  Model Predictive Control (MPC) is a classic tool for optimal control of
complex, real-world systems. Although it has been successfully applied to a
wide range of challenging tasks in robotics, it is fundamentally limited by the
prediction horizon, which, if too short, will result in myopic decisions.
Recently, several papers have suggested using a learned value function as the
terminal cost for MPC. If the value function is accurate, it effectively allows
MPC to reason over an infinite horizon. Unfortunately, Reinforcement Learning
(RL) solutions to value function approximation can be difficult to realize for
robotics tasks. In this paper, we suggest a more efficient method for value
function approximation that applies to goal-directed problems, like reaching
and navigation. In these problems, MPC is often formulated to track a path or
trajectory returned by a planner. However, this strategy is brittle in that
unexpected perturbations to the robot will require replanning, which can be
costly at runtime. Instead, we show how the intermediate data structures used
by modern planners can be interpreted as an approximate value function. We show
that that this value function can be used by MPC directly, resulting in more
efficient and resilient behavior at runtime.
