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Dynamic Balance

10.5 Dynamic Balance

Walking gait patterns relying on static balance are not very efficient. They require large foot areas and only relatively slow gaits are possible, in order to keep dynamic forces low. Walking mechanisms with dynamic balance, on the other hand, allow the construction of robots with smaller feet, even feet that only have a single contact point, and can be used for much faster walking gaits or even running.

As has been defined in the previous section, dynamic balance means that at least during some phases of a robot’s gait, its center of mass is not supported by its foot area. Ignoring any dynamic forces and moments, this means that the robot would fall over if no counteraction is taken in real time. There are a number of different approaches to dynamic walking, which are discussed in the following.

10.5.1 Dynamic Walking Methods

In this section, we will discuss a number of different techniques for dynamic walking together with their sensor requirements.

1.Zero moment point (ZMP)

[Fujimoto, Kawamura 1998], [Goddard, Zheng, Hemami 1992], [Kajita, Yamaura, Kobayashi 1992], [Takanishi et al. 1985]

This is one of the standard methods for dynamic balance and is published in a number of articles. The implementation of this method requires the knowledge of all dynamic forces on the robot’s body plus all torques between the robot’s foot and ankle. This data can be determined by using accelerometers or gyroscopes on the robot’s body plus pressure sensors in the robot’s feet or torque sensors in the robot’s ankles.

With all contact forces and all dynamic forces on the robot known, it is possible to calculate the “zero moment point” (ZMP), which is the dynamic equivalent to the static center of mass. If the ZMP lies within the support area of the robot’s foot (or both feet) on the ground, then the robot is in dynamic balance. Otherwise, corrective action has to be taken by changing the robot’s body posture to avoid it falling over.

2.Inverted pendulum

[Caux, Mateo, Zapata 1998], [Park, Kim 1998], [Sutherland, Bräunl 2001] A biped walking robot can be modeled as an inverted pendulum (see also the balancing robot in Chapter 9). Dynamic balance can be achieved by constantly monitoring the robot’s acceleration and adapting the corresponding leg movements.

3.Neural networks

[Miller 1994], [Doerschuk, Nguyen, Li 1995], [Kun, Miller 1996]

As for a number of other control problems, neural networks can be used to

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achieve dynamic balance. Of course, this approach still needs all the sensor feedback as in the other approaches.

4.Genetic algorithms

[Boeing, Bräunl 2002], [Boeing, Bräunl 2003]

A population of virtual robots is generated with initially random control settings. The best performing robots are reproduced using genetic algorithms for the next generation.

This approach in practice requires a mechanics simulation system to evaluate each individual robot’s performance and even then requires several CPU-days to evolve a good walking performance. The major issue here is the transferability of the simulation results back to the physical robot.

5.PID control

[Bräunl 2000], [Bräunl, Sutherland, Unkelbach 2002]

Classic PID control is used to control the robot’s leaning front/back and left/right, similar to the case of static balance. However, here we do not intend to make the robot stand up straight. Instead, in a teaching stage, we record the desired front and side lean of the robot’s body during all phases of its gait. Later, when controlling the walking gait, we try to achieve this offset of front and side lean by using a PID controller. The following parameters can be set in a standard walking gate to achieve this leaning:

•Step length

•Height of leg lift

•Walking speed

•Amount of forward lean of torso

•Maximal amount of side swing

6.Fuzzy control

[Unpublished]

We are working on an adaptation of the PID control, replacing the classic PID control by fuzzy logic for dynamic balance.

7.Artificial horizon

[Wicke 2001]

This innovative approach does not use any of the kinetics sensors of the other approaches, but a monocular grayscale camera. In the simple version, a black line on white ground (an “artificial horizon”) is placed in the visual field of the robot. We can then measure the robot’s orientation by changes of the line’s position and orientation in the image. For example, the line will move to the top if the robot is falling forward, it will be slanted at an angle if the robot is leaning left, and so on (Figure 10.8).

