  This paper proposes two new algorithms for certified perception in
safety-critical robotic applications. The first is a Certified Visual Odometry
algorithm, which uses a RGBD camera with bounded sensor noise to construct a
visual odometry estimate with provable error bounds. The second is a Certified
Mapping algorithm which, using the same RGBD images, constructs a Signed
Distance Field of the obstacle environment, always safely underestimating the
distance to the nearest obstacle. This is required to avoid errors due to VO
drift. The algorithms are demonstrated in hardware experiments, where we
demonstrate both running online at 30FPS. The methods are also compared to
state-of-the-art techniques for odometry and mapping.
