Technical Report on Optimal Linear Multiple Estimation for Landmark-Based Planning via Control Synthesis

TL;DR

This paper introduces virtual landmarks as linear combinations of measurements to reduce uncertainty in landmark-based robot navigation, enabling less conservative control and improved navigation performance.

Contribution

It proposes a novel method to synthesize virtual landmarks that minimize control input variance, decoupling landmark design from controller synthesis.

Findings

Virtual landmarks reduce control input variance.

Navigation becomes faster and smoother with the new method.

Decoupling landmark and controller design simplifies the process.

Abstract

A common way to implement navigation in mobile robots is through the use of landmarks. In this case, the main goal of the controller is to make progress toward a goal location (stability), while avoiding the boundary of the environment (safety). In our previous work, we proposed a method to synthesize global controllers for environments with a polyhedral decomposition; our solution uses a Quadratically Constrained Quadratic Program with Chance Constraints to take into account the uncertainty in landmark measurements. Building upon this work, we introduce the concept of virtual landmarks, which are defined as linear combinations of actual landmark measurements that minimize the uncertainty in the resulting control actions. Interestingly, our results show that the first minimum-variance landmark is independent of the feedback control matrix, thus decoupling the design of the landmark from the one of the controller; attempting to derive additional, statistically independent landmarks, however, requires solving non-convex problems that involve also the controller. Numerical experiments demonstrate that, by minimizing the variance of the inputs, the resulting controller will be less conservative, and the robot is able to complete navigation tasks more effectively (faster and with less jitter in the trajectory).