Reliable inspection of resident space objects requires trajectories that maximize sensing quality while respecting the stringent propellant and safety constraints of small inspector satellites. While prior work has explored trajectory planning for such missions, most approaches optimize the vehicle's translational path first and treat attitude control as a secondary consideration. This decoupling can be suboptimal when sensor pointing strongly influences the quality of information collected.
We formulate multi-spacecraft inspection as a multiphase six-degree-of-freedom (6-DOF) optimal control problem that simultaneously optimizes each inspector's translation and attitude trajectories. A differentiable visibility metric—incorporating surface-normal alignment, field-of-view constraints, range attenuation, and motion penalties—serves as a proxy for observation quality within the optimizer. Numerical simulations with up to three inspectors and up to 50 inspection points demonstrate that the algorithm produces coordinated, fuel-efficient, information-rich trajectories while ensuring collision avoidance.
We develop a differentiable visibility metric that considers surface-normal alignment, field-of-view constraints, distance attenuation, and motion penalties to quantify observation quality. This enables gradient-based optimization while ensuring realistic sensor constraints.
The approach models complete spacecraft motion using Clohessy-Wiltshire equations for translation and quaternion-based attitude dynamics. This allows simultaneous optimization of both translational and rotational trajectories.
The optimization balances control effort against information gain while enforcing safety constraints including collision avoidance and standoff distances. A warm-start strategy using 3-DOF solutions improves convergence.
We use pseudospectral methods with Legendre-Gauss transcription to solve the optimal control problem. The approach scales to multiple agents (N=3) and numerous inspection points (M=50).
Rapid transitions between optimal observation points for maximum information gain
Smooth, continuous movements prioritizing fuel efficiency over speed
Path color indicates spacecraft speed, inspection point colors show information density (darker = uninspected)
Dual spacecraft coordination with effective workspace partitioning
Three-agent swarm achieving comprehensive coverage with collision avoidance
Interactive Visualizations: Use mouse controls to rotate, zoom, and explore the 3D trajectory plots. Sensor body-frame axes: Red = x-axis (boresight), Blue = y-axis, Green = z-axis
CAMSAT 2025 • Accepted Oral Presentation
This work has been accepted as oral presentation for the IFAC CAMSAT 2025. The research presents novel contributions to multi-agent trajectory optimization for spacecraft inspection missions.
