SMC Rover : Planetary Rover with transformable wheels
SMC Rover : Planetary Rover with transformable wheels ATSUSHI KAWAKAMI, AKINORI TORII, KAZUHIRO MOTOMURA, and SHIGEO HIROSE Department of Mechano-Aerospace Engineering , Tokyo Institute of Technology, 2-12-1 Oh-okayama, Meguro-ku, Tokyo, 152-8552, Japan Abstract: We are proposing a new planetary rover system called “SMC rover”. This system consists of one main body and some wheel units, which are detachable and able to work as child rovers, called “Uni-Rover”. Trial models of “Uni-Rover” and “SMC rover” have been designed. This paper explains the mechanisms of this rover, and also the results of basic experiments on locomotion, manipulation and transformation. Keywords: Super-Mechano-Colony, Planetary Rover, Arm Equipped Single Wheel Rover
1. Introduction Planetary rover systems are expected to undergo various missions on other planets employing various different abilities. In the construction of large-scale facilities and detailed investigation at wide areas, rovers have an advantage over conventional probes and landing. For such missions, several abilities are required, such as high mobility on rough terrain, position identifying ability and special devices for each mission. However, severe financial restrictions must be taken into account when transporting probes and rovers to a target planet. It is undesirable to make rovers large and heavy when trying to accomplish these abilities. Therefore, we have proposed a new concept of planetary rover system called SMC rover [1][2]. This paper explains the mechanisms of the trial model and shows results of basic experiments of the trial model.
Child rovers
Main body
Fig. 1. Overall view of SMC-Rover
2. The design of SMC Rover 2.1 The concept of SMC Rover SMC-Rover consists of one main body and multiple child units as shown in Fig.1. The main body has solar battery cell, communication devices, sample analyzer, battery chargers and tool changers for the child rovers. Each child rover has a wheel for locomotion and an arm for manipulation. This system has the following characteristics: 1. The main body cannot move by itself, but the child rovers hold the main body of SMC rover by their manipulators and act as active wheels of the main body. If it is necessary, each child rover can separate from the main body and move around to undergo separate missions. 2. Each child rover is composed of a single wheel and a single arm. When the wheel unit is in “locomotion mode” as shown in Fig.2a, with extended arm, it caster
arm
wheel
manipulator (arm) base (wheel)
connecter (a) locomotion mode
Fig. 2. Child rover
(b) manipulation mode
gripper
(a) transform into manipulation mode
(b) transform into locomotion mode
Fig. 3. Transformation of child rover
can move around on the ground with high mobility. The arm of the child rover has a caster around the wrist. By changing the orientation (yaw angle) of this caster with the wrist motion, it is possible to steer the child rover. 3. The child rover can be converted into the “manipulation mode” by adopting the posture as shown in Fig.2b, and acts as a manipulator with a gripper. 4. The child rover can change between the locomotion mode and the manipulation mode by its arm motion, shown in Fig.3. 5. Still in the manipulation mode, the child rover can change its position by “pivot turn” motion of Fig.4a, pushing the ground with its arm. 6. By grasping another child rover, child rovers can take the shape of a multiple-wheel rover to go over rough terrain, as shown in Fig.4b. 7. Using multiple child rovers, SMC rover achieves fault tolerance and high reliability. Adopting heterogeneous, hierarchical system, it also achieves high controllability.
Move Direction
Wheel Lotation
(a) pivot turn
(b) combined locomotion mode
Fig. 4. Various locomotion modes of the child rover
8. Using the wheels of child rovers as wheels of the main body and the arms of child rovers as connecters between them and the main body, the SMC rover can cut down total weight and size of the system. 9. Each child rover has only one wheel because its diameter can be larger than in the case of a rover with multiple wheels. With larger wheels, this system achieves high mobility on rough terrain. Moreover, in this propulsive motion, the arm sustains the reaction moment, generated by pressing the wrist caster against the ground while the wheel rotates. 10.Child rovers cannot equip a large solar battery cell, but they can be supplied electric energy from the solar battery cell on the main body, while they are connected to the main body.
