Understanding the final-state control from the standpoint of the model predictive control and its application to a three-dimensional trajectory control problem

Updating final-state control methods taking input constraints at final time into account (Adaptive flight trajectory design of fixed-wing UAVs)

“…In conventional researches, a huge control input often occurs at the final control time for numerical simulation results, which apply UFSC to the simulations (Hara, et al, 2019), (Hara, et al, 2020). Control inputs usually contain constraints, and it is not practical to provide huge control inputs in a short duration.…”

“…Takeuchi, Nakamura, Hara and Miyata, Journal of Advanced Mechanical Design, Systems, and Manufacturing, Vol.14, No.7 (2020) Figure 2 shows a dynamic system of the fixed-wing airplane. The system has a 12-dimensional variable state and a 4-dimensional input as follows (Roskam 1998), (Hara et al, 2020 Takeuchi, Nakamura, Hara and Miyata, Journal of Advanced Mechanical Design, Systems, and Manufacturing, Vol.14, No.7 (2020) Here, v x , v y , and v z are translation velocities, p, q, and r are angular velocities, , , and  are Euler angles, X, Y  , and Z  are airplane displacements from a target position,  a ,  e , and  r are the steering angles of the aileron, elevator, and rudder, respectively, and T is the thrust of a propeller. Y  and Z  denote the reference displacements that enable the airplane to enter the target point with a horizontal entry angle  e and vertical angle  e , as shown in Fig.…”

“…

Recently, the authors have also studied FSC and discussed its applications to the mid-air retrieval of low-speeddescent objects by a fixed-wing airplane (Hara, et al, 2019), (Hara, et al, 2020). However, the dynamics of a fixed-wing airplane contain nonlinear characteristics.

…”

Positioning and recovering of fixed-wing UAV using updating final-state control and adaptive nonstationary control

“…where 𝑣 , 𝑣 , 𝑣 are the speeds of 𝑥, 𝑦, 𝑧 for each axis direction, respectively, 𝑝, 𝑞, 𝑟 are the angular velocities of 𝑥, 𝑦, 𝑧, respectively, 𝜓, 𝜃, 𝜙 are the Euler angles, and 𝑋 is the displacement based on the earth-fixed coordinate system. The reference displacements 𝑌 and 𝑍 are variables introduced to enable the aircraft to reach the target point at the specified approach angles of 𝜓 and 𝜃 in the approach trajectory design (Hara et al, 2020). The control inputs were the aileron, elevator, and rudder steering angles represented by 𝛿 , 𝛿 , 𝛿 , respectively, and the thrust from the propeller T.…”

“…However, it is difficult to control the drop point during low-speed descents resulting in concerns regarding the risk of accidents owing to insufficient deceleration, and adverse environmental effects owing to improper disposal of unrecovered objects (Ministry of Land, Infrastructure, Transport and Tourism, 2021). To solve these problems, we proposed a control method for the aerial recovery of low-speed descent objects using fixed-wing unmanned aerial vehicles (UAVs) (Hara and Yokoo, 2018;Hara et al, 2020;Nakamura et al, 2020;Takeuchi et al, 2020). The aim of this study is to develop a flight trajectory generation method that uses an updating final-state control (UFSC) (Yoshiura and Hara, 2014;Yoshiura et al, 2015) to handle variations in the termination target state until the object is recovered.…”