Fundamental Limits for Sensor-Based Robot Control
This provides a theoretical framework for evaluating sensor limitations in robotics, which is foundational for designing and optimizing robot control systems.
The paper tackles the problem of establishing fundamental performance limits for robots based on their sensors by defining a task-relevant information quantity and using a novel generalized Fano inequality to derive upper bounds on achievable reward, demonstrating strong limits in examples like obstacle avoidance and object catching.
Our goal is to develop theory and algorithms for establishing fundamental limits on performance imposed by a robot's sensors for a given task. In order to achieve this, we define a quantity that captures the amount of task-relevant information provided by a sensor. Using a novel version of the generalized Fano inequality from information theory, we demonstrate that this quantity provides an upper bound on the highest achievable expected reward for one-step decision making tasks. We then extend this bound to multi-step problems via a dynamic programming approach. We present algorithms for numerically computing the resulting bounds, and demonstrate our approach on three examples: (i) the lava problem from the literature on partially observable Markov decision processes, (ii) an example with continuous state and observation spaces corresponding to a robot catching a freely-falling object, and (iii) obstacle avoidance using a depth sensor with non-Gaussian noise. We demonstrate the ability of our approach to establish strong limits on achievable performance for these problems by comparing our upper bounds with achievable lower bounds (computed by synthesizing or learning concrete control policies).