Significance of low-level control to string stability under adaptive cruise control: Algorithms, theory and experiments

Commercial adaptive cruise control (ACC) systems are bi-level: an upper-level planner decides the target trajectory and the low-level system executes it. Existing literature on ACCs mostly focus on the planner algorithms or the actuator delay, while the transition process between them, e.g. the low-level control design and its impact are often ignored. This paper tries to fill this gap by digging into the codebase of a recent open-source self-driving system, Openpilot (OP), Comma.ai, from which we extract and formulate the algorithms at both the upper and lower levels. For linear ACCs, the paper extends the transfer function analysis from planners only to full control loops and investigates the impact of slow/fast low-level control on the overall string stability (SS). For MPC ACCs, it studies their planning characteristics based its optimization objectives and approximates the low-level impact using an ODE approach.We find that low-level control has a significant impact on the overall SS of ACCs: (i) slow low-level control undermines SS under small frequencies and improves SS given large frequencies for linear systems, (ii) MPC features a varying gain throughout an oscillation, where the fast low-level control typically results in a 'fast-slow' changing process of the MPC gain, which benefits the SS, whereas the slow low-level control leads to a 'slow-fast' varying gain which undermines the SS, (iii) slow low-level control are common as they arise from comfort oriented control gains, from a "weak" actuator performance or both, and (iv) the SS is very sensitive to the integral gain under slow low-level control for both PI and PIF controllers. Overall, the study recommends fast low-level control for ensuring vehicular SS to reduce traffic congestion, considering that large congestion waves usually feature both small frequencies and large amplitudes, although slow controllers could perform even better provided a short and small leader perturbation. The findings of this paper are verified both numerically and experimentally. For the first time in the literature we implement custom ACC algorithms on market cars, and achieve SS on open roads with a random leader by only tuning the low-level controllers. The source code is shared at https://github.com/HaoZhouGT/openpilot to support on-road experiments of arbitrary car-following models, which may be of interest to other studies.