Robust Control Under Uncertainty via Bounded Rationality and Differential Privacy
This work addresses robustness and computational efficiency in robotics control, but it is incremental as it applies existing differential privacy theory to a new domain.
The paper tackles the challenges of designing robust controllers for robots with high-fidelity sensors by using differential privacy to bound sensitivity to state estimation errors and impose bounded rationality, resulting in a framework that provides an upper-bound on cost with faulty estimators in terms of perfect estimator cost, error magnitude, and privacy level, demonstrated numerically on robotics problems like nonlinear stabilization and motion planning.
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.