With a more powerful controller for image processing, the same principle can be applied even without the need for an artificial horizon. As long as there is enough texture in the background, general optical flow can be used to determine the robot’s movements.

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Figure 10.8: Artificial horizon

Figure 10.9 shows Johnny Walker during a walking cycle. Note the typical side-swing of the torso to counterbalance the leg-lifting movement. This creates a large momentum around the robot’s center of mass, which can cause problems with stability due to the limited accuracy of the servos used as actuators.

Figure 10.9: Johnny walking sequence

Figure 10.10 shows a similar walking sequence with Andy Droid. Here, the robot performs a much smoother and better controlled walking gait, since the mechanical design of the hip area allows a smoother shift of weight toward the side than in Johnny’s case.

10.5.2 Alternative Biped Designs

All the biped robots we have discussed so far are using servos as actuators. This allows an efficient mechanical and electronic design of a robot and therefore is a frequent design approach in many research groups, as can be seen from the group photo of FIRA HuroSot World Cup Competition in 2002 [Baltes, Bräunl 2002]. With the exception of one robot, all robots were using servos (see Figure 10.11).

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Figure 10.10: Andy walking sequence

Figure 10.11: Humanoid robots at FIRA HuroSot 2002 with robots from (left to right): Korea, Australia, Singapore, New Zealand, and Korea

Other biped robot designs also using the EyeCon controller are Tao Pie Pie from University of Auckland, New Zealand, and University of Manitoba, Canada, [Lam, Baltes 2002] and ZORC from Universität Dortmund, Germany [Ziegler et al. 2001].

As has been mentioned before, servos have severe disadvantages for a number of reasons, most importantly because of their lack of external feedback. The construction of a biped robot with DC motors, encoders, and endswitches, however, is much more expensive, requires additional motor driver electronics, and is considerably more demanding in software development. So instead of redesigning a biped robot by replacing servos with DC motors and keeping the same number of degrees of freedom, we decided to go for a minimal approach. Although Andy has 10 dof in both legs, it utilizes only three

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Figure 10.12: Minimal biped design Rock Steady

independent dof: bending each leg up and down, and leaning the whole body left or right. Therefore, it should be possible to build a robot that uses only three motors and uses mechanical gears or pulleys to achieve the articulated joint motion.

Figure 10.13: Dynamic walking sequence

The CAD designs following this approach and the finished robot are shown in Figure 10.12 [Jungpakdee 2002]. Each leg is driven by only one motor, while the mechanical arrangement lets the foot perform an ellipsoid curve for each motor revolution. The feet are only point contacts, so the robot has to

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keep moving continuously, in order to maintain dynamic balance. Only one motor is used for shifting a counterweight in the robot’s torso sideways (the original drawing in Figure 10.12 specified two motors). Figure 10.13 shows the simulation of a dynamic walking sequence [Jungpakdee 2002].

10.6 References

BALTES. J., BRÄUNL, T. HuroSot - Laws of the Game, FIRA 1st Humanoid Robot Soccer Workshop (HuroSot), Daejeon Korea, Jan. 2002, pp. 43-68 (26)

BOEING, A., BRÄUNL, T. Evolving Splines: An alternative locomotion controller for a bipedal robot, Seventh International Conference on Control, Automation, Robotics and Vision, ICARV 2002, CD-ROM, Singapore, Dec. 2002, pp. 1-5 (5)

BOEING, A., BRÄUNL, T. Evolving a Controller for Bipedal Locomotion, Proceedings of the Second International Symposium on Autonomous Minirobots for Research and Edutainment, AMiRE 2003, Brisbane, Feb. 2003, pp. 43-52 (10)

BRÄUNL, T. Design of Low-Cost Android Robots, Proceedings of the First IEEE-RAS International Conference on Humanoid Robots, Humanoids 2000, MIT, Boston, Sept. 2000, pp. 1-6 (6)

BRÄUNL, T., SUTHERLAND, A., UNKELBACH, A. Dynamic Balancing of a Hu-

manoid Robot, FIRA 1st Humanoid Robot Soccer Workshop (HuroSot), Daejeon Korea, Jan. 2002, pp. 19-23 (5)

