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

2026-05-13

AI Summary

This work addresses the high computational complexity of existing semidefinite programming (SDP) solvers, which hinders real-time motion planning on embedded systems. The authors propose TinySDP—the first real-time SDP solver tailored for embedded platforms—by integrating a cached Riccati-based ADMM algorithm with an efficient positive semidefinite cone projection and introducing a post-hoc rank-1 certificate to convert relaxed solutions into geometrically verifiable trajectories. This approach enables, for the first time, real-time SDP optimization with non-convex obstacle constraints on embedded hardware while providing certifiable geometric safety guarantees. Experimental results demonstrate that TinySDP achieves millisecond-scale solve times on a Crazyflie quadrotor, reducing path length by up to 73% compared to state-of-the-art methods and significantly enhancing both real-time performance and navigation agility.

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) 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 semidefinite constraints can be enforced at real-time rates for agile embedded robotics.

Problem

• semidefinite programming
• real-time control
• embedded systems
• nonconvex constraints
• motion planning

Innovation

• semidefinite programming
• embedded optimization
• real-time MPC
• ADMM solver
• certifiable robotics