# MODELING AND OPTIMAL TRAJECTORY PLANNING OF A BIPED ROBOT USING NEWTON-EULER FORMULATION

### David Tlalolini, Yannick Aoustin, Christine Chevallereau

#### Abstract

The development of an algorithm to achieve optimal cyclic gaits in space for a thirteen-link biped and twelve actuated joints is proposed. The cyclic walking gait is composed of successive single support phases and impulsive impacts with full contact between the sole of the feet and the ground. The evolution of the joints are chosen as spline functions. The parameters to define the spline functions are determined using an optimization under constraints on the dynamic balance, on the ground reactions, on the validity of impact, on the torques and on the joints velocities. The criterion considered is represented by the integral of the torque norm. The algorithm is tested for a biped robot whose numerical walking results are presented.

#### References

- Beletskii, V. V. and Chudinov, P. S. (1977). Parametric optimization in the problem of bipedal locomotion.
- Izv. An SSSR. Mekhanika Tverdogo Tela [Mechanics of Solids], (1):25-35.
- Bessonnet, G., Chesse, S., and Sardin, P. (2002). Generating optimal gait of a human-sized biped robot. In Proc. of the fifth International Conference on Climbing and Walking Robots, pages 717-724.
- Channon, P. H., Hopkins, S. H., and Pham, D. T. (1992). Derivation of optimal walking motions for a bipedal walking robot. Robotica, 2(165-172).
- Chevallereau., C. and Aoustin, Y. (2001). Optimal reference trajectories for walking and running of a biped. Robotica, 19(5):557-569.
- Formal'sky, A. (1982). Locomotion of Anthropomorphic Mechanisms. Nauka, Moscow [In Russian].
- Grishin, A. A., Formal'sky, A. M., Lensky, A. V., and Zhitomirsky, S. V. (1994). Dynamic walking of a vehicle with two telescopic legs controlled by two drives. Int. J. of Robotics Research, 13(2):137-147.
- Khalil, W. and Dombre, E. (2002). Modeling, identification and control of robots. Hermes Sciences Europe.
- L. Hu, C. Z. and Sun, Z. (2006). Biped gait optimization using spline function based probability model. in Proc. of the IEEE Conference on Robotics and Automation, pages 830-835.
- M. Sakaguchi, J. Furushu, A. S. and Koizumi, E. (1995). A realization of bunce gait in a quadruped robot with articular-joint-type legs. Proc. of the IEEE Conference on Robotics and Automation, pages 697-702.
- Miossec, S. and Aoustin, Y. (2006). Dynamical synthesis of a walking cyclic gait for a biped with point feet. Special issue of lecture Notes in Control and information Sciences, Ed. Morari, Springer-Verlag.
- M.W.Walker and D.E.Orin (1982). Efficient dynamic computer simulation of robotics mechanism. Trans. of ASME, J. of Dynamic Systems, Measurement and Control, 104:205-211.
- Rostami, M. and Besonnet, G. (1998). Impactless sagital gait of a biped robot during the single support phase. In Proceedings of International Conference on Robotics and Automation, pages 1385-1391.
- Roussel, L., de Wit, C. C., and Goswami, A. (2003). Generation of energy optimal complete gait cycles for biped. In Proc. of the IEEE Conf. on Robotics and Automation, pages 2036-2042.
- Saidouni, T. and Bessonnet, G. (2003). Generating globally optimised saggital gait cycles of a biped robot. Robotica, 21(2):199-210.
- Vukobratovic, M. and Stepanenko, Y. (1972). On the stability of anthropomorphic systems. Mathematical Biosciences, 15:1-37.
- Zonfrilli, F., Oriolo, M., and Nardi, T. (2002). A biped locomotion strategy for the quadruped robot sony ers-210. In Proc. of the IEEE Conf. on Robotics and Automation, pages 2768-2774.

#### Paper Citation

#### in Harvard Style

Tlalolini D., Aoustin Y. and Chevallereau C. (2007). **MODELING AND OPTIMAL TRAJECTORY PLANNING OF A BIPED ROBOT USING NEWTON-EULER FORMULATION** . In *Proceedings of the Fourth International Conference on Informatics in Control, Automation and Robotics - Volume 4: ICINCO,* ISBN 978-972-8865-83-2, pages 76-83. DOI: 10.5220/0001628200760083

#### in Bibtex Style

@conference{icinco07,

author={David Tlalolini and Yannick Aoustin and Christine Chevallereau},

title={MODELING AND OPTIMAL TRAJECTORY PLANNING OF A BIPED ROBOT USING NEWTON-EULER FORMULATION},

booktitle={Proceedings of the Fourth International Conference on Informatics in Control, Automation and Robotics - Volume 4: ICINCO,},

year={2007},

pages={76-83},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0001628200760083},

isbn={978-972-8865-83-2},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the Fourth International Conference on Informatics in Control, Automation and Robotics - Volume 4: ICINCO,

TI - MODELING AND OPTIMAL TRAJECTORY PLANNING OF A BIPED ROBOT USING NEWTON-EULER FORMULATION

SN - 978-972-8865-83-2

AU - Tlalolini D.

AU - Aoustin Y.

AU - Chevallereau C.

PY - 2007

SP - 76

EP - 83

DO - 10.5220/0001628200760083