用神经网络求解哈密顿-雅可比方程，生成更安全的机器人控制屏障函数。
Reachability Barrier Networks: Learning Hamilton-Jacobi Solutions for Smooth and Flexible Control Barrier Functions
- 用物理信息神经网络求解哈密顿-雅可比方程，生成平滑的控制屏障函数。
- 在9维多车避障中，比传统神经屏障函数安全5.5倍、保守性低1.9倍。
- 支持训练后调节保守性，并用可信预测保证安全性，适合高维非线性系统。
自动驾驶与机器人领域对安全控制的需求日益迫切。控制屏障函数（CBFs）虽能为控制系统添加安全约束，但高维场景下难以生成，现有方法常产生不光滑或不准确的近似，破坏安全保证。本文提出可达性屏障网络（RBNs），利用物理信息神经网络（PINNs）求解哈密顿-雅可比（HJ）最优控制问题，生成平滑的CBF近似，突破传统维度限制。通过参数化折扣项，可在训练后灵活调节保守性。为保障折扣解的鲁棒性，引入可信预测方法，获得概率性安全保证。实验显示，RBNs在低维场景中精度高，在高维场景中更安全：在9维多车避障任务中，相比标准神经CBFs，其安全性提升5.5倍，保守性降低1.9倍，为一般非线性自主系统提供了有前景的CBF合成方法。
原文摘要 · Abstract (English)
Recent developments in autonomous driving and robotics underscore the necessity of safety-critical controllers. Control barrier functions (CBFs) are a popular method for appending safety guarantees to a general control framework, but they are notoriously difficult to generate beyond low dimensions. Existing methods often yield non-differentiable or inaccurate approximations that lack integrity, and thus fail to ensure safety. In this work, we use physics-informed neural networks (PINNs) to generate smooth approximations of CBFs by computing Hamilton-Jacobi (HJ) optimal control solutions. These reachability barrier networks (RBNs) avoid traditional dimensionality constraints and support the tuning of their conservativeness post-training through a parameterized discount term. To ensure robustness of the discounted solutions, we leverage conformal prediction methods to derive probabilistic safety guarantees for RBNs. We demonstrate that RBNs are highly accurate in low dimensions, and safer than the standard neural CBF approach in high dimensions. Namely, we showcase the RBNs in a 9D multi-vehicle collision avoidance problem where it empirically proves to be 5.5x safer and 1.9x less conservative than the neural CBFs, offering a promising method to synthesize CBFs for general nonlinear autonomous systems.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。