# A QUADRATIC PROGRAMMING APPROACH TO THE MINIMUM ENERGY PROBLEM OF A MOBILE ROBOT

### Alain Segundo Potts, José Jaime da Cruz, Reinaldo Bernardi

#### Abstract

As a consequence of physical constraints and of dynamical nonlinearities, optimal control problems involving mobile robots are generally difficult ones. Many algorithms have been developed to solve such problems, the more common being related to trajectory planning, minimum-time control or any specific performance index. Nevertheless optimal control problems associated to mobile robots have not been reported. Minimum energy problems subject to both equality and inequality constraints are generally intricate ones to be solved using classical methods. In this paper we present an algorithm to solve it using a Quadratic Programming approach. In order to illustrate the application of the algorithm, one practical problem was solved.

#### References

- Abderrahim, M., Balaguer, C., Gimenez, A., Pastor, J. M., Padrón, V. M., 1999. ROMA: A Climbing Robot for Inspection Operations. In, Proceedings of the IEEE International Conference on Robotics and Automattion, Vol 3, pp 10-15.
- Armada, M., Santos, P. G. de, Jiménez, M. A., Prieto, M. 2003. Application of CLAWAR Machines. In, The International Journal of Robotics Research. Vol. 22, nº3-4, pp. 251-264.
- Avriel, M, 1976. Nonlinear Programming. Analysis and Methods. Prentice-Hall. New Jersey, 1st edition.
- Bernardi, R., Cruz, J.J. 2006. KAMANBARÉ. A treeclimbing biomimetic robotic platform for environmental research. In, International Conference on Informatics in Control, Automation and Robotics.
- Bobrow, J.E., Park, F.C., Sideris, A. 2004. Recent Advances on the Algorithmic Optimization of Robot Motion. Departament of Mechanical and Aerospace Engineering, University of California.
- Dudek, G., Jenkin, M., 2000. Computational Principles of mobile Robotics. Cambridge Press. 1st edition.
- Galvez, J. A., Santos, P. G. de, Pfeiffer, F., 2001. Intrinsic Tactile Sensing for the Optimization of Force Distribution in a Pipe Crawling Robot. In, IEEE/ASME Transactions on Mechatronics, Vol. 6, n°1.
- Garg, D. P., Kumar, M., 2002. Optimization Thecniques applied to multiple manipulators for path planning and torque minimization. In Eng. Applications Art, Int., Vol 15, pp 241-252.
- Kirk, D., 1998. Optimal Control Theory an Introduction. Dover Publication, New York, 2nd edition.
- Lin, Ch., Chang P., Luh, J.Y.S. 1983 Formulation and Optimization of Cubic Polynomial Joint Trajectories for Industrial Robots. In IEEE Transactions on Automatic Control, Vol AC-28, No 12, December.
- Luk, B., Cooke, D., Galt, S., Collie, A., Chen, S. 2005. Intelligent legged climbing service robot for remote Maintenance applications in hazardous environments. In Robotics and Autonomous Systems. Accepted June 2005.
- Luo, X., Fan, X., Zhang, H., Chen T., 2004. Integrated Optimization of Trajectories Planning for Robots Manipulators Based on Intensified Evolutionary Programming. Proceedings of the 2004 IEEE, International Conference on Robotics and Biomimetics.
- Saundersa, A., Goldmanb, D., Fullb,R., Buehlera, M. 2006. The RiSE Climbing Robot: Body and Leg Design. In, Proceeding of SPIE, Vol. 6230, 623017.
- Spong, M., Vidyasagar, M., 1989. Robot Dynamics and Control. John Wiley & Sons, Canada, 1st edition.
- Virk, G. S. 2005. The CLAWAR Project: Developments in The Oldest Robotics Thematic Network. IEEE Robotics & Automation Magazine, pp. 14-20.
- Winston, W. 1995. Introduction to Mathematical Programming. Applications and Algorithms. Duxbury Press. California, 2nd edition.

#### Paper Citation

#### in Harvard Style

Segundo Potts A., Jaime da Cruz J. and Bernardi R. (2008). **A QUADRATIC PROGRAMMING APPROACH TO THE MINIMUM ENERGY PROBLEM OF A MOBILE ROBOT** . In *Proceedings of the Fifth International Conference on Informatics in Control, Automation and Robotics - Volume 2: ICINCO,* ISBN 978-989-8111-31-9, pages 245-251. DOI: 10.5220/0001499102450251

#### in Bibtex Style

@conference{icinco08,

author={Alain Segundo Potts and José Jaime da Cruz and Reinaldo Bernardi},

title={A QUADRATIC PROGRAMMING APPROACH TO THE MINIMUM ENERGY PROBLEM OF A MOBILE ROBOT},

booktitle={Proceedings of the Fifth International Conference on Informatics in Control, Automation and Robotics - Volume 2: ICINCO,},

year={2008},

pages={245-251},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0001499102450251},

isbn={978-989-8111-31-9},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the Fifth International Conference on Informatics in Control, Automation and Robotics - Volume 2: ICINCO,

TI - A QUADRATIC PROGRAMMING APPROACH TO THE MINIMUM ENERGY PROBLEM OF A MOBILE ROBOT

SN - 978-989-8111-31-9

AU - Segundo Potts A.

AU - Jaime da Cruz J.

AU - Bernardi R.

PY - 2008

SP - 245

EP - 251

DO - 10.5220/0001499102450251