2.2 Previous research There has been increasing research interest in multiple autonomous robot system with cooperative behavior, focusing on fault tolerance, reliability, and scalability [3]. Such research interest is not restricted to decentralized homogeneous system [4][5][6], but also includes heterogeneous parent-children type systems to achieve the advantages of well-regulated coordination control [7][8]. However, the parent-children type rover system with detachable wheels described in this paper is very different. The child units are not simply carried by the mother unit, but they act as propulsion mechanisms of the main unit, characteristics mentioned in item 8 of Sect. 2.1. This characteristic is very new and there are no previous studies about it. On the other hand, there have been several works about single-wheel type locomotive robots [9][10][11]. A single-wheel shaped robot with no arm can generate limited propulsion torque, so the locomotion ability on rough terrain of this kind of robot is very limited. But the child unit of the system discussed in this paper is shaped with a single wheel and single arm, and it can generate
RC Servo motor
θ3
θ1 θ2
θ4 DC motor (wheel) Battery
Fig. 5. Mechanisms of Uni-Rover
enough propulsion torque even on rough terrain, as mentioned in items 2 and 9 of Sect. 2.1. This concept is also very new.
3. Development of the trial model of Uni-Rover 3.1 Composition of new trial model of Uni-Rover We have designed and developed a trial model of “Uni-Rover”, a child unit of SMC-Rover. The trial model consists of a single wheel (diameter: 190mm, width: 140mm) and a single manipulator with three joints (length of upper arm and lower arm: 170mm) as shown in Fig.5. At the end of the manipulator there is a caster and a gripper with four fingers. One DC motor for the rotation of the wheel is located inside the wheel. The controller circuits, transmitter and batteries for motors are also located inside the wheel. To actuate the manipulator, one RC-servo motor is located in each of the four joints of the manipulator. The total weight of the rover is 3.2kg. The trial model is driven with a wireless manual controller.
3.2 Improvement of new trial model of Uni-Rover We have set the mass balance of the mechanism inside the wheel with a wide eccentricity between the center of mass and the axis of rotation of the wheel. Because of this mass property, Uni-Rover is very stable in manipulation mode
θ2
Unstable side (Easy to fall down)
Stable side (Good at manipulation)
Center of mass in wheel
Fig. 6. Stability of Uni-Rover
when the arm takes the position of the stable side, and it is also easy to bring it down during transformation, when the arm takes the position of the unstable side as shown in Fig.6.
4.Development of the trial model of SMC rover We have also designed and developed a trial model of SMC rover to be used with the trial models of Uni-Rover, as shown in Fig.7a. The trial model of SMC rover has a main body, four dummy wheel units and two connecters for Uni-Rover. The dummy wheels can rotate freely without motors, but they have been designed in a way that they can be motorized and replaced by real Uni-Rovers with the connecter in future works. The connecters for Uni-Rover consists of a handle for the gripper and two supporting plates to hold the manipulator of Uni-Rover as shown in Fig.7b. Solar battery cell (Dummy)
Connecters Supporting Plates
Child rovers (Dummy)
(a) Overall view of main body
Fig. 7. Mechanisms of main body
Handle
(b) Connecter
5.Experiments of Uni-Rover and SMC rover 5.1 Experiment of Uni-Rover in locomotion mode On a flat surface, we carried out propulsion and steering experiment with the rover in locomotion posture as shown in Fig.2a. The orientation of propulsion is controlled by changing the orientation of the caster with the joints of the manipulator as shown in Fig.8. Moreover, we carried out experiments of climbing over small obstacles. It was confirmed that Uni-Rover can climb over gaps of 5cm of height, but there were problems at the control of the orientation of Uni-Rover on rough terrain.
5.2 Experiment of Uni-Rover in manipulation mode With the rover in the manipulation mode, experiments of the manipulator were carried out, as shown in Fig.2b. With those experiments, it was possible to confirm that each joint is controllable by the wireless controller. It was verified that the manipulator has enough ability to actually hold and transport various objects in several shapes (a pen cap, a small bottle, a grip of a driver, and so on), as shown in Fig.9.
Turn direction
(a) posture of right turn
Fig. 8. Steering motion of Uni-Rover
Turn direction
(b) posture of left turn
box
tape
driver
stone
Fig. 9. Handling various objects
Furthermore, we carried out experiments of “pivot turn”, which is the locomotion method in manipulation mode, as shown in Fig.4a. It was confirmed that the Uni-Rover can change its position by this “pivot turn” motion while in the manipulation mode.
