Gait Analysis of Martial Arts for Anthropomorphic Robots

Spring 2006 KDC Course Project

 

Takeshi Takahashi, Abhinav Kalamdani

 

 

Motivation

When we saw HONDA ASIMO moving, we noticed that his waking was similar to the walking style in karate. ASIMO doesn't change the height of his waist and he always bends his knees. Actually this walking is very stable because the center of mass is maintained at a low level and this height doesn't change a lot. A position of a fighter must be maneuverable even while he is moving (walking) in order to defend from enemy's attacks swiftly. Karate was invented by combining Chinese martial arts with Japanese old martial arts. This means that people have developed efficient, strong and stable moving for hundreds years. Then we believe that one of the optimized stable moving is the moving of karate. We think analyzing the moving of karate is helpful for analyzing human's natural walking.

 

Several attempts have been made to generate anthropomorphic gaits for biped robots. However considering the static configuration of the bipeds, adapting normal human gait is not easy. The configuration of bent knees and vertically static waist of the bipeds like Asimo, HOAP-I is similar to basic karate walking.

 

[Courtesy: Honda]

 

 

Related Work

Koshiro Noritake et. al. generated Tai Chi motion for bipeds using pre-defined postures and evaluation using metric based on COM [1]. They captured the key postures from the tutorials for Tai Chi and based on smooth interpolation between the postures the individual dynamic trajectories were generated.

Johannes Mezger et. al. proposed trajectory synthesis using movement primitives and evaluation using ZMP criterion [2]. The trajectory synthesis is done by using the space-time correspondence of the motion sequences.

Dewei Mao et. al. evaluated stability of Tai Chi motion by considering the support area of the stance and the height of the center of mass. They proved that a kind of Tai Chi motion is useful in development of the thigh muscles and also the stability and balance control of the people.

 

Proposed Method

In order to analyze karate motion, the joint angles are the most important data to be analyzed. And to do this analysis we collected the Kinematical data from motion capture setup. The markers were placed on the karate expert at the positions shown in figure 2. Totally there are well distributed 31 markers. The expert performed the Gedanbarai (basic movement) motion and his motion was captured as shown here (C3D file of Gedanbarai).

 

 

    

Figure 2: Marker placement details [CMU Motion Capture Lab]

 

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Figure 3: Marker positions (blue), COM of links (red), COM of whole body (green)

 

 

The figure 3 shows the (x, y, z) positions of the markers for Gedanbarai and also the center of masses (COM) for the links as well the whole body. The assumption was made that the mass distribution is uniform and hence the geometrical centroids themselves are the center of masses. The next components to be computed are the joint angles. Considering only the lower limbs, the joint angles are computed using the center of mass positions and the joint positions as shown in the figure 4.

 

Figure 4 : Joint angle definitions

 

They can be obtained by the expression given as:

 

 

The joint velocities are then computed differentiating numerically the joint angles and then smoothening them and differentiating again to obtain the joint accelerations. These components are used to compute the zero-moment point (ZMP).

 

Vukobratovic and Juricic (1969) defined the ZMP as, “point of resulting reaction forces at the contact surface between the extremity and the ground” which has been interpreted by Popovic et. al. as the point on the ground surface about which the horizontal component of the moment of the ground reaction force is zero expressed by,

 

                                     (1)

 

The ZMP may also be defined as appoint on the ground at which the net moment due to the inertial and gravitational forces has no component along horizontal axis. [Hirai et.al, 1998] which is expressed by,

 

                             (2)

 

The horizontal component of the total body moment about the ZMP is given by,

 

                 (3)

 

where  is the center of mass of the total body,   is the center of mass of the  link,  is the mass of the   link,  is the linear acceleration of the  link COM,  is the inertia tensor of the  link about the link’s COM, and  is the angular velocity of the  link. The equation (3) is solved to get the ZMP point on the ground surface [Popovic et. al.],

 

             (4)

 

              (5)

 

So now, with all the kinematical data the ZMP is computed for the complete gait. The ZMP for the Gedanbarai and normal walking were compared.

