Methods for autonomous docking usually rely on high-dimensional or complex optimizations which are required to run in real-time. Unfortunately, it is well-known that spacecraft flight-computers are highly limited in their computational power, rendering many current methods impractical. In this work, a novel approach to autonomous docking is explored within the framework of Lyapunov vector fields. A substantial extension (herein referred to as a cascaded Lyapunov vector field) is first presented which allows the desired final trajectory to be defined in a tumbling and accelerating reference frame. The docking path constraints are satisfied by vector field constructions, and the acceleration is constrained by bounding guidance parameters. Moreover, a performance optimization technique is developed based on estimations of fuel usage and maneuver time. This novel docking method requires no in-the-loop optimizations, and therefore retains feasibility for real-time implementation. The performance of this docking technique is confirmed in simulation and in planar experiments.