基于罚函数序列凸规划的多无人机轨迹规划

多无人机（UAVs）轨迹规划是具有非线性运动约束和非凸路径约束的最优控制问题。引入序列凸规划思想，将非凸最优控制问题近似为一系列凸优化子问题，并利用成熟的凸优化算法进行求解，以更好地权衡最优性和时效性。首先，建立了多无人机协同轨迹规划的非凸最优控制模型。然后，利用离散化和凸近似方法将其转换为凸优化问题，包括对无人机运动模型的线性化，以及对威胁规避约束和无人机碰撞约束的凸化。同时，提出了一种离散点间的威胁规避方法，保证无人机在离散轨迹点间的飞行安全。在凸优化模型的基础上，给出了基于罚函数序列凸规划求解多无人机轨迹规划的具体框架。最后，通过数值仿真验证了方法的有效性，结果表明该方法在多机轨迹规划结果的最优性和时效性都要优于伪谱法，而且优势随编队数量的增加而增大。

Trajectory planning for multi-UAVs using penalty sequential convex pro-gramming

Trajectory planning of multiple unmanned aerial vehicles (UAVs) is an optimal control problem which subjects to nonlinear motion and nonconvex path constraints. Based on the sequential convex programming approach, such nonconvex optimal control is approximated to be a series of convex optimization subproblems, which can be solved by the state-of-the-art convex optimization algorithm. A good balance between solution quality and computational tractability can then be achieved. Nonconvex optimal control model for multi-UAV trajectory planning is formulated first, and is then approximated to be a convex optimization by discretization and convexification methods. To convexify the nonconvex model, equations of motion of UAVs are linearized, and constraints of threat avoidance and inter-UAVs collision avoidance are convexified. Meanwhile, an inter-sample threat avoidance method is provided to guarantee UAVs' safety at intervals between discrete trajectory points. Based on convex optimization formulation, the detailed procedure of using sequential convex programming based on penalty function to solve multi-UAV trajectory planning is provided. Numerical simulations are conducted to show the effectiveness of the proposed method. The results show that the method can acquire the solution with better optimality and efficiency than the pseudospectral method, especially for larger scale UAV formation.