Closed-form solutions for a real-time energy-optimal and collision-free speed planner with limited information

Abstract

Under real-world driving conditions, connected and automated vehicles (CAVs) must plan and follow an energy-optimal and collision-free speed trajectory with a high updating rate, based on available information limited by its communication range. This paper presents a speed planner using analytical closed-form optimal solutions. Using the simplest vehicle model, we derive closed-form solutions as functions of boundary conditions (BCs) and summarize them without and with pure state variable inequality constraints imposed by speed limits and the preceding vehicle. Then we introduce multiple driving modes (e.g., eco-approach to a traffic signal) for responding to dynamically changing situations and show how to set BCs for each mode while retaining the nature of globally optimal solutions. Finally, we perform a large-scale simulation study to identify and quantify the energy impacts of CAVs for real-world driving routes. A simple but effective planner based on closed-form solutions shows a significant energy saving potential compared with human-driven vehicles and adaptive cruise controlled vehicles with connectivity.