5.3 Experiment of transformation of Uni-Rover We also carried out experiments on the transformation sequence of Uni-Rover. Initially, we measured the N.E.S.M. (Normalized Energy Stability Margin) [12] of Uni-Rover by changing its shoulder angle, as shown in Fig.10. According to this graph, it was confirmed that the N.E.S.M of the stable side is higher than the N.E.S.M of the unstable side, so Uni-Rover achieves both high stability in manipulation and high transformability. Secondly, experiments of transformation from locomotion mode to manipulation mode were carried out, and it was confirmed that the Uni-Rover can stand up by
N.E.S.M.[mm]
30
Stable
20
Unstable 10 :result of experiment
0 -90
-45
0
45
Shoulder Angle θ2 [deg] Fig. 10. N.E.S.M. of Uni-Rover in manipulation mode
90
Fig. 11. Detaching wheel units
using its manipulator, as shown in Fig.3a. Experiments of its transformation from manipulation mode to locomotion mode were also performed as shown in Fig.3b, and we verified that the Uni-Rover can fall down into manipulation mode by using the kinetic effect of the manipulator motion in unstable position.
5.4 Experiment of SMC rover with Uni-Rovers We carried out experiments of SMC rover with Uni-Rovers as detachable wheel units, as shown in Fig.11. It was confirmed that the Uni-Rovers can transport the trial model of SMC rover and can detach from the connecters of SMC rover.
6.Conclusion and future work In this paper, the design and development of the trial models of Uni-Rover and SMC rover have been explained. The results of experiments in locomotion and manipulation mode and transformation experiments have also been mentioned. In the future, propulsion experiments over rough terrain and docking experiments will be carried out, and the control system of the unit will be improved. Besides, combined locomotion and cooperative work by multiple units will be achieved.
Acknowledgment This research is supported by the grant-in-aid for COE Research Project of Super-Mechano-Systems by The Ministry of Education, Culture, Sports, Science and Technology of Japan.
References 1.
S. Hirose, A. Kawakami, K. Kato and H. Kuwahara, “Super-Mechano-Colony and SMC Rover with Detachable Wheel Units”, Proc. COE workshop ’99, pp.67-72 (1999) 2. R. Damoto, A. Kawakami and S. Hirose, “Study of Super-Mechano Colony : concept and basic experimental set-up”, Advanced Robotics, 15 ,4, pp.391-408 (2001) 3. R.C.Arkin and G.A.Bekey, “Robot Colonies”, Kluwer, Dordrecht (1997) 4. M. Hashimoto, F. Oba and T. Eguchi, “Dynamic control approach for motion coordination of multiple wheeled mobile robots transporting a single object”, Proc. IEEE/RSJ IROS, pp.1944-1951(1993) 5. M. N. Ahmadabadi and N. Eiji, “A unified distributed cooperation strategy for multiple object handling robots”, Proc. IEEE ICRA, pp.3625-3630 (1998) 6. T. Fukuda, H. Mizoguchi, K. Sekiyama and F. Arai, “Group Behavior Control for MARS (Micro Autonomous Robotic System)”, Proc. IEEE ICRA, pp.1550-1555 (1999) 7. R. R. Murphy, M. Ausmus, M. Bugajska, T. Ellis, T. Johnson, N. Kelley J. Kiefer, and L. Pollock, “Marsupial-like mobile robot societies”, Proc. Agents'99, pp. 364-365 (1999) 8. D. F. Hougen, S. Benjaafar, J. C. Bonney, J. R. Budenske, M. Dvorak, M. Gini, H. French, D. G. Krantz, P. Y. Li, F. Malver, B. Nelson, N. Papanikolopous, P. E. Rybski, S. A. Stoeter, R. Voyles and K. B. Yesin, “A Miniature Robotic System for Reconnaissance and Surveillance”, Proc. IEEE ICRA, pp.501-507 (2000) 9. Koshiyama, H. Yoshinada and K. Yamafuji, “Development and Motion Control of the All-Direction Steering-Type Mobile Robot”, Proc. 24th Int. Symp. On Industrial Robots”, pp.445-453 (1993) 10. Chemel, E. Mutshler and H. Schempf, “Cyclops: Miniature Robotic Reconnaissance System”, Proc. IEEE ICRA, pp.2298-2302 (1999) 11. S. J. Tsai, E. D. Ferreira and C. J. J. Paredis, “Control of the Gyrover, A Single-Wheel Gyroscopically Stabilized Robot”, Proc. IEEE/RSJ IROS, pp.179-184 (1999) 12. Shigeo Hirose, Hideyuki Tsukagoshi, Kan Yoneda, “Normalized Energy Stability Margin and its Contour of Walking Vehicles on Rough Terrain”, Proc. IEEE ICRA, pp.181-186 (2001)
1. Introduction Planetary rover systems are expected to undergo various missions on other planets employing various different abilities. In the construction of large-scale facilities and detailed investigation at wide areas, rovers have an advantage over conventional probes and landing. For such missions, several abilities are required, such as high mobility on rough terrain, position identifying ability and special devices for each mission. However, severe financial restrictions must be taken into account when transporting probes and rovers to a target planet. It is undesirable to make rovers large and heavy when trying to accomplish these abilities. Therefore, we have proposed a new concept of planetary rover system called SMC rover [1][2]. This paper explains the mechanisms of the trial model and shows results of basic experiments of the trial model.
