Sliding mode guidance for impact time and angle constraints

Abstract

This paper proposes a guidance strategy, which caters to both impact angle and impact time terminal constraints. This guidance scheme is based on switching between impact time and impact angle guidance laws. Unlike the existing impact time guidance laws, the proposed guidance strategy takes into account the curvature of the trajectory due to requirement of impact angle. The guidance law is derived using sliding mode control theory with the switching surface based on impact time error. The interceptor first corrects its course to nullify the impact time error and then aims to achieve interception with desired impact angle. In order to reduce transitions between the two guidance laws, a novel hysteresis loop is introduced in the switching conditions. The guidance law is initially designed for stationary targets, and later it is extended to constant velocity targets using the notion of predicted interception point. In order to validate the efficacy of the proposed guidance strategy, simulation results are presented with constant as well as realistic time-varying speed interceptor models for different engagement scenarios against stationary and constant velocity targets. The performance of the guidance law is evaluated under noisy measurements and the presence of system lag and its performance is compared with other existing guidance laws.

Three-dimensional cooperative guidance law to control impact time and angle with fixed-time convergence

“…Theorem 2. Consider equation (21) with fixed-time NFTSM surface (22) and feedback control law (25), the LOS angles of multiple missiles can reach the corresponding setting angles within fixed-time, and the settling time T 2 is bounded by…”

“…Remark 5. Similarly, the new designed disturbance observer is adopted to attenuate or eliminate the chattering effect caused by the high-frequency switching term δ q signðs i Þ in equation (25), and this term is replaced by the disturbance observation vector b d q i . In addition, to satisfy the impact angle constraint before interception (i.e., T max 2 ≤ T max 1 ), the parameters of this guidance law (i.e., α, β, γ j and k 1 , k 2 , a j with j ¼ 1; 2) might be increased.…”

“…Thereafter, the shaping process idea was adopted by an augmented polynomial guidance law in Kim et al, 24 where the intercept trajectory and acceleration command profile were shaped to obtain the arbitrary guidance gains and implement the zero-miss distance as well as the impact time and angle constraints. Another SM guidance law was shown by Kumar and Ghose, 25 where a new control frame was proposed to enable that any existing guidance law with impact time constraint can be easily extended to control both of the impact time and angle. Exactly, the guidance law with impact time constraint was designed first; then the required time-to-go value was estimated by the formula that included the desired impact angle.…”

Integrated impact time guidance and control against non-maneuvering targets

“…In the last decade, several works addressed the problem of achieving target interception at desired impact time using various control techniques. [1][2][3][4][5][6][7][8][9][10][11][12] The variants of proportional navigation (PN) guidance were proposed in Refs. [1][2][3] to control impact time along with the target interception.…”

Impact Time Control Cooperative Guidance Law Design Based on Modified Proportional Navigation

“…The impact time and angle control guidance (ITACG) law has received attention recently when the impact angle constraint is also considered [22][23][24][25][26][27]. In [22,23], based on the impact angle control guidance law introduced in [24], an impact time control guidance law was proposed based on the sliding mode theory, as well as the design of a switching logic path. The guidance law converted between impact angle control guidance law and the impact time control guidance law according to the size of impact time error.…”