CAUX, S., MATEO, E., ZAPATA, R. Balance of biped robots: special double-in- verted pendulum, IEEE International Conference on Systems, Man, and Cybernetics, 1998, pp. 3691-3696 (6)

CHO, H., LEE, J.-J. (Eds.) Proceedings 2002 FIRA Robot World Congress, Seoul, Korea, May 2002

DOERSCHUK, P., NGUYEN, V., LI, A. Neural network control of a three-link leg, in Proceedings of the International Conference on Tools with Artificial Intelligence, 1995, pp. 278-281 (4)

FUJIMOTO, Y., KAWAMURA, A. Simulation of an autonomous biped walking robot including environmental force interaction, IEEE Robotics and Automation Magazine, June 1998, pp. 33-42 (10)

GODDARD, R., ZHENG, Y., HEMAMI, H. Control of the heel-off to toe-off motion of a dynamic biped gait, IEEE Transactions on Systems, Man, and Cybernetics, vol. 22, no. 1, 1992, pp. 92-102 (11)

HARADA, H. Andy-2 Visualization Video, http://robotics.ee.uwa.edu.au /eyebot/mpg/walk-2leg/, 2006

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References

JUNGPAKDEE, K., Design and construction of a minimal biped walking mechanism, B.E. Honours Thesis, The Univ. of Western Australia, Dept. of Mechanical Eng., supervised by T. Bräunl and K. Miller, 2002

KAJITA, S., YAMAURA, T., KOBAYASHI, A. Dynamic walking control of a biped robot along a potential energy conserving orbit, IEEE Transactions on Robotics and Automation, Aug. 1992, pp. 431-438 (8)

KUN, A., MILLER III, W. Adaptive dynamic balance of a biped using neural networks, in Proceedings of the 1996 IEEE International Conference on Robotics and Automation, Apr. 1996, pp. 240-245 (6)

LAM, P., BALTES, J. Development of Walking Gaits for a Small Humanoid Robot, Proceedings 2002 FIRA Robot World Congress, Seoul, Korea, May 2002, pp. 694-697 (4)

MILLER III, W. Real-time neural network control of a biped walking robot, IEEE Control Systems, Feb. 1994, pp. 41-48 (8)

MONTGOMERY, G. Robo Crop - Inside our AI Labs, Australian Personal Computer, Issue 274, Oct. 2001, pp. 80-92 (13)

NICHOLLS, E. Bipedal Dynamic Walking in Robotics, B.E. Honours Thesis, The Univ. of Western Australia, Electrical and Computer Eng., supervised by T. Bräunl, 1998

PARK, J.H., KIM, K.D. Bipedal Robot Walking Using Gravity-Compensated Inverted Pendulum Mode and Computed Torque Control, IEEE International Conference on Robotics and Automation, 1998, pp. 3528-3533

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SUTHERLAND, A., BRÄUNL, T. Learning to Balance an Unknown System, Proceedings of the IEEE-RAS International Conference on Humanoid Robots, Humanoids 2001, Waseda University, Tokyo, Nov. 2001, pp. 385-391 (7)

TAKANISHI, A., ISHIDA, M., YAMAZAKI, Y., KATO, I. The realization of dynam-

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UNKELBACH, A. Analysis of sensor data for balancing and walking of a biped robot, Project Thesis, Univ. Kaiserslautern / The Univ. of Western Australia, supervised by T. Bräunl and D. Henrich, 2002

WICKE, M. Bipedal Walking, Project Thesis, Univ. Kaiserslautern / The Univ. of Western Australia, supervised by T. Bräunl, M. Kasper, and E. von Puttkamer, 2001

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ZIEGLER, J., WOLFF, K., NORDIN, P., BANZHAF, W. Constructing a Small Hu-

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ZIMMERMANN, J., Balancing of a Biped Robot using Force Feedback, Diploma Thesis, FH Koblenz / The Univ. of Western Australia, supervised by T. Bräunl, 2004

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