In this work, we consider the problem of learning a feed-forward neural network controller to safely steer an arbitrarily shaped planar robot in a compact and obstacle-occluded workspace. Unlike existing methods that depend strongly on the density of data points close to the boundary of the safe state space to train neural network controllers with closed-loop safety guarantees, here we propose an alternative approach that lifts such strong assumptions on the data that are hard to satisfy in practice and instead allows for graceful safety violations, i.e., of a bounded magnitude that can be spatially controlled. To do so, we employ reachability analysis techniques to encapsulate safety constraints in the training process. Specifically, to obtain a computationally efficient over-approximation of the forward reachable set of the closed-loop system, we partition the robot's state space into cells and adaptively subdivide the cells that contain states which may escape the safe set under the trained control law. Then, using the overlap between each cell's forward reachable set and the set of infeasible robot configurations as a measure for safety violations, we introduce appropriate terms into the loss function that penalize this overlap in the training process. As a result, our method can learn a safe vector field for the closed-loop system and, at the same time, provide worst-case bounds on safety violation over the whole configuration space, defined by the overlap between the over-approximation of the forward reachable set of the closed-loop system and the set of unsafe states. Moreover, it can control the tradeoff between computational complexity and tightness of these bounds. Our proposed method is supported by both theoretical results and simulation studies.
翻译:在这项工作中,我们考虑了学习一个向导神经网络控制器的问题,以便安全地在一个紧凑和障碍封闭的工作空间中引导一个任意形成的板状机器人。与目前非常依赖靠近安全状态空间边界的数据点密度的当前方法不同的是,我们用封闭环安全保障措施对神经网络控制器进行培训,我们在这里建议了一种替代方法,对在实践中难以满足的数据进行如此强烈的假设,从而允许有优厚的安全侵犯,即可以空间控制的封闭尺寸。为了做到这一点,我们采用了可达性分析技术,以包罗训练过程中的安全限制。具体地说,为了获得一个在离近安全状态边界的高度数据点的高度密度,我们把机器人的状态空间控制器分成了不同的部分,适应性地分解了那些包含在实际中难以达到安全状态的状态的细胞。然后,利用每个细胞前方可达标数和不可靠的机器人配置之间的重叠,作为安全违反安全状态的衡量尺度。具体地说,我们将一个在封闭轨道系统的可达标值上进行适当的超度交易功能, 将这个固定的计算法将这个固定路段的计算结果纳入整个系统。