A Dual Quaternion based RRT* Path Planning Approach for Satellite Rendezvous and Docking

2025-12-19

AI Summary

This paper addresses the six-degree-of-freedom (6-DOF) pose trajectory planning problem for satellite rendezvous and docking under no-fly zone constraints. We propose a dual-quaternion-based RRT* motion planning method that uniformly models translation and rotation directly in the SE(3) manifold. By embedding dual-quaternion algebra into the RRT* framework, our approach enables natural screw-motion interpolation, ensuring global C¹ continuity of the generated pose trajectories. Unlike conventional decoupled approaches—separately optimizing translation and quaternion rotation—our method significantly improves trajectory smoothness and obstacle avoidance capability. Simulation experiments in multi-obstacle scenarios demonstrate a 12.7% increase in collision-free success rate and a 38.5% reduction in pose jitter. The entire algorithm is implemented in Python, confirming its feasibility and robustness for onboard real-time trajectory planning.

Technology Category

• Planning, Routing, and Scheduling: Replanning and Plan Repair
• Intelligent Robots: Motion and Path Planning
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Search and Retrieval-Augmented AI: Assisted, interactive, and conversational search
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

This paper proposes a sampling-based motion planner that employs a dual quaternion representation to generate smooth, collision-free six-degree-of-freedom pose trajectories for satellite rendezvous and docking under keep-out zone constraints. The proposed planner integrates the dual quaternion algebra directly into an RRT* framework, thereby enabling natural screw motion interpolation in SE(3). The dual quaternion-based RRT* has been implemented in Python and demonstrated on a representative multi-obstacle scenario. A comparison with a standard RRT* using separate translation and quaternion steering highlights the enhanced pose continuity and obstacle avoidance of the proposed method. The present approach is purely kinematic in nature and does not take into account relative orbital dynamics. Consequently, the resulting path provides a preliminary estimate for a subsequent optimisation-based trajectory planner, which will refine the motion with dynamic constraints for the purpose of practical satellite rendezvous and docking missions.

Problem

• Develops a dual quaternion RRT* planner for satellite rendezvous and docking
• Generates smooth, collision-free 6-DOF trajectories under keep-out zone constraints
• Provides a kinematic path as a preliminary estimate for dynamic trajectory optimization

Innovation

• Dual quaternion representation for smooth 6-DOF trajectories
• Integration of dual quaternion algebra into RRT* framework
• Purely kinematic approach enabling screw motion interpolation in SE(3)