A computational-geometry-based 3-dimensional guidance law to control impact time and angle

Distributed Analytical Formation Control and Cooperative Guidance for Gliding Vehicles

“…where _ y d is the desired change rate of altitude of a HGV. Under the control law (20), y i can achieve consensus asymptotically and _ y i can asymptotically converge to _ y d . The actual control inputs in formation are the angle of attack α i and bank angle σ i .…”

“…The actual control inputs in formation are the angle of attack α i and bank angle σ i . α i and σ i are implicit in the terms D i , L i cos σ i , L i sin σ i in the left side of equations (18) and (20). In other words, equations (18) and (20) are nonlinear functions of two independent variables about α i and σ i .…”

“…α i and σ i are implicit in the terms D i , L i cos σ i , L i sin σ i in the left side of equations (18) and (20). In other words, equations (18) and (20) are nonlinear functions of two independent variables about α i and σ i . However, equations (18) and (20) cannot be solved analytically and it is too complicated using numerical methods.…”

“…First, calculate the drag accelerations D i using the angle of attack α i of the last guidance cycle. Then, L i cos σ i can be solved in the equation (20) with the calculated D i . After that, D i and L i cos σ i are known in equation 18, and L i sin σ i can be derived.…”

“…In open-loop cooperative guidance, which is also called time-constrained guidance, the expected time value has been determined before launching and no information interaction is needed between vehicles during the flight. Since Jeon et al [10] first proposed a time-constrained guidance law for antiship missiles in 2006, scholars have extensively studied open-loop cooperative guidance using different methods, such as improved proportional navigation [10][11][12], optimal control [13,14], sliding mode control [15][16][17], trajectory shaping [18][19][20], and trajectory optimization [9,21,22]. On the other hand, closed-loop cooperative guidance can be divided into centralized cooperative guidance and distributed cooperative guidance according to the different communication modes among vehicles.…”