Constrained Near Optimal Path in Powered Descent Planetary Pinpoint Landing via Bezier Curves

Document Type : Original Article

Authors
Amirreza Kosari 1
S. Aliakbar Razavi 1
Hadi Jalili 2
1 University of Tehran
2 Iranian space Research Center
10.22034/jssta.2026.552402.1269
Abstract
This study addresses constrained and optimized offline trajectory generation for the powered descent phase of planetary landing by formulating as an optimal control problem. The descent trajectory is subject to multiple mission constraints, including terrain and obstacle avoidance as well as bounded thrust capabilities. To generate a smooth collision-free trajectory, the position states and time are first parameterized using fifth-degree Bézier curves, then the governing dynamic equations and constraints are discretized. Within the proposed framework, the Bézier control points serve as dynamic waypoints that simultaneously shape the trajectory while satisfying both terminal and path constraints. A Genetic Algorithm (GA) is then employed to optimize the Bézier control points and obtain the optimal descent trajectory. To validate the proposed approach, the generated trajectories are compared with those obtained using the improved Zero-Effort-Miss/Zero-Effort-Velocity (ZEM/ZEV) guidance law and the two-phase ZEM/ZEV feedback guidance method. The simulation results demonstrate that the Bézier-based approach produces smoother collision-free trajectories without the trial-and-error tuning typically required by ZEM/ZEV-based methods, while simultaneously achieving accurate pinpoint landing at the desired target location.
Keywords
Planetary Landing
Path Constraint Maneuver
Obstacle Avoidance
Bezier Curve
Genetic Algorithm
Subjects
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Space Science, Technology and Applications
Volume 6, Issue 1
September 2026
Pages 161-171

  • Receive Date 13 October 2025
  • Revise Date 11 August 2026
  • Accept Date 09 September 2026