Swimmer simulation using robot manipulator dynamics under steady water

Author(s)
Kazunori Shinohara

ABSTRACT

To help swimmers improve, we have developed a computational swimming model using underwater manipulator dynamics. We formulate the equations of the underwater manipulator dynamics using the fluid drag, which is proportional to the square of the velocity. We construct a swimming model consisting of several links based on these equations. The distance traveled by the optimal swimming motion is derived using the model. The input parameters are the joint torques. The arm and leg positions in the model are determined from the joint torques. The force transmitted from the water to the manipulator is defined to be the action force, and the force transmitted from the manipulator to the water is defined to be the reaction force. This reaction force is defined to be the propulsion force. By combining the propulsion force generated by the arms and legs and the frictional drag with respect to the body we can calculate the distance traveled. To optimize the propulsion, which depends on the swimmer’s motion, a variational approach using the Lagrange function is applied. We can use the model to simulate 2D pseudo-backstroke motion. Our model has a lower cost than other techniques in the literature, because it does not require computational fluid dynamics (CFD). The swimmer velocity calculated by our model agrees quite closely with the results in the literature. The model qualitatively captures the movement of an actual swimmer.

To help swimmers improve, we have developed a computational swimming model using underwater manipulator dynamics. We formulate the equations of the underwater manipulator dynamics using the fluid drag, which is proportional to the square of the velocity. We construct a swimming model consisting of several links based on these equations. The distance traveled by the optimal swimming motion is derived using the model. The input parameters are the joint torques. The arm and leg positions in the model are determined from the joint torques. The force transmitted from the water to the manipulator is defined to be the action force, and the force transmitted from the manipulator to the water is defined to be the reaction force. This reaction force is defined to be the propulsion force. By combining the propulsion force generated by the arms and legs and the frictional drag with respect to the body we can calculate the distance traveled. To optimize the propulsion, which depends on the swimmer’s motion, a variational approach using the Lagrange function is applied. We can use the model to simulate 2D pseudo-backstroke motion. Our model has a lower cost than other techniques in the literature, because it does not require computational fluid dynamics (CFD). The swimmer velocity calculated by our model agrees quite closely with the results in the literature. The model qualitatively captures the movement of an actual swimmer.

Cite this paper

Shinohara, K. (2010) Swimmer simulation using robot manipulator dynamics under steady water.*Natural Science*, **2**, 959-967. doi: 10.4236/ns.2010.29117.

Shinohara, K. (2010) Swimmer simulation using robot manipulator dynamics under steady water.

References

[1] Laffite, L., Vilas-Boas, J.P., Demarle, A., Silva, J., Fernandes, R. and Billat, V. (2004) Changes in physiological and stroke parameters during a maximal 400-m free swimming test in elite swimmers. Canadian Journal of Applied Physiology, 229, S17-31.

[2] Silva, A.J., Machado, R. V., Guidetti, L., Bessone, A. F., Mota, P., Freitas, J. and Baldari, C. (2007) Effect of creatine on swimming velocity, body composition and hydrodynamic variables. Journal of Sports Medicine and Physical Fitness, 47(1), 58-64.

[3] Soons, B., Colman, V., Persyn, U. and Silva, A. (2003) Specific movement variables important for performance in different breaststroke styles. In Biomechanics and Medicine in Swimming, IX, 295-300.

[4] Barbosa, T.M., Bragada, J.A., Reis, V.M., Marinho, D.A., Carvalho, C. and Silva, A.J. (2010) Energetics and biomechanics as determining factors of swimming performance: updating the state of the art. Journal of Science and Medicine in Sport, 13(2), 262-269.

[5] Silva, A., Costa, A.M., Oliveira, P.M., Reis V., Saavedra, J., Perl, J., Rouboa, A. and Marinho, D. (2007) The use of neural network technology to model swimming performance. Journal of Sports Science and Medicine 6(1), 117-125.

[6] Arellano, R., Nicoli-Terrés, J.M. and Redondo, J.M. (2006) Fundamental hydrodynamics of swimming propulsion. Portuguese Journal of Sport Sciences, 6(Suppl. 2), 15-20.

[7] H?rtel, T. and Axel, S. (2008) Evaluation of start techniques in sports swimming by dynamics simulation. The Engineering of Sport, 7(1), 89-96.

[8] Kwatra, N., Wojtan, C., Carlson, M., Essa, I., Mucha, P.J., and Turk, G. (2010) Fluid simulation with articulated bodies. IEEE Transactions on Visualization and Computer Graphics, 16(1), 70-80.

[9] Nakashima, M., Satou, K. and Mura, Y. (2007) Development of swimming human simulation model considering rigid body dynamics and unsteady fluid force for whole body. Journal of Fluid Science and Technology, 2(1), 56-67.

