Abstract: Traditional optimal control trajectory planning algorithms take precise landing against the wind and low energy consumption as the optimization objectives. However, the control process is usually a continuous curve, which is difficult to implement in engineering. Though the traditional multiphase trajectory planning algorithm can achieve the goal of precise upwind landing with a simple control process, the control energy consumption is large. To balance the objectives of precise upwind landing, low energy consumption, obstacle avoidance, and simple control operations, an optimal segment constant trajectory planning algorithm for parafoil systems based on the gradient descent method is proposed in this paper. In this algorithm, the control variable is parameterized, and the multi-objective optimization problems such as precise upwind landing, low control energy consumption and obstacle avoidance are transformed into weighted single objective optimization problems, and the optimal problem is solved using the gradient descent method. This paper further compares the proposed trajectory planning algorithm, the Gaussian pseudo-spectral optimal control trajectory planning algorithm, and the genetic multiphase trajectory planning algorithm, showing that the proposed optimal segment constant trajectory planning algorithm can achieve high landing precision, low control energy consumption, upwind landing and obstacle avoidance, with the control value being segment constant, which is easy to implement in engineering.

Key words: parafoil systems, trajectory planning, optimal control, multiphase homing, segment constant, obstacle avoidance