## 8 Conclusions  
In this paper, a multiobjective optimization approach is proposed using the improved NSGA-II algorithm. This approach considers various constraints and flight states during the FPTLIR flight missions, using the derived energy consumption model as the objective function. The main objective is to minimize the energy consumption of the system and ensure the shortest mission execution time under corresponding energy consumption, while satisfying the constraints. 1. A mathematical model of system-level energy consumption was derived. The relationship between the mission path and energy consumption of the FPTLIR was established by progressively deriving from the FPTLIR kinematics to end-effector motor dynamics, making the model more suitable for constructing the multiobjective optimization model. The incorporation of the blade unit theory and aerodynamic analysis improved the accuracy of the energy consumption model. The prediction accuracy of the energy consumption model is further improved by using a self-built test platform to measure and fit the energy consumption model parameters. After experimental validation in different paths and flight states, the model showed good performance with an average relative error ranging from 0.76% to 3.24% compared to actual power predictions;
2. A multiobjective optimization model was constructed based on the energy consumption model, considering energy consumption and execution time under the flight mission path. The adaptability to real mission requirements was improved by quantifying the stability, safety, and other relevant constraints of the FPTLIR during mission execution, along with integrating the analysis of energy consumption in complex flight states;
3. An optimization approach based on the improved NSGA-II algorithm was proposed to optimize the energy consumption and mission execution time of the FPTLIR during flight missions. The NSGA-II optimization algorithm was improved by incorporating the Cauchy variation operator and integrating the principles of simulated annealing, thereby improving its robustness and local search capability in complex constraint scenarios. The optimal energy consumption for completing the on-line mission in the shortest time of 8.22 s was determined as 1.3750 \(\times\) 10\({}^{5}\) J. Following optimization, the shortest total time for completing the on-line mission with the lowest energy consumption of 1.3017 \(\times\) 10\({}^{5}\) J was determined as 17.77 s, saving 5.33% of energy consumption. Similarly, for completing off-line missions within a minimal timeframe of 9.84 s, the optimal energy consumption was found to be 1.3667 \(\times\) 10\({}^{5}\) J. After optimization, the shortest time for completing the off-line mission was 28.78 s with the minimum energy consumption of 1.2983 \(\times\) 10\({}^{5}\) J, saving 5.01% of energy consumption. The proposed optimization approach effectively minimized energy consumption while ensuring minimal mission execution times at corresponding energy consumption levels, thereby improving the overall system flight efficiency. Conceptualization, Y.W., W.J. and J.L. ; methodology, Y.W., X.Q., W.J. and J.L. ; software, Y.W., X.Q. and W.J. ; validation, Y.W., X.Q., W.J., D.W. and T.F. ; formal analysis, Y.W. and T.F. ; investigation, Y.W., W.J., J.L. and T.F. ; resources, Y.W., Y.Z. and J.S. ; data curation, Y.W., W.J., J.L. and D.W.; writing--original draft preparation, Y.W., W.J. and J.L. ; writing--review and editing, Y.W. and J.L. All authors have read and agreed to the published version of the manuscript. Funding: This study was supported by the Financial Science and Technology Program of the XPCC (grant nos. 2022 CB002-07 and 2022 CB011) and the National Natural Science Foundation of China (grant nos. 62063030 and 62163032). Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: Data is contained within the article. Conflicts of Interest: The authors declare no conflicts of interest.