[10] Za?di, H., Ta?ar, R., Fohanno, S. and Polidori, G. (2008) Analysis of the effect of swimmer’s head position on swimming performance using computational fluid dynamics. Journal of Biomechanics, 41(6), 1350-1358.

[11] Lecrivain, G., Slaouti, A., Payton, C. and Kennedy, I. (2008) Using reverse engineering and computational fluid dynamics to investigate a lower arm amputee swim- mer’s performance. Journal of Biomechanics, 41(13), 2855-2859.

[12] Silva, A.J., Rouboa, A., Moreira, A., Reis, V.M., Alves, F., Vilas-Boas, J.P. and Marinho, D.A. (2008) Analysis of drafting effects in swimming using computational fluid dynamics. Journal of Sports Science and Medicine, 7(1), 60-66.

[13] Marinho, D.A., Reis, V.M., Alves, F.B., Vilas-Boas, J.P., Machado, L., Silva, A.J. and Rouboa, A.I. (2009) Hydrodynamic drag during gliding in swimming. Journal of Applied Biomechanics, 25(3), 253-257.

[14] Cohen, R.C.Z., Cleary, P.W. and Mason, B. (2009) Simu- lations of human swimming using smoothed particle hydrodynamics. 7th International Conference on CFD in the Minerals and Process Industries, Commonwealth Scientific and Industrial Research Organisation.

[15] Marinho, D., Barbosa, T., Reis, V.M., Kjendlie, P.-L. and Alves, F.B., (2010) Swimming propulsion forces are enhanced by a small finger spread. Journal of Applied Biomechanics, 26(1), 87-92.

[16] Marinho, D.A., Barbosa, T.M., Kjendlie, P.L., Vilas- Boas, J.P., Alves, F.B., Rouboa, A.I. and Silva, A.J. (2009) Swimming simulation: A new tool for swimming research and practical applications. Computational Fluid Dynamics for Sport Simulation, 33-61.

[17] Rouboa, A., Silva, A., Leal, L., Rocha, J. and Alves, F. (2006) The effect of swimmer’s hand/forearm acceleration on propulsive forces generation using Computational Fluid Dynamics. Journal of Biomechanics, 39(7), 1239- 1248.

[18] Shinohara, K., Furukawa, T. and Yagawa, G. (2002) Simulation and sub-optimal motion planning of a swimmer under hydrodynamics. Transactions of the Japan Society of Mechanical Engineers, 68(673), 2643-2650.

[19] Takagi, H., Shimizu, Y. and Kodan, N. (1999) A hydrodynamic study of active drag in swimming. JSME International Journal Series B, 42(2), 171-177.

[20] Marinho, D.A., Barbosa, T.M., Kjendlie, P.L., Mantri- pragada, N., Vilas-Boas, J.P., Machado, L., Alves, F.B., Rouboa, A.I. and Silva, A.J. (2010) Modelling hydrodynamic drag in swimming using computational fluid dynamics. Computational Fluid Dynamics, 17, 391-404.

[21] Arellano, R., Pardillo, S. and Gavilan, S. (2002) Underwater undulatory swimming: Kinematic characteristics, vortex generation and application during the start, turn and swimming strokes.

[22] Proceedings of the 20th International Symposium on Biomechanics in Sports, Universidad de Granada. Nakashima, M. (2007) Analysis of breast, back and butterfly strokes by the swimming human simulation model swum. In: Kato, N. and Kamimura, S., Eds., Biomechanisms of Animals in Swimming and Flying-Fluid Dynamics, Biomimetic Robots, and Sports Science, Springer- Verlag, 361-367.

[1] Laffite, L., Vilas-Boas, J.P., Demarle, A., Silva, J., Fernandes, R. and Billat, V. (2004) Changes in physiological and stroke parameters during a maximal 400-m free swimming test in elite swimmers. Canadian Journal of Applied Physiology, 229, S17-31.

[2] Silva, A.J., Machado, R. V., Guidetti, L., Bessone, A. F., Mota, P., Freitas, J. and Baldari, C. (2007) Effect of creatine on swimming velocity, body composition and hydrodynamic variables. Journal of Sports Medicine and Physical Fitness, 47(1), 58-64.

[3] Soons, B., Colman, V., Persyn, U. and Silva, A. (2003) Specific movement variables important for performance in different breaststroke styles. In Biomechanics and Medicine in Swimming, IX, 295-300.

[4] Barbosa, T.M., Bragada, J.A., Reis, V.M., Marinho, D.A., Carvalho, C. and Silva, A.J. (2010) Energetics and biomechanics as determining factors of swimming performance: updating the state of the art. Journal of Science and Medicine in Sport, 13(2), 262-269.

