The rapid development of affordable and compact high-fidelity sensors (e.g., cameras and LIDAR) allows robots to construct detailed estimates of their states and environments. However, the availability of such rich sensor information introduces two technical challenges: (i) the lack of analytic sensing models, which makes it difficult to design controllers that are robust to sensor failures, and (ii) the computational expense of processing the high-dimensional sensor information in real time. This paper addresses these challenges using the theory of differential privacy, which allows us to (i) design controllers with bounded sensitivity to errors in state estimates, and (ii) bound the amount of state information used for control (i.e., to impose bounded rationality). The resulting framework approximates the separation principle and allows us to derive an upper-bound on the cost incurred with a faulty state estimator in terms of three quantities: the cost incurred using a perfect state estimator, the magnitude of state estimation errors, and the level of differential privacy. We demonstrate the efficacy of our framework numerically on different robotics problems, including nonlinear system stabilization and motion planning.
翻译:迅速发展负担得起和紧凑的高纤维传感器(例如照相机和LIDAR),使机器人能够对其状态和环境作出详细估计,然而,这种丰富的传感器信息的提供带来了两个技术挑战:(一) 缺乏分析感测模型,因此难以设计对传感器失灵十分有力的控制器;(二) 实时处理高维感应信息的计算费用;本文件使用不同隐私理论来应对这些挑战,这种理论使我们能够(一) 设计控制器对国家估计错误有一定的敏感性,(二) 约束用于控制的国家信息的数量(即强制实行限制性合理性),由此形成的框架接近分离原则,并使我们能够从错误的国家估计器引起的费用上乘三个数量:使用完美的国家估计器引起的费用、国家估计错误的程度以及差异隐私的程度。我们用数字方式展示了我们框架在各种机器人问题上的效力,包括非线性系统稳定和移动规划。