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

TL;DR

TinySDP is a novel semidefinite programming solver optimized for embedded systems, enabling real-time, collision-free motion planning for edge robotics with explicit geometric guarantees.

Contribution

It introduces the first real-time SDP solver for embedded systems, integrating cone projections with a cached-Riccati ADMM approach for agile edge robotics.

Findings

Achieves up to 73% shorter collision-free paths in benchmarks.

Enables real-time semidefinite constraint enforcement on a Crazyflie quadrotor.

Successfully navigates complex obstacle scenarios with explicit geometric guarantees.

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.