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).

Funding Acknowledgement

This work was supported by the National Science Foundation (under Awards 2144634, 2231350, and 2411369) and by the Center of AI Technology (CAIT) in collaboration with Amazon. Any opinions, findings, conclusions, or recommendations expressed in this material are those of the authors and do not necessarily reflect those of the funding organizations.