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

An Integrated Real-time UAV Trajectory Optimization with Potential Field Approach for Dynamic Collision Avoidance