基于可达性的动力系统运动策略安全证书

中文摘要 AI 辅助

动力系统（DS）是反应式运动策略，代表具有稳定性和收敛性理论保证的向量场。为了在未知环境中部署时确保安全性，必须通过调制或几何控制屏障函数策略对其进行局部重塑。然而，根据障碍物的几何形状和DS的复杂性，这些局部策略可能导致系统发生不可避免的碰撞或产生虚假吸引子。在本工作中，我们利用从后向可达管概念中提取的值函数来认证安全性，该值函数衡量名义DS沿滚动轨迹的最坏情况安全性。通常，对于受控系统，由于维度灾难，这样的值函数是难以处理的。我们表明，在基于DS的从示范学习中，控制输入的缺失将可达性问题简化为确定性滚动，而某些稳定性条件的存在将无限时域截断为有限时域，从而产生定义良好的值函数。我们进一步表明，我们设计的值函数是名义DS流在无障碍区域内的最大前向不变子集。该证书函数的应用在五种DS构造上得到验证——解析型、神经ODE、微分同胚潜空间、LPV-DS、SE(3)——并在Franka机械臂上进行了验证。在正面接近不安全区域的情况下，调制和几何CBF也会遭受鞍点问题。我们表明，CBF-on-V完全避免了这一缺陷。

英文摘要

Dynamical Systems (DS) are reactive motion policies representing vector fields trained with theoretical guarantees of stability and convergence. To ensure safety during deployment in unknown environments they must be locally reshaped, either through modulation or geometric control barrier function strategies. However, depending on the geometry of the obstacles and the complexity of the DS, these local strategies can lead the system to unavoidable collisions or spurious attractors. In this work, we certify safety with a value function drawn from the notion of backward reachability tube, which measures the worst-case safety along a rollout trajectory of the nominal DS. Usually, such a value function is intractable for a controlled system due to curse of dimensionality. We show that in the DS-based learning-from-demonstration setting, the absence of a control input collapses the reachability problem to a deterministic rollout, and the presence of certain stability conditions truncates the infinite horizon to a finite one, resulting in a well-defined value function. We further show that the value function we devised is the maximal forward-invariant subset of the obstaclefree region for the nominal DS flow. The application of this certificate function is validated across five DS constructions - analytical, Neural ODE, diffeomorphic latent space, LPV-DS, SE(3)and validate it on a Franka manipulator. Modulation and geometric CBFs also suffer from saddle point in cases of headon approach towards an unsafe zone. We show that CBF-on-V avoids this pitfall entirely.

发表机构

• University of Pennsylvania（宾夕法尼亚大学）

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