A general real-time optimization framework for polynomial-based trajectory planning of autonomous flying robots

This paper presents a general real-time, numerically stable optimization framework for time polynomial-based trajectory generation of autonomous aerial robots. The proposed general optimization framework (GOF) allows various optimization criteria for trajectory generation cost-function, such as minimizing the trajectory total length, time, and position derivatives. Minimizing position derivatives includes velocity, acceleration, jerk, and snap, or any combination of them. This study considers the quadrotor as the test platform. By exploiting tools from the calculus of variations, differential flatness property, and polynomial-based trajectories, the developed algorithm finds feasible trajectories without extensive computational sampling and iterative searching in the high-dimensional state space of quadrotor dynamics. The GOF includes a segment-wise gradient descent-like algorithm to iteratively decrease the allowed time of each segment individually so as to avoid getting stuck at a local minimum. The comparison analysis with existing methods validated the numerical stability and computational speed advantages of the proposed approach. It also shows that the algorithm is suitable for the real-time generation of high-performance long-range trajectories consisting of a large number of waypoints and high-order piecewise polynomials. An animated simulation of this work is available at https://youtu.be/E1AC1vyPqOE