This paper presents an integrated approach that combines trajectory optimization and Artificial Potential Field (APF) method for real-time optimal Unmanned Aerial Vehicle (UAV) trajectory planning and dynamic collision avoidance. A minimum-time trajectory optimization problem is formulated with initial and final positions as boundary conditions and collision avoidance as constraints. It is transcribed into a nonlinear programming problem using Chebyshev pseudospectral method. The state and control histories are approximated by using Lagrange polynomials and the collocation points are used to satisfy constraints. A novel sigmoid-type collision avoidance constraint is proposed to overcome the drawbacks of Lagrange polynomial approximation in pseudospectral methods that only guarantees inequality constraint satisfaction only at nodal points. Automatic differentiation of cost function and constraints is used to quickly determine their gradient and Jacobian, respectively. An APF method is used to update the optimal control inputs for guaranteeing collision avoidance. The trajectory optimization and APF method are implemented in a closed-loop fashion continuously, but in parallel at moderate and high frequencies, respectively. The initial guess for the optimization is provided based on the previous solution. The proposed approach is tested and validated through indoor experiments.

翻译：本文提出了一种集成轨迹优化与人工势场法（APF）的无人机实时最优轨迹规划与动态避障方法。以初始位置和终止位置为边界条件、避障为约束条件，构建了最小时间轨迹优化问题。利用切比雪夫伪谱法将该问题转化为非线性规划问题，通过拉格朗日多项式近似状态变量和控制变量，并采用配点法满足约束条件。针对伪谱法中拉格朗日多项式近似仅能保证节点处不等式约束成立的缺陷，提出了一种新型S形避障约束函数。采用自动微分技术快速求解代价函数的梯度与约束条件的雅可比矩阵，并利用APF方法更新最优控制输入以保证避障性能。轨迹优化与APF方法以闭环方式连续执行，分别以中等频率和高频率并行运行，优化初始值由前次解提供。通过室内实验对所提方法进行了测试与验证。