5. Conclusion

The paper investigated the time-energy minimization onto the multi-robot case. A global objective function is formulated as the sum of individual robot objectives in time and energy. Constraints are divided into two sets, namely, robot-individual constraints and robots' interaction constraints. The problem is decomposed into L subproblems with L being the number of robot systems. The subproblems are coupled with each other by the collision avoidance information. Applying a distributed algorithm solved the problem iteratively. The overall output gives optimized motions for all robots in time and energy while adhering and not colliding with each other. We applied our approach to the case of three wheeled mobile robots: we generated in parallel for each robot an optimized control input trajectory.

An extension to this study is to generate optimized motion trajectories and apply them experimentally. A possible area for experimentation is full-scale autonomous vehicles. Issues related to communication and distributing information during the parallel algorithm will need to be incorporated and investigated. Also, aspects of state estimation and localization of the robot system will come into the place which were not considered in this work. A possible other investigation is to distribute the problem further onto the time variable k; this will lead the problem to the domain of distributed model predictive control. This will, possibly, pave the way to faster deployment into autonomous vehicles.

Author details

Canada

133

Giza, Egypt

Mohamad T. Shahab<sup>1</sup>

\* and Moustafa Elshafei<sup>2</sup>

Distributed Optimization of Multi-Robot Motion with Time-Energy Criterion

DOI: http://dx.doi.org/10.5772/intechopen.85668

\*Address all correspondence to: m4shahab@uwaterloo.ca

provided the original work is properly cited.

1 Department of Electrical and Computer Engineering, University of Waterloo, ON,

2 Zewail City of Science and Technology, October Gardens, 6th of October City,

© 2019 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium,

## Acknowledgements

The authors would like to thank King Fahd University of Petroleum and Minerals supporting this work.

Distributed Optimization of Multi-Robot Motion with Time-Energy Criterion DOI: http://dx.doi.org/10.5772/intechopen.85668
