Robotics: Science and Systems XXII

TinySDP: Real Time Semidefinite Optimization for Certifiable and Agile Edge Robotics

Ishaan Mahajan, Jon Arrizabalaga, Andrea Grillo, Fausto Vega, Zac Manchester, James Anderson, Brian Plancher

Abstract:

Semidefinite programming (SDP) provides a principled framework for convex relaxations of nonconvex geometric constraints in motion planning, yet existing solvers are too computationally expensive for real-time control, particularly on resource-constrained embedded systems. To address this gap, we introduce TinySDP, the first semidefinite programming solver designed for embedded systems, enabling real-time model-predictive control (MPC) with formal safety guarantees on microcontrollers for problems with nonconvex obstacle constraints. Our approach integrates positive-semidefinite cone projections into a cached-Riccati-based ADMM solver, leveraging computational structure for embedded tractability. We pair this solver with an a posteriori rank-1 certificate that converts relaxed solutions into explicit geometric guarantees at each timestep. On challenging benchmarks, e.g., cul-de-sac and dynamic obstacle avoidance scenarios that induce failures in local methods, TinySDP achieves collision-free navigation with up to 73% shorter paths than state-of-the-art baselines. We validate our approach on a Crazyflie quadrotor, demonstrating that certifiable semidefinite constraints can be enforced at real-time rates for agile embedded robotics.

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Bibtex:

  
@INPROCEEDINGS{MahajanI-RSS-26, 
    AUTHOR    = {Ishaan Mahajan AND Jon Arrizabalaga AND Andrea Grillo AND Fausto Vega AND Zac Manchester AND James Anderson AND Brian Plancher}, 
    TITLE     = {{TinySDP: Real Time Semidefinite Optimization for Certifiable and Agile Edge Robotics}}, 
    BOOKTITLE = {Proceedings of Robotics: Science and Systems}, 
    YEAR      = {2026}, 
    ADDRESS   = {Sydney, Australia}, 
    MONTH     = {July}, 
    DOI       = {10.15607/RSS.2026.XXII.110} 
}