**Time-Energy Optimal Cluster Space Motion Planning for Mobile Robot Formations**

Kyle Stanhouse, Chris Kitts and Ignacio Mas

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/64615

### **Abstract**

The motions of a formation of mobile robots along predetermined paths are opti‐ mized according to a tunable time-energy cost function using the cluster space approach to multiagent system specification and control. Upon path-parameterizing cluster state variables describing the geometry and pose of a multirobot group, an optimal control problem is formulated that incorporates formation dynamics and state constraints. The optimal trajectory is derived numerically via a gradient search, iterating over the initial value of one costate. A multirobot formation control simulation is then used to demonstrate the effectiveness of the technique. Results indicate that a substantial tradeoff is made between energy expenditure and motion time when considered as minimization criteria in varying proportions, allowing the operator to tailor mission trajectories according to desired levels of each.

**Keywords:** time-energy optimization, motion planning, multirobot systems, cluster control
