**5. Conclusion**

This chapter presented a technique to generate a time-energy optimal trajectory for a cluster of mobile robots with predetermined paths. The method is uniquely applied in a parameter‐ ized formation state space and incorporates the nonlinear dynamics of the cluster and actuator constraints to enable intuitive optimal trajectory planning for time varying formations. Simulation results verified the generated trajectories and demonstrated the advantages of using a time-energy tunable objective function. The ability to choose more energy-efficient trajectories reduces the strain on actuator components and energy reserves, thereby promoting longevity in both. The tool in **Figure 9** also demonstrates that the operator has access to a substantial path-specific time/energy range, within which one must choose a missionappropriate combination.

We plan to incorporate several extensions to this work in the future. First, we will integrate cluster space obstacle avoidance [62] into the optimal trajectory-tracking controller. In addi‐ tion, we will develop cluster space velocity and acceleration bounds to include the charac‐ terization of a velocity limit curve as well as a phase plane description of the admissible range. With these bounds, which are a function of the cluster states and are therefore varia‐ ble in the choice of path, one could derive the time optimal cluster trajectory, approximated with small in the simulations of the previous section. We will also attempt to address prac‐ tical issues such as friction, gravity, and motor dynamics into the formulation in order to make the technique more applicable to a wide range of multirobot systems. Finally, we will experimentally verify and validate the technique with several existing multirobot experi‐ mental test beds, to include terrestrial rovers, surface and underwater marine vehicles, and aerial vehicles.
