A quasi-steady-state framework for the control of vehicles in transient on-limit manoeuvres
Creators: name: Tucker, Kyle
Publisher: name: RMIT University
Year: 2024
Subjects: classificationCode: 400204
subject: Automotive safety engineering
classificationCode: 401702
subject: Dynamics, vibration and vibration control

description: Control technologies for every day driving tasks in autonomous vehicles (e.g. lane keeping) are all but complete. As autonomy increases, and the responsibility of the controller is transferred from the human to the mathematical control framework, an increase in the capabilities of the controller for extreme manoeuvres (e.g. collision avoidance) must be established. It is expected in these cases that the vehicle acts at its maximum capacity to ensure safety for all stakeholders.  Many vehicle control architectures have been reviewed for use in these manoeuvring types (e.g. PID, kinematic, linear explicit, etc), however their consideration of the non-linear characteristics of the vehicle response at the limits of performance is insufficient. For vehicles acting in these transient on-limit manoeuvres, predictive controllers (i.e. MPC) provide the required control accuracy, however the computational effort required for such calculations can be prohibitive. This thesis focuses on the development of a new vehicle control framework that is capable of providing accurate vehicle control in transient on-limit manoeuvres, whilst providing a pathway for real-time implementation. 

Lap time simulation (LTS) is an optimisation tool used within motorsports to assess the fastest way around a racing track for a racing vehicle. As racing vehicles are almost exclusively acting in transient on-limit manoeuvres, the technology of LTS provides a potential platform for which an efficient vehicle controller can be established. One of the most common ways that LTS methods overcomes the contrast between vehicle response prediction accuracy and computation time is through the use of a point mass model that is constrained by a strategically developed acceleration envelope (called a Quasi-Steady-State (QSS) model). The acceleration envelope is formulated on the basis that the acceleration capacity of the vehicle with QSS constraints is well aligned with that of the transient vehicle, without giving additional capacity to the point mass model to which it would exploit. QSS models have not been used as a basis for control in autonomous vehicles to date on account of three fundamental reasons. Firstly, there are notable concerns with regard to accuracy, with QSS models reporting approximately a 3% difference to the transient vehicle counterpart. The second reason being that minimum time optimisations require fast and reliable initialisations, which have not yet been established. Lastly, QSS models operate on the planar kinematics directly, rather than traditional vehicle controls (e.g. steering, throttle, brake), leaving control actions unresolved. Overcoming these three challenges is the focus of this doctoral thesis. 

The accuracy of the QSS model is dependent upon the development of the acceleration envelope, though its development is inconsistent in the literature. Additionally, QSS models have been controlled with accelerations directly, which is non-physical (discontinuous vehicle forces) and provides unrestricted articulation (ignoring yaw inertia). This work improves the accuracy of the QSS vehicle model by consolidating the QSS constraints, evaluating the acceleration envelope directly in the natural coordinate frame, and controlling the vehicle with planar jerks. Improvements to the QSS model are observed in several LTS examples with the final comparison of minimum time performance within 0.25% of the transient vehicle counterpart.

The minimum time MPC problem is a non-linear and non-convex optimisation problem, requiring that initial guesses to be sufficiently close to optimal and be feasible for reliable convergence. Whilst many initial guess models are formulated using a two-stage path planning and velocity analysis process, path planning models seldom consider the vehicle model capabilities, resulting in initial guesses that are not necessarily feasible. This work provides the mathematical basis for a feasible path planning model, which is founded on the capabilities of the QSS model. By establishing a new equation for path curvature relative to a nominal reference line, a minimum curvature trajectory can be used to assess the dynamic feasibility of the vehicle across the path. Several examples in this section provide a review of the minimum curvature cost model (to better align results with the minimum time solution), and also provide an assessment of the capabilities of the feasible trajectory planner at the limits of handling. Results here are provided within 0.04%-3% at the extremities of the vehicle’s operating range, highlighting the capabilities of this approach. 

To resolve the challenge associated with extracting traditional vehicle controls from the QSS model, a hierarchical controller is established as the proposed final control format. The three-tier architecture utilises a conservative feasible path planning model, a QSS minimum time model, and a transient path following model. The transient path following model, which would have previously been excluded from real time implementation, is employed with a short horizon length to reduce computational effort. Implementation of the short horizon length, however, also introduces open loop reliability concerns in the MPC controller, as reduced preview information can lead to dynamic failures. The importance of QSS prediction accuracy is therefore vital in this stage as strategic sequencing between the models is used to establish a basis for improved reliability. The final results of the hierarchical controller presented in this thesis are extremely positive, with two full circuit minimum time results reported to be within 1% - 1.41% (slower) of the transient LTS solution, highlighting the capabilities of the controller. 

During an assessment of the final control format it is shown that the alignment between the jerk capacity of the QSS vehicle model and the transient path following controller is imperfect. This is observed through a phenomenon referred to as velocity overrun, where the transient vehicle does not have the capacity to articulate at the same rate as the QSS model during braking manoeuvres, limiting the minimum transient path following horizon length. Development of an improved jerk constraint format will allow increased accuracy and reliability in future work, leading to real time implementation of the hierarchical controller, and improved autonomous vehicle safety in transient on-limit manoeuvres.