“Proximally Optimal Predictive Control Algorithm for Path Tracking of Self-Driving Cars

[WANGzl33]

Dear Authors of the Tinker-Twins,
First of all, thank you sincerely for your detailed reply and for generously sharing your preprint, paper, and video materials! After studying your recommended “Proximally Optimal Predictive Control Algorithm for Path Tracking of Self-Driving Cars” and the related references in depth, I have gained an initial understanding of the overall POP controller concept. However, I still have a few questions in the following two areas and would greatly appreciate your guidance:
1.Details of the Hybrid Scheme in the POP Controller
In your paper, you describe the POP controller as a lightweight optimization loop that combines Pure Pursuit with an MPC-style optimization strategy.
a.Could you please elaborate on exactly how these two methods are coupled? For example, in the implementation flow, how does the geometric steering command generated by Pure Pursuit work in concert with the analytical/numerical solver of the MPC component?
b.Do you have a more detailed algorithm flowchart or pseudocode that shows the complete steps from perception input → trajectory prediction → cost formulation → solution output → execution feedback?
c.In your derivation, how do you balance the error compensation from Pure Pursuit against the prediction error terms in the MPC cost function? Would you be willing to share the corresponding mathematical derivation or constraint definitions?
2.Specific Process and Derivation for Introducing Steering-Angle Information into Longitudinal Speed Regulation
Your paper mentions incorporating the vehicle’s current steering angle as a modulation factor into the longitudinal control channel to improve speed stability in curves. tau = k_tau + [ (v_lim - v) / v_lim - |delta| / delta_lim ] * (1 - k_tau)
a.In the design of the control law, how exactly does this steering-angle factor influence longitudinal acceleration or braking?
b.Could you provide the detailed process diagram or equation derivation for this module—for instance, how you define the steering-angle weight and combine it with a longitudinal prediction model (such as a first-order inertia or integrator model)?
c.I have already studied the papers referenced in your work, but this handling approach remains somewhat unclear. I would greatly appreciate a deeper explanation of its essence and implementation details.
Thank you again for taking the time to advise me! If convenient, I would be delighted to continue discussing validation details on simulation or real-vehicle platforms, as well as any available code or demo examples. I sincerely look forward to your suggestions and guidance.
Best regards,
@WANGzl33
May 19, 2025