Vision-based formation control systems are attractive because they can use inexpensive sensors and can work in GPS-denied environments. The safety assurance for such systems is challenging: the vision component's accuracy depends on the environment in complicated ways, these errors propagate through the system and lead to incorrect control actions, and there exists no formal specification for end-to-end reasoning. We address this problem and propose a technique for safety assurance of vision-based formation control: First, we propose a scheme for constructing quantizers that are consistent with vision-based perception. Next, we show how the convergence analysis of a standard quantized consensus algorithm can be adapted for the constructed quantizers. We use the recently defined notion of perception contracts to create error bounds on the actual vision-based perception pipeline using sampled data from different ground truth states, environments, and weather conditions. Specifically, we use a quantizer in logarithmic polar coordinates, and we show that this quantizer is suitable for the constructed perception contracts for the vision-based position estimation, where the error worsens with respect to the absolute distance between agents. We build our formation control algorithm with this nonuniform quantizer, and we prove its convergence employing an existing result for quantized consensus.

翻译：基于视觉的编队控制系统因其可使用低成本传感器并在无GPS环境中运行而具有吸引力。此类系统的安全保障面临挑战：视觉组件的精度以复杂方式依赖于环境，这些误差通过系统传播并导致错误的控制动作，且缺乏用于端到端推理的形式化规范。我们针对这一问题提出一种基于视觉编队控制的安全保障技术：首先，我们提出一种构建与基于视觉感知相一致的量化器方案。其次，我们展示了如何将标准量化一致性算法的收敛性分析适配于所构建的量化器。我们利用近期定义的感知合约概念，基于来自不同真实状态、环境和天气条件的采样数据，为实际视觉感知管线创建误差边界。具体而言，我们采用对数极坐标下的量化器，并证明该量化器适用于基于视觉位置估计的感知合约构建，其中误差随智能体间绝对距离增大而恶化。我们使用此非均匀量化器构建编队控制算法，并利用量化一致性问题的现有结果证明其收敛性。