Child rovers
Main body
Fig. 1. Overall view of SMC-Rover
2. The design of SMC Rover 2.1 The concept of SMC Rover SMC-Rover consists of one main body and multiple child units as shown in Fig.1. The main body has solar battery cell, communication devices, sample analyzer, battery chargers and tool changers for the child rovers. Each child rover has a wheel for locomotion and an arm for manipulation. This system has the following characteristics: 1. The main body cannot move by itself, but the child rovers hold the main body of SMC rover by their manipulators and act as active wheels of the main body. If it is necessary, each child rover can separate from the main body and move around to undergo separate missions. 2. Each child rover is composed of a single wheel and a single arm. When the wheel unit is in “locomotion mode” as shown in Fig.2a, with extended arm, it caster
arm
wheel
manipulator (arm) base (wheel)
connecter (a) locomotion mode
Fig. 2. Child rover
(b) manipulation mode
gripper
(a) transform into manipulation mode
(b) transform into locomotion mode
Fig. 3. Transformation of child rover
can move around on the ground with high mobility. The arm of the child rover has a caster around the wrist. By changing the orientation (yaw angle) of this caster with the wrist motion, it is possible to steer the child rover. 3. The child rover can be converted into the “manipulation mode” by adopting the posture as shown in Fig.2b, and acts as a manipulator with a gripper. 4. The child rover can change between the locomotion mode and the manipulation mode by its arm motion, shown in Fig.3. 5. Still in the manipulation mode, the child rover can change its position by “pivot turn” motion of Fig.4a, pushing the ground with its arm. 6. By grasping another child rover, child rovers can take the shape of a multiple-wheel rover to go over rough terrain, as shown in Fig.4b. 7. Using multiple child rovers, SMC rover achieves fault tolerance and high reliability. Adopting heterogeneous, hierarchical system, it also achieves high controllability.
Move Direction
Wheel Lotation
(a) pivot turn
(b) combined locomotion mode
Fig. 4. Various locomotion modes of the child rover
8. Using the wheels of child rovers as wheels of the main body and the arms of child rovers as connecters between them and the main body, the SMC rover can cut down total weight and size of the system. 9. Each child rover has only one wheel because its diameter can be larger than in the case of a rover with multiple wheels. With larger wheels, this system achieves high mobility on rough terrain. Moreover, in this propulsive motion, the arm sustains the reaction moment, generated by pressing the wrist caster against the ground while the wheel rotates. 10.Child rovers cannot equip a large solar battery cell, but they can be supplied electric energy from the solar battery cell on the main body, while they are connected to the main body.
2.2 Previous research There has been increasing research interest in multiple autonomous robot system with cooperative behavior, focusing on fault tolerance, reliability, and scalability [3]. Such research interest is not restricted to decentralized homogeneous system [4][5][6], but also includes heterogeneous parent-children type systems to achieve the advantages of well-regulated coordination control [7][8]. However, the parent-children type rover system with detachable wheels described in this paper is very different. The child units are not simply carried by the mother unit, but they act as propulsion mechanisms of the main unit, characteristics mentioned in item 8 of Sect. 2.1. This characteristic is very new and there are no previous studies about it. On the other hand, there have been several works about single-wheel type locomotive robots [9][10][11]. A single-wheel shaped robot with no arm can generate limited propulsion torque, so the locomotion ability on rough terrain of this kind of robot is very limited. But the child unit of the system discussed in this paper is shaped with a single wheel and single arm, and it can generate
RC Servo motor
θ3
θ1 θ2
θ4 DC motor (wheel) Battery
Fig. 5. Mechanisms of Uni-Rover
enough propulsion torque even on rough terrain, as mentioned in items 2 and 9 of Sect. 2.1. This concept is also very new.
