TinySDP (Robotics: Science and Systems 2026)

Real-time semidefinite optimization for certifiable edge robotics.

TinySDP extends TinyMPC with small structured semidefinite relaxations, enabling obstacle-aware MPC to run onboard resource-constrained robots such as the Crazyflie 2.1 Brushless.

✅ Runs onboard at 25 Hz
✅ Supports PSD-relaxed obstacle avoidance
✅ Static-memory embedded implementation
✅ Hardware demos on Crazyflie

Why TinySDP?

Robots running on small processors usually cannot afford generic semidefinite programming. TinySDP keeps the optimization structure small and fixed, so certifiable obstacle-aware control can run in real time without dynamic memory allocation or desktop-class hardware.

This repository contains the reusable C++ solver in include/solver and src/solver, plus three standalone TinySDP examples:

• ushape_demo: closed-loop 2D U-shape obstacle avoidance with rank-1 certificate logging
• sweeping_gate_3d_demo: 3D sweeping gate
• rising_gate_3d_demo: 3D rising gate

Benchmarks

In the dynamic moving-gap benchmark, TinySDP maintains safety with a final goal distance of 0.018, while zero-margin TinyMPC-LIN and TinyMPC-HOCBF collide.

Method	Goal distance	Safe
TinySDP (ours)	0.018	✓
RPCBF	0.069	✓
TinyMPC-LIN (m=1.5m)	0.023	✓
TinyMPC-LIN (m=0m)	—	✗
TinyMPC-HOCBF (m=3m)	0.077	✓
TinyMPC-HOCBF (m=0m)	—	✗

For more information, visit the project page.

Dependencies

• CMake 3.15 or newer
• A C++17 compiler
• Eigen 3
• Matplotlib for plotting example outputs

On macOS with Homebrew:

brew install eigen cmake
python -m pip install matplotlib

Quick Start

cmake -S . -B build
cmake --build build

Run the demos:

./build/examples/ushape_demo
./build/examples/sweeping_gate_3d_demo
./build/examples/rising_gate_3d_demo

Example CSV outputs are written to outputs/ by default. Set TINYSDP_OUTPUT_DIR=/path/to/output to write them elsewhere.

The U-shape demo defaults to the inside-the-cul-de-sac start. Other starts are available with:

./build/examples/ushape_demo --start edge_up
./build/examples/ushape_demo --start edge_down
./build/examples/ushape_demo --start outside_center
./build/examples/ushape_demo --start above
./build/examples/ushape_demo --start below

Plot any generated trajectory CSVs:

python scripts/plot_examples.py

The plotting script scans outputs/ and writes trajectory PNGs to outputs/plots/. Use --input-dir or --output-dir to override those paths.

Project Layout

• include/solver: public solver headers
• src/solver: solver implementation
• examples: TinySDP-only demos
• scripts: plotting and utility scripts
• assets: README media

Getting Help

Open a GitHub issue for bugs, build problems, or questions about the examples.

Citation

If you use our code, please cite:

@inproceedings{mahajan2026tinysdp,
  title={TinySDP: Real Time Semidefinite Optimization for Certifiable and Agile Edge Robotics},
  author={Ishaan Mahajan and Jon Arrizabalaga and Andrea Grillo and Fausto Vega and James Anderson and Zachary Manchester and Brian Plancher},
  booktitle={Robotics Science and Systems (RSS)},
  address = {Sydney, Australia},
  month={July},
  year = {2026}
}

Maintainers

TinySDP is maintained by the Accessible and Accelerated Robotics Lab (A²R Lab).