This paper describes a finite-horizon receding horizon trajectory optimization scheme which uses an approximation of the value function to provide cost-to-go (CTG) and associated state information. The value function approximation is computed using a finite-state, motion primitive automaton approximation of the vehicle dynamics. Using an actual value function approximation instead of heuristic CTG allows a tighter integration between the planning and control layers needed for vehicles operating in challenging spatial environments. It also enables a more rigorous use of the receding horizon control framework for autonomous control applications. The paper describes the finite-state value function approximation and its integration into the receding horizon scheme. Simulation examples illustrate the scheme's capabilities and highlight interesting open issues that will need to be addressed to take full advantage of the approach.