We present a multi-layered mapping, planning, and command execution system developed and tested on the LAGR mobile robot. Key to robust performance under uncertainty is the combination of a short-range perception system operating at high frame rate and low resolution and a long-range, adaptive vision system operating at lower frame rate and higher resolution. The short-range module performs local planning and obstacle avoidance with fast reaction times, while the long-range module performs strategic visual planning. Probabilistic traversability labels provided by the perception modules are combined and accumulated into a robot-centered hyperbolic-polar map with a 200 meter effective range. Instead of using a dynamical model of the robot for short-range planning, the system uses a large lookup table of physically-possible trajectory segments recorded on the robot in a wide variety of driving conditions. Localization is performed using a combination of GPS, wheel odometry, IMU, and a high-speed, low-complexity rotational visual odometry module. The end to end system was developed and tested on the LAGR mobile robot, and was verified in independent government tests.