  We present an approach for safe motion planning under robot state and
environment (obstacle and landmark location) uncertainties. To this end, we
first develop an approach that accounts for the landmark uncertainties during
robot localization. Existing planning approaches assume that the landmark
locations are well known or are known with little uncertainty. However, this
might not be true in practice. Noisy sensors and imperfect motions compound to
the errors originating from the estimate of environment features. Moreover,
possible occlusions and dynamic objects in the environment render imperfect
landmark estimation. Consequently, not considering this uncertainty can wrongly
localize the robot, leading to inefficient plans. Our approach thus
incorporates the landmark uncertainty within the Bayes filter estimation
framework. We also analyze the effect of considering this uncertainty and
delineate the conditions under which it can be ignored. Second, we extend the
state-of-the-art by computing an exact expression for the collision probability
under Gaussian distributed robot motion, perception and obstacle location
uncertainties. We formulate the collision probability process as a quadratic
form in random variables. Under Gaussian distribution assumptions, an exact
expression for collision probability is thus obtained which is computable in
real-time. In contrast, existing approaches approximate the collision
probability using upper-bounds that can lead to overly conservative estimate
and thereby suboptimal plans. We demonstrate and evaluate our approach using a
theoretical example and simulations. We also present a comparison of our
approach to different state-of-the-art methods.
