  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).