3. Development of the trial model of Uni-Rover 3.1 Composition of new trial model of Uni-Rover We have designed and developed a trial model of “Uni-Rover”, a child unit of SMC-Rover. The trial model consists of a single wheel (diameter: 190mm, width: 140mm) and a single manipulator with three joints (length of upper arm and lower arm: 170mm) as shown in Fig.5. At the end of the manipulator there is a caster and a gripper with four fingers. One DC motor for the rotation of the wheel is located inside the wheel. The controller circuits, transmitter and batteries for motors are also located inside the wheel. To actuate the manipulator, one RC-servo motor is located in each of the four joints of the manipulator. The total weight of the rover is 3.2kg. The trial model is driven with a wireless manual controller.
3.2 Improvement of new trial model of Uni-Rover We have set the mass balance of the mechanism inside the wheel with a wide eccentricity between the center of mass and the axis of rotation of the wheel. Because of this mass property, Uni-Rover is very stable in manipulation mode
θ2
Unstable side (Easy to fall down)
Stable side (Good at manipulation)
Center of mass in wheel
Fig. 6. Stability of Uni-Rover
when the arm takes the position of the stable side, and it is also easy to bring it down during transformation, when the arm takes the position of the unstable side as shown in Fig.6.
4.Development of the trial model of SMC rover We have also designed and developed a trial model of SMC rover to be used with the trial models of Uni-Rover, as shown in Fig.7a. The trial model of SMC rover has a main body, four dummy wheel units and two connecters for Uni-Rover. The dummy wheels can rotate freely without motors, but they have been designed in a way that they can be motorized and replaced by real Uni-Rovers with the connecter in future works. The connecters for Uni-Rover consists of a handle for the gripper and two supporting plates to hold the manipulator of Uni-Rover as shown in Fig.7b. Solar battery cell (Dummy)
Connecters Supporting Plates
Child rovers (Dummy)
(a) Overall view of main body
Fig. 7. Mechanisms of main body
Handle
(b) Connecter
5.Experiments of Uni-Rover and SMC rover 5.1 Experiment of Uni-Rover in locomotion mode On a flat surface, we carried out propulsion and steering experiment with the rover in locomotion posture as shown in Fig.2a. The orientation of propulsion is controlled by changing the orientation of the caster with the joints of the manipulator as shown in Fig.8. Moreover, we carried out experiments of climbing over small obstacles. It was confirmed that Uni-Rover can climb over gaps of 5cm of height, but there were problems at the control of the orientation of Uni-Rover on rough terrain.
5.2 Experiment of Uni-Rover in manipulation mode With the rover in the manipulation mode, experiments of the manipulator were carried out, as shown in Fig.2b. With those experiments, it was possible to confirm that each joint is controllable by the wireless controller. It was verified that the manipulator has enough ability to actually hold and transport various objects in several shapes (a pen cap, a small bottle, a grip of a driver, and so on), as shown in Fig.9.
Turn direction
(a) posture of right turn
Fig. 8. Steering motion of Uni-Rover
Turn direction
(b) posture of left turn
box
tape
driver
stone
Fig. 9. Handling various objects
Furthermore, we carried out experiments of “pivot turn”, which is the locomotion method in manipulation mode, as shown in Fig.4a. It was confirmed that the Uni-Rover can change its position by this “pivot turn” motion while in the manipulation mode.
