# Sequential Convex Programming for Nonlinear Optimal Control in UAV Trajectory Planning
## 3 Problem Formulation
### Sequential Convex Programming
Since the control effort was minimized, these trajectories are the shortest possible trajectories under the collision avoidance constraints. The simulation results show that, in different scenarios, this method can generate collision-free trajectories from the beginning point to the target point. Furthermore, the simulation results demonstrate the computational effort, and the performance indicates that this algorithm can be used in real-life applications with well-tuned hyper-parameters. These collision-free trajectories can be generated online. Conceptualization, Q.Z. and Y.L. ; methodology, Y.L. and Q.Z. ; software, Y.L. and A.E. ; validation, Y.L. and A.E. ; formal analysis, Y.L. ; investigation, Y.L. ; resources, Q.Z. ; writing-original draft preparation, Y.L. ; writing-review and editing, Y.L. and A.E. ; visualization, Y.L. ; supervision, Q.Z. ; project administration, Q.Z. ; funding acquisition, Q.Z. All authors have read and agreed to the published version of the manuscript. This research received no external funding. Data are contained within the article. The authors declare no conflicts of interest. ## References

* [PERSON] et al. (2012) [PERSON]; [PERSON] [PERSON]; [PERSON] [PERSON]; [PERSON] Versatile distributed pose estimation and sensor self-calibration for an autonomous MAV. In Proceedings of the IEEE International Conference on Robotics and Automation, Saint Paul, MN, USA, 14-18 May 2012; pp. 31-38. * [PERSON] et al. (2007) [PERSON]; [PERSON]; [PERSON]; [PERSON] A prototype of an autonomous controller for a quadrotor UAV. In Proceedings of the European Control Conference, Kos, Greece, 2-5 July 2007; pp. 1-8. * [PERSON] et al. (2010) [PERSON]; [PERSON]; [PERSON]; [PERSON] [PERSON] A simple learning strategy for high-speed quadrocopter multi-flips. In Proceedings of the IEEE International Conference on Robotics and Automation, Anchorage, AK, USA, 3-7 May 2010; pp. 1642-1648. * [PERSON] et al. (2009) [PERSON]; [PERSON] [PERSON]; [PERSON]; [PERSON] [PERSON] Coordination of helicopter UAVs for aerial forest-fire surveillance. In _Applications of Intelligent Control to Engineering Systems; Intelligent Systems, Control, and Automation: Science and Engineering;_ Springer: Dordrecht, The Netherlands, 2009; Volume 39. [CrossRef]
* [PERSON] (2011) [PERSON] Autonomous Quadrotor Unmanned Aerial Vehicle for Culvert Inspection. Ph.D. Dissertation, Massachusetts Institute of Technology, Cambridge, MA, USA, 2011. \[s.t.f_{i}(x)\leq 0,\forall i=1,2,\ldots,m\]5 Objective value plotted against the number of iterations. * (6) [PERSON]; [PERSON]; [PERSON] Generation of collision-free trajectories for a quadrocopter fleet: A sequential convex programming approach. In Proceedings of the 2012 IEEE /RSJ International Conference on Intelligent Robots and Systems, Vilamoura-Algarve, Portugal, 7-12 October 2012; IEEE: Piscataway, NJ, USA, 2012; pp. 1917-1922. * (7) [PERSON]; [PERSON] Trajectory generation for multiagent point-to-point transitions via distributed model predictive control. _IEEE Robot. Autom. Lett._**2019**, \(4\), 375-382. [CrossRef]
* (8) [PERSON]; [PERSON]; [PERSON] Decoupled multiagent path planning via incremental sequential convex programming. In Proceedings of the 2015 IEEE International Conference on Robotics and Automation (ICRA), Seattle, WA, USA, 26-30 May 2015; pp. 5954-5961. * (9) [PERSON]; [PERSON]; [PERSON] Geometric tracking control of a quadrotor UAV on SE(3). In Proceedings of the 49 th IEEE Conference on Decision and Control (CDC), Atlanta, GA, USA, 15-17 December 2010; pp. 5420-5425. * (10) [PERSON]; [PERSON] Minimum snap trajectory generation and control for quadrotors. In Proceedings of the 2011 IEEE International Conference on Robotics and Automation, Shanghai, China, 9-13 May 2011; pp. 2520-2525. * (11) [PERSON]; [PERSON]; [PERSON] _Introduction to Autonomous Mobile Robots_; MIT Press: Cambridge, MA, USA, 2011. * (12) [PERSON]; [PERSON]; [PERSON]; [PERSON] Applications of hybrid reachability analysis to robotic aerial vehicles. _Int. J. Robot. Res._**2011**, _30_, 335-354.