 

The next component of the project was to compute the joint torques. The joint torques using inverse dynamics assuming a 2D model were computed using the Art Kuo’s Dynamics Workbench running on the Mathematica platform. The equations of motion were exported to the Matlab environment. The function could just take in the joint angles, velocities and accelerations and give out the joint torques. The 2D model used was approximated to with a lumped mass above the waist with no involvement of the dynamics of hand, and the assumption that the support foot is clamped to the ground. The torque trajectories were generated for a segment of gait where the right leg is the support leg and the start time was when the subject lifts the left foot off the ground and the end time was when the subject is about to touch the left leg to the ground after performing the whole swing phase for left leg and support phase for the right leg.

 

 

Experimentation and Result

 

The figure 5 shows the comparison of the height of center of mass for Gedanbarai and normal walking and figure 6 shows the comparison of the ZMP for Gedanbarai and normal walking. From figure 5 we see that in Gedanbarai the COM is much lower relative to the height of the person. And it is a fact that, lower the center of mass more stable is the system. Hence the bipeds would stay much stable with Gedanbarai. However from the figure 6, we see that the ZMP in Gedanbarai is oscillating more on the ground surface and from figure 7, which shows the locus of ZMP around the support polygon when right leg is in support phase, sometimes the ZMP is out of support polygon. This can be seen clearly in the visual simulation in this video. This might contradict and question the stability of Gedanbarai, but ZMP stability criterion is more viable when tipping is considered. But however due to the inertial balance recovery in humans is so good, this slight instability in Gedanbarai might turn on as an advantage in terms of maneuverability. So if we need to make our biped robots more maneuverable, then adapting Gedanbarai would be a feasible option.

 

Figure 5: Comparison of the height of center of mass for Gedanbarai and normal walking

 

 

 

Figure 6: Comparison of the ZMP trajectories for Gedanbarai and normal walking

 

 

Figure 7: The locus of the ZMP when the right leg is in the support phase

 

The figure 8 shows the torque profiles for Gedanbarai and figure 9 shows the torque profiles for normal walking, computed from the inverse dynamics. These were computed when the right leg was in support phase and the left leg was in the swing phase. We see that the profile in Gedanbarai is much smoother than the normal walking. The spikes in the torques during normal walking show the amount of stress that is exerted in the joints especially the hip. The exaggerated spikes might be due to numerical instability, but in general there are spikes seen in normal walking. Hence Gedanbarai again wins over the normal walking proving it to be low stressing on the joint actuators of the biped robots.

 

Figure 8: The torque profiles for Gedanbarai                                                                                           Figure 9: The torque profiles for Normal walking

 

Conclusions

We conclude that although the normal walking wins over in terms of stability in ZMP analysis, but Gedanbarai shows a good stability in terms of height of COM and more maneuverability in terms of ZMP. Also from the torque profiles we can conclude the smoother motions in Gedanbarai. In short, adapting martial arts gaits for biped robots will make them easier to move around and with lower stress.

 

Future Work

Although theoretically and using the simulation techniques we did prove the advantage of Gedanbarai, but it would be really good if it will be tried on the real biped and evaluated. We did not consider computing the dynamics when both the feet are on ground forming a closed chain, so it might be a good challenge to analyze that part too. There are a bunch of other martial arts walking styles which might show a better performance than Gedanbarai.

 

Acknowledgement

We are grateful to Mike Duray for performing in the MOCAP studio, we are grateful to the MOCAP lab of CMU for providing us the data and also we are grateful to Chris Messom for making our lives easier for helping us to get the torque profiles.

 

References

[1]. Koshiro Noritake, Shohei Kato, Takanori Yamakita, Hidenori Itoh, “A Motion Generation System for Humanoid Robots”, Proc 2003 Intl Symp. on Micromechatronics and Human Science.

[2]. J.Mezger, W.Ilg, M.A.Giese, “Trajectory Synthesis by Hierarchical Spatio-temporal Correspondance: Comparison of Different Methods”, Proceedings of the 2nd symposium on Appied perception in graphics and visualization, ACM International Conference Proceeding Series; Vol. 95.

[3]. Dewei Mao, Youllian Hong, J.Li, “The Kinematical Characteristics of the lower extremities during Tai Chi Chuan exercise”, International Society of Biomechanics of Sports Congress XXII, Ottawa, Canada, 2004.

[4]. M.B.Popovic, A.Goswami, H.Herr, “Ground Reference Points in legged locomiton: definitions, biological trajectories and control implications”, Intl Journal of Robotics Research, Vol 24, No.10, Oct 2005.

 

Note:

The code which we wrote is attached here.