Online reentry guidance algorithm based on trajectory analytical solutions

doi:10.23919/JSEE.2026.000089

Abstract

Abstract:

To enhance the real-time performance and accuracy of guidance command generation, we propose an online reentry guidance algorithm based on analytical solutions of the hypersonic glide trajectory (HGT). Initially, an altitude-velocity profile is designed in the longitudinal plane to satisfy both path and terminal constraints. Based on this profile, we derive analytical solutions for the flight path angle (FPA) and bank angle. Subsequently, by employing the Newton-Raphson method to linearize the reentry motion equations, analytical solutions for the latitude and heading angle are obtained. Furthermore, we introduce an improved particle swarm optimization (IPSO) algorithm to optimize the profile parameters. This approach significantly enhances the algorithm’s global convergence by narrowing the parameter optimization range and adaptively adjusting the inertia weight and cognitive factors. Finally, we present an online guidance algorithm that combines the HGT analytical solutions with the IPSO algorithm. This algorithm effectively achieves longitudinal and lateral guidance by continuously updating the altitude-velocity profile and bank angle symbol in real time. Simulation results demonstrate that the proposed algorithm is fast, efficient, accurate, and holds significant potential for broader application.

Key words: altitude-velocity profile, analytical solution, improved particle swarm optimization (IPSO), online reentry guidance

Weibo SUN, Ping MA, Xiaonan LI, Songyan WANG, Tao CHAO. Online reentry guidance algorithm based on trajectory analytical solutions[J]. Journal of Systems Engineering and Electronics, 2026, 37(3): 1002-1018.

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Example	ORME	ROME	HGT analytical solution
Example 1	$ 1 \times {10^{ - 1}} $	$ 6.1 \times {10^{ - 2}} $	$ 9.7 \times {10^{ - 3}} $
Example 2	$ 1.3 \times {10^{ - 1}} $	$ 5.8 \times {10^{ - 2}} $	$10.2 \times {10^{ - 3}}$
Example 3	$ 1.1 \times {10^{ - 1}} $	$ 6.1 \times {10^{ - 2}} $	$9.2 \times {10^{ - 3}}$

Example	Initial condition						Terminal condition
Example	${H_0}$/km	${V_0}$/(m/s)	${\lambda _0}$/(°)	${\phi _0}$/(°)	${\gamma _0}$/(°)	${\psi _0}$/(°)	${H_{\text{f}}}$/km	${V_{\text{f}}}$/(m/s)	${\lambda _{\text{f}}}$/(°)	${\phi _{\text{f}}}$/(°)	${\gamma _{\text{f}}}$/(°)	${R_{{\text{stogof}}}}$/km
Example 1	60	6800	0	0	−0.2	−60	30	2000	−53.3	31.65	−1	200
Example 2	68	6980	0	0	−0.1	70	28	2000	140	45	−2	200
Example 3	64	6000	0	0	−0.15	122	30	2000	134	−10	−2	200
Example 4	60	6200	0	0	−0.1	−120	28	2000	−110	−23	−2	200

Parameter	Value
$ t_{{\text{ci}}}^{{\text{max}}} $	20
${N_{\text{p}}}$	20
${w_1}$	0.1
${w_2}$	0.9
$c_1^0$	2
$c_2^0$	0.9

Example	$H\left( {{t_{\text{f}}}} \right)$/km	$V\left( {{t_{\text{f}}}} \right)$/(m/s)	$\lambda \left( {{t_{\text{f}}}} \right)$/(°)	$\phi \left( {{t_{\text{f}}}} \right)$/(°)	$\gamma \left( {{t_{\text{f}}}} \right)$/(°)	${R_{{\text{stogo}}}}\left( {{t_{\text{f}}}} \right)$/km
Example 1	30	2000	−51.98	32.24	−1	139.26
Example 2	28	2000	138.86	44.56	−2	101.32
Example 3	30	2000	134.33	−11.22	−2	138.86
Example 4	28	2000	−110	−23.60	−1.99	66

Algorithm	Best cost	Iterations number	Optimization time/s
IPSO	$2.3 \times {10^{ - 3}}$	18	1.6
BPSO	$7.0 \times {10^{ - 4}}$	44	5.3
ZPSO	$1.6 \times {10^{ - 2}}$	30	4.1