[5] Silva, A., Costa, A.M., Oliveira, P.M., Reis V., Saavedra, J., Perl, J., Rouboa, A. and Marinho, D. (2007) The use of neural network technology to model swimming performance. Journal of Sports Science and Medicine 6(1), 117-125.

[6] Arellano, R., Nicoli-Terrés, J.M. and Redondo, J.M. (2006) Fundamental hydrodynamics of swimming propulsion. Portuguese Journal of Sport Sciences, 6(Suppl. 2), 15-20.

[7] H?rtel, T. and Axel, S. (2008) Evaluation of start techniques in sports swimming by dynamics simulation. The Engineering of Sport, 7(1), 89-96.

[8] Kwatra, N., Wojtan, C., Carlson, M., Essa, I., Mucha, P.J., and Turk, G. (2010) Fluid simulation with articulated bodies. IEEE Transactions on Visualization and Computer Graphics, 16(1), 70-80.

[9] Nakashima, M., Satou, K. and Mura, Y. (2007) Development of swimming human simulation model considering rigid body dynamics and unsteady fluid force for whole body. Journal of Fluid Science and Technology, 2(1), 56-67.

[10] Za?di, H., Ta?ar, R., Fohanno, S. and Polidori, G. (2008) Analysis of the effect of swimmer’s head position on swimming performance using computational fluid dynamics. Journal of Biomechanics, 41(6), 1350-1358.

[11] Lecrivain, G., Slaouti, A., Payton, C. and Kennedy, I. (2008) Using reverse engineering and computational fluid dynamics to investigate a lower arm amputee swim- mer’s performance. Journal of Biomechanics, 41(13), 2855-2859.

[12] Silva, A.J., Rouboa, A., Moreira, A., Reis, V.M., Alves, F., Vilas-Boas, J.P. and Marinho, D.A. (2008) Analysis of drafting effects in swimming using computational fluid dynamics. Journal of Sports Science and Medicine, 7(1), 60-66.

[13] Marinho, D.A., Reis, V.M., Alves, F.B., Vilas-Boas, J.P., Machado, L., Silva, A.J. and Rouboa, A.I. (2009) Hydrodynamic drag during gliding in swimming. Journal of Applied Biomechanics, 25(3), 253-257.

[14] Cohen, R.C.Z., Cleary, P.W. and Mason, B. (2009) Simu- lations of human swimming using smoothed particle hydrodynamics. 7th International Conference on CFD in the Minerals and Process Industries, Commonwealth Scientific and Industrial Research Organisation.

[15] Marinho, D., Barbosa, T., Reis, V.M., Kjendlie, P.-L. and Alves, F.B., (2010) Swimming propulsion forces are enhanced by a small finger spread. Journal of Applied Biomechanics, 26(1), 87-92.

[16] Marinho, D.A., Barbosa, T.M., Kjendlie, P.L., Vilas- Boas, J.P., Alves, F.B., Rouboa, A.I. and Silva, A.J. (2009) Swimming simulation: A new tool for swimming research and practical applications. Computational Fluid Dynamics for Sport Simulation, 33-61.

[17] Rouboa, A., Silva, A., Leal, L., Rocha, J. and Alves, F. (2006) The effect of swimmer’s hand/forearm acceleration on propulsive forces generation using Computational Fluid Dynamics. Journal of Biomechanics, 39(7), 1239- 1248.

[18] Shinohara, K., Furukawa, T. and Yagawa, G. (2002) Simulation and sub-optimal motion planning of a swimmer under hydrodynamics. Transactions of the Japan Society of Mechanical Engineers, 68(673), 2643-2650.

[19] Takagi, H., Shimizu, Y. and Kodan, N. (1999) A hydrodynamic study of active drag in swimming. JSME International Journal Series B, 42(2), 171-177.

[20] Marinho, D.A., Barbosa, T.M., Kjendlie, P.L., Mantri- pragada, N., Vilas-Boas, J.P., Machado, L., Alves, F.B., Rouboa, A.I. and Silva, A.J. (2010) Modelling hydrodynamic drag in swimming using computational fluid dynamics. Computational Fluid Dynamics, 17, 391-404.

[21] Arellano, R., Pardillo, S. and Gavilan, S. (2002) Underwater undulatory swimming: Kinematic characteristics, vortex generation and application during the start, turn and swimming strokes.

[22] Proceedings of the 20th International Symposium on Biomechanics in Sports, Universidad de Granada. Nakashima, M. (2007) Analysis of breast, back and butterfly strokes by the swimming human simulation model swum. In: Kato, N. and Kamimura, S., Eds., Biomechanisms of Animals in Swimming and Flying-Fluid Dynamics, Biomimetic Robots, and Sports Science, Springer- Verlag, 361-367.