5.3 Experiment of transformation of Uni-Rover We also carried out experiments on the transformation sequence of Uni-Rover. Initially, we measured the N.E.S.M. (Normalized Energy Stability Margin) [12] of Uni-Rover by changing its shoulder angle, as shown in Fig.10. According to this graph, it was confirmed that the N.E.S.M of the stable side is higher than the N.E.S.M of the unstable side, so Uni-Rover achieves both high stability in manipulation and high transformability. Secondly, experiments of transformation from locomotion mode to manipulation mode were carried out, and it was confirmed that the Uni-Rover can stand up by
N.E.S.M.[mm]
30
Stable
20
Unstable 10 :result of experiment
0 -90
-45
0
45
Shoulder Angle θ2 [deg] Fig. 10. N.E.S.M. of Uni-Rover in manipulation mode
90
Fig. 11. Detaching wheel units
using its manipulator, as shown in Fig.3a. Experiments of its transformation from manipulation mode to locomotion mode were also performed as shown in Fig.3b, and we verified that the Uni-Rover can fall down into manipulation mode by using the kinetic effect of the manipulator motion in unstable position.
5.4 Experiment of SMC rover with Uni-Rovers We carried out experiments of SMC rover with Uni-Rovers as detachable wheel units, as shown in Fig.11. It was confirmed that the Uni-Rovers can transport the trial model of SMC rover and can detach from the connecters of SMC rover.
6.Conclusion and future work In this paper, the design and development of the trial models of Uni-Rover and SMC rover have been explained. The results of experiments in locomotion and manipulation mode and transformation experiments have also been mentioned. In the future, propulsion experiments over rough terrain and docking experiments will be carried out, and the control system of the unit will be improved. Besides, combined locomotion and cooperative work by multiple units will be achieved.
Acknowledgment This research is supported by the grant-in-aid for COE Research Project of Super-Mechano-Systems by The Ministry of Education, Culture, Sports, Science and Technology of Japan.
References 1.
S. Hirose, A. Kawakami, K. Kato and H. Kuwahara, “Super-Mechano-Colony and SMC Rover with Detachable Wheel Units”, Proc. COE workshop ’99, pp.67-72 (1999) 2. R. Damoto, A. Kawakami and S. Hirose, “Study of Super-Mechano Colony : concept and basic experimental set-up”, Advanced Robotics, 15 ,4, pp.391-408 (2001) 3. R.C.Arkin and G.A.Bekey, “Robot Colonies”, Kluwer, Dordrecht (1997) 4. M. Hashimoto, F. Oba and T. Eguchi, “Dynamic control approach for motion coordination of multiple wheeled mobile robots transporting a single object”, Proc. IEEE/RSJ IROS, pp.1944-1951(1993) 5. M. N. Ahmadabadi and N. Eiji, “A unified distributed cooperation strategy for multiple object handling robots”, Proc. IEEE ICRA, pp.3625-3630 (1998) 6. T. Fukuda, H. Mizoguchi, K. Sekiyama and F. Arai, “Group Behavior Control for MARS (Micro Autonomous Robotic System)”, Proc. IEEE ICRA, pp.1550-1555 (1999) 7. R. R. Murphy, M. Ausmus, M. Bugajska, T. Ellis, T. Johnson, N. Kelley J. Kiefer, and L. Pollock, “Marsupial-like mobile robot societies”, Proc. Agents'99, pp. 364-365 (1999) 8. D. F. Hougen, S. Benjaafar, J. C. Bonney, J. R. Budenske, M. Dvorak, M. Gini, H. French, D. G. Krantz, P. Y. Li, F. Malver, B. Nelson, N. Papanikolopous, P. E. Rybski, S. A. Stoeter, R. Voyles and K. B. Yesin, “A Miniature Robotic System for Reconnaissance and Surveillance”, Proc. IEEE ICRA, pp.501-507 (2000) 9. Koshiyama, H. Yoshinada and K. Yamafuji, “Development and Motion Control of the All-Direction Steering-Type Mobile Robot”, Proc. 24th Int. Symp. On Industrial Robots”, pp.445-453 (1993) 10. Chemel, E. Mutshler and H. Schempf, “Cyclops: Miniature Robotic Reconnaissance System”, Proc. IEEE ICRA, pp.2298-2302 (1999) 11. S. J. Tsai, E. D. Ferreira and C. J. J. Paredis, “Control of the Gyrover, A Single-Wheel Gyroscopically Stabilized Robot”, Proc. IEEE/RSJ IROS, pp.179-184 (1999) 12. Shigeo Hirose, Hideyuki Tsukagoshi, Kan Yoneda, “Normalized Energy Stability Margin and its Contour of Walking Vehicles on Rough Terrain”, Proc. IEEE ICRA, pp.181-186 (2001)
