TinySDP让嵌入式机器人实时求解非凸障碍物约束，实现安全敏捷控制。
TinySDP: Real Time Semidefinite Optimization for Certifiable and Agile Edge Robotics
- 将半定锥投影融入缓存Riccati ADMM，适配微控制器计算资源。
- 在复杂场景下路径比现有方法短73%，且全程无碰撞。
- 适合需要实时安全性保障的无人机等嵌入式智能系统。
半定规划（SDP）为运动规划中的非凸几何约束提供了严格的凸松弛框架，但现有求解器计算开销过大，难以在资源受限的嵌入式系统上实现实时控制。为此，我们提出TinySDP，首个专为嵌入式系统设计的半定规划求解器，实现了在微控制器上对非凸障碍物约束问题的实时模型预测控制（MPC）。该方法将正半定锥投影集成到基于缓存Riccati的ADMM求解器中，利用计算结构提升嵌入式可实现性。同时结合后验秩-1证书，在每个时间步将松弛解转化为显式的几何安全保证。在挑战性基准测试中，如死胡同和动态障碍物避障场景，传统局部方法会失败，而TinySDP实现了无碰撞导航，路径长度比最先进基线缩短高达73%。我们在Crazyflie四轴飞行器上验证了该方法，证明半定约束可在实时速率下对敏捷嵌入式机器人进行强制执行。
原文摘要 · Abstract (English)
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.
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