mexico, USA, 1997, 3, 2458−2464.

[3] Kuroda Y, Kondo K, Nakamura K, Kunii Y, Kubota T. Low power mobility system for micro planetary rover “Micro5”. Proceedings of the 5th International Symposium on Artifi-cial Intelligence, Robotics and Automation in Space. Noordwijk, The Netherlands, 1999, 77−82.

[4] Kuroda Y, Teshima T, Sato Y, Kubota T. Mobility perform-ance evaluation of planetary rover with similarity model experiment. Proceedings of IEEE International Conference on Robotics and Automation, LA, USA, 2004, 2, 2098−2103.

[5] Estier T, Crausaz Y, Merminod B, Lauria M, Piguet R, Siegwart R. An innovative space rover with extended climbing abilities. Proceedings of the Space and Robotics 2000, New Mexico, USA, 2000, 333−339.

[6] Thueer T, Lamon P, Krebs A, Siegwart R. CRAB-Ex-ploration rover with advanced obstacle negotiation capa-bilities. Proceedings of the 9th ESA Workshop on Advanced Space Technologies for Robotics and Automation, Nordwijk, The Netherlands, 2006.

[7] Chugo D, Kawabata K, Kaetsu H, Asama H, Mishima T. Development of a control system for an omni directional vehicle with step-climbing ability. Advanced Robotics, 2005,

19, 51−71. [8] Isoda in IIZUKA Campus, Kyushu Institute of Technology.

“I.Lab.Movie”, [2007–11–30], http://www.brain.kyutech.ac.jp/~ishii/Movie/movie.html

[9] Levin A U, Narendra K S. Control of nonlinear dynamical systems using neural networks: Controllability and stabili-zation. IEEE Transactions on Neural Networks, 1993, 4, 192−206.

[10] Levin A U, Narendra K S. Control of nonlinear dynamical systems using neural networks-part II: Observability, iden-tification, and Control. IEEE Transactions on Neural Net-works, 1996, 7, 30−42.

[11] Ishii K, Fujii T, Ura T. On-line adaptation method in a neural network based control system for AUVs. IEEE Journal of Oceanic Engineering, 1995, 20, 221−228.

[12] Ishii K, Fujii T, Ura T. Neural network system for on-line controller adaptation and its application to underwater robot. Proceedings of the 1998 IEEE International Conference on Robotics and Automation, Leuven, Belgium, 1998, 756− 761.

[13] Sato M, Ishii K. A neural network based control system for a mobile robot employing link mechanism. Proceeding of the 2005 IEEE/ADME International Conference on Advanced Intelligent Mechatronics, Monterey, USA, 2005, 426−431.

[14] Sato M, Ishii K. A neural network based controller system for a wheel type mobile robot. In: Brain Inspired Informa-tion Technology II, Elsevier, Amsterdam, 2006, 1291, 261−264.

[15] Sato M, Kanda A, Ishii K. Performance evaluation of a neural network controller for a wheel type mobile robot. In: Brain Inspired Information Technology III, Elsevier, Am-sterdam, 2007, 1301, 160−163.

[16] Kohonen T. Self-organized formation of topologically cor-rect feature maps. Biological Cybernetics, 1982, 43, 59−69.