Sonar detection is a cornerstone capability in anti-submarine warfare, where the remote and accurate deployment of sensing devices must be completed within the shortest possible time. To this end, this paper proposes a missile-based concept for delivering a deployable sonar device and develops a three-dimensional adaptive guidance law with fixed-time convergence. To reduce the impact kinetic energy at water entry and to deploy the deployable sonar device with a prescribed attitude, constraints on the impact velocity and impact angle are explicitly imposed. To avoid the range unreachability induced by deceleration-based guidance laws and to prevent excessive flight time, a two-phase guidance strategy with smooth switching is devised along the line-of-sight direction. To further enhance the stability of the guidance process, an adaptive term is incorporated into the double-power reaching law to alleviate the acceleration saturation that may occur during the initial guidance stage. Simulation results demonstrate that, under the proposed guidance law, the missile can accurately reach the target with the desired impact velocity and impact angle, while alleviating early-stage acceleration saturation and effectively reducing the load on the onboard actuators. Consequently, this study provides a feasible solution for delivering the deployable sonar device with favorable maneuverability and flexible deployment capability, and it shows certain potential in adapting to different meteorological conditions, reducing reliance on real-time human intervention, and improving missions execution efficiency.
Citation: Jian Huang, Zhanpeng Gao, Jun Liu, Wenjun Yi. Three-dimensional adaptive guidance law for a missile delivering a deployable sonar device under impact velocity and angle constraints[J]. AIMS Mathematics, 2026, 11(5): 12500-12533. doi: 10.3934/math.2026514
Sonar detection is a cornerstone capability in anti-submarine warfare, where the remote and accurate deployment of sensing devices must be completed within the shortest possible time. To this end, this paper proposes a missile-based concept for delivering a deployable sonar device and develops a three-dimensional adaptive guidance law with fixed-time convergence. To reduce the impact kinetic energy at water entry and to deploy the deployable sonar device with a prescribed attitude, constraints on the impact velocity and impact angle are explicitly imposed. To avoid the range unreachability induced by deceleration-based guidance laws and to prevent excessive flight time, a two-phase guidance strategy with smooth switching is devised along the line-of-sight direction. To further enhance the stability of the guidance process, an adaptive term is incorporated into the double-power reaching law to alleviate the acceleration saturation that may occur during the initial guidance stage. Simulation results demonstrate that, under the proposed guidance law, the missile can accurately reach the target with the desired impact velocity and impact angle, while alleviating early-stage acceleration saturation and effectively reducing the load on the onboard actuators. Consequently, this study provides a feasible solution for delivering the deployable sonar device with favorable maneuverability and flexible deployment capability, and it shows certain potential in adapting to different meteorological conditions, reducing reliance on real-time human intervention, and improving missions execution efficiency.
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Jian Huang, Zhanpeng Gao, Jun Liu, Wenjun Yi. Three-dimensional adaptive guidance law for a missile delivering a deployable sonar device under impact velocity and angle constraints[J]. AIMS Mathematics, 2026, 11(5): 12500-12533. doi: 10.3934/math.2026514
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