Sequential Convex Program for Collision Avoidance Manoeuvres (SCP CAM)

A complete software framework for computing collision avoidance manoeuvres (CAMs) using Sequential Convex Programming (SCP). Handles single and multiple secondary objects in both short- and long-term conjunction scenarios across LEO and GEO orbits.

Overview

SCP CAM uses successive convexification to optimize trajectories that avoid collisions while minimizing fuel consumption. The system supports:

• Single and multiple secondary objects
• LEO and GEO orbits
• Short-term and long-term conjunctions
• Station-keeping and operational constraints
• Advanced environment models (atmosphere, SRP, third-body perturbations)

System Requirements

• MATLAB: R2022a or newer (tested up to R2025b)
• MOSEK: 10.0 (optimization solver)
• WSL (Ubuntu) with the following:
  • DACE (Differential Algebra Computational Engine)
  • CSPICE (Navigation Toolkit)
  • Astrotools (Astrodynamics library)
  • nlohmann-json3-dev
  • libeigen3-dev, libjsoncpp-dev, libdlib-dev

Installation

1. Install Dependencies

Run the dependency checker script on Windows:

check_deps.bat

This script automatically:

• Detects MOSEK installation
• Detects MATLAB installation
• Detects WSL installation
• Installs/verifies DACE in WSL
• Installs/verifies CSPICE
• Installs/verifies Astrotools and pre-requisites
• Installs/verifies JSON

Note: Ensure you have a valid MOSEK license before proceeding.

2. Build the Project

Run the build script:

build_scp.bat

This compiles the C++ backend using CMake within WSL and generates the necessary binaries.

Quick Start

1. Configure the scenario in userParams.m:

   up.orbit      = 'leo';              % or 'geo'
   up.scenario   = 'single-short';     % scenario type
   up.uMax       = 1e-8;               % max thrust [km/s²]
   up.iterMaxMaj = 10;                 % major iterations

2. Run the main script:

   main

3. View results via generated figures in postprocessing.

Configuration Files

userParams.m

User-facing parameters for scenario definition:

• Orbit selection (LEO/GEO)
• Scenario type (single/multiple, short/long-term)
• Discretization and time windows
• Propulsion limits
• Optimizer stopping criteria
• Environmental model flags

defaultParams.m

Internal defaults for:

• Orbital mechanics (GM constant)
• Objective weights
• NLI (nonlinear inequality) limits
• SMD gradient constraints
• Operational toggles

scenarioParams.m

Builds the unscaled scenario by merging user and default parameters, then:

• Generates initial orbits
• Sets up discretization and time grids
• Configures collision avoidance windows

scalingParams.m

Applies nondimensionalization and derives scaled limits.

simProperties.m

Master configuration function that orchestrates all parameter assembly and consistency checks.

High-Level Algorithm Flow

1. Initialize: Set up MATLAB path and load toolboxes
2. Configure: Assemble full configuration via simProperties()
3. Optimize: Run runSCP() for major-iteration loop with successive convexification
4. Validate: Check solution feasibility and constraint satisfaction
5. Postprocess: Generate visualizations and reports via mainPostProcess()

Output

• pp.majorIter: Per-iteration data (trajectories, costs, convergence metrics)
• Figures: Trajectory plots, risk profiles, state evolution (via selectFigs())
• Logs: Installation and build logs for troubleshooting

Troubleshooting

• MOSEK not found: Install MOSEK or verify license file location
• WSL user detection failed: Ensure Ubuntu WSL distribution is installed and accessible
• DACE/CSPICE build errors: Check install_log.txt for detailed error messages
• Astrotools missing: Verify source repository is available and re-run check_deps.bat

Author

Zeno Pavanello
E-mail: zeno.pavanello@polimi.it
Date: 2022–2026

Compatibility

• MATLAB R2022a–R2025b
• MOSEK 10.0
• Windows 10/11 with WSL2 (Ubuntu)
• GCC 64-bit (Linux backend)

Credits

If you use this work, please cite the following papers:

-Pavanello, Zeno, Laura Pirovano, and Roberto Armellin. ‘Long-Term Fuel-Optimal Collision Avoidance Maneuvers with Station-Keeping Constraints’. Journal of Guidance, Control, and Dynamics 47, no. 9 (2024): 1855–71. https://doi.org/10.2514/1.G007839.

-Pavanello, Zeno, Laura Pirovano, Roberto Armellin, Andrea De Vittori, and Pierluigi Di Lizia. ‘Collision Avoidance Maneuvers Optimization in the Presence of Multiple Encounters’. Journal of Guidance, Control, and Dynamics 49, no. 1 (2026): 130–48. https://doi.org/10.2514/1.G008332.