Real-Time Rulebook-Aware Nonlinear MPC for Autonomous Driving with Priority-Biased Tiered Slacks

Jul 16, 2026

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Real-Time Rulebook-Aware Nonlinear MPC targets autonomous-driving motion planning that resolves a priority-ordered rulebook (safety before regulatory compliance, comfort, and efficiency) at the vehicle control rate while remaining auditable. The approach introduces W-SQP, a weighted soft-constrained quadratic-penalty NMPC that compiles nine rule families into a four-tier shared-slack CasADi program. It preserves hard actuation bounds, biases residual violations toward comfort/efficiency rather than safety, replans from executed state at 10 Hz, and logs normalized per-rule residuals. Closed-loop evaluation on 150 WOMD scenarios shows strong log-independent safety/regulatory behavior and quantified imitation-aware metrics.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages20

Reading Time50 min

Introduction

Method: W-SQP (Weighted soft-constrained quadratic-penalty NMPC)

Evaluation methodology and metric decomposition

Closed-loop study on WOMD scenarios

Contributions

Real-Time Rulebook-Aware Nonlinear MPC for Autonomous Driving with Priority-Biased Tiered Slacks⋆ Hadi Hajieghrarya , Benedikt Waltera , Chaitanya Shindea , Paul Schmittb , Miguel Hurtadoa aTORC Robotics LLC, an independent subsidiary of Daimler Truck AG, USA b Reynolds & Moore and MassRobotics, USA regulatory rules, with several localized regressions in the hardest, highest-divergence scenarios. The results characterize an auditable, priority-biased, anytime-capable NMPC prototype rather than a hard-real-time or formally safe controller. 1. Introduction We are interested in motion planners for autonomous driving that do more than avoid collisions and reach a goal: planners that resolve a priority-ordered rulebook—safety before regulatory compliance, comfort, and efficiency—at the vehicle’s control rate. Such conflicts are routine: a vehicle may briefly cross a lane boundary to pass a stopped obstacle, and braking early for comfort can disrupt following traffic. Planners must also be auditable: after an objective conflict, an engineer should be able to identify which rule was relaxed and by how much (Censi a sequential formulation requires multiple nonlinear-program solves and tier-freezing at every cycle, increasing latency and disrupting warm starts. Learned planners scale well but expose limited per-rule structure for audit (Dauner et al., 2023; Chenget al., 2023, 2024), whereas conventional penalty stacks do not directly reveal how conflicts were resolved. W-SQP.. Our primary contribution is W-SQP, a weighted softconstrained quadratic-penalty NMPC, also referred to as tieredslack NMPC. W-SQP compiles nine rule families into a four-tier shared-slack nonlinear program built in CasADi and solved with . 10975v 1 [ cs .RO] et al., 2019; Collin et al., 2020) . These requirements are difficult to combine. Lexicographic schemes make priorities explicit, and cascaded strict-priority quadratic programs reach kilohertz rates in whole-body control (Kanoun et al., 2011; Escande et al., 2014); however, when applied to nonconvex driving NMPC, ⋆ This paper represents research activities conducted within TORC Robotics LLC. It does not describe any production system, does not constitute the safety case for any Daimler Truck AG product or development program, and has not been reviewed by Daimler Truck AG for regulatory compliance or product liability purposes. The research was conducted using public benchmark data and does not reflect the proprietary safety architecture of any deployed or indevelopment TORC Robotics or Daimler Truck product. Email addresses: Hadi .Hajieghrary@Torc .ai (Hadi Hajieghrary), [Benedikt.Walter@Torc.ai](Benedikt.Walter@Torc.ai) (Benedikt Walter), Chaitanya .Shinde@Torc .ai (Chaitanya Shinde), [pauls@massrobotics.org](pauls@massrobotics.org) (Paul Schmitt), [Miguel.Hurtado@Torc.ai](Miguel.Hurtado@Torc.ai)[ ](Miguel.Hurtado@Torc.ai)(Miguel Hurtado) arXiv:2607 IPOPT (Andersson et al., 2019; Wächter and Biegler, 2006) . Strongly separated penalties bias residual violations toward comfort and efficiency and away from safety and regulatory rules, while physical actuation bounds remain hard. This scalar penalty provides a priority bias, not lexicographic priority preservation (Sec. 3) . W-SQP replans from its executed state at 10 Hz; under a 90 ms solver-time limit, IPOPT returns its best iterate, which is projected through the dynamics before execution. Each cycle also records normalized per-rule residuals for audit. Evaluating a non-imitative controller.. Because W-SQP plans from its executed state, it may select a valid path that differs from the recorded human trajectory. Closed-loop benchmarks evaluate executed states against reactive agents (Caesar et al., 2021; Gulino et al., 2023), but some catalogues also include path-tracking or route-adherence rules defined relative to the Preprint submitted to Control Engineering Practice July 14, 2026 human log. Such rules measure imitation

FAQs

What problem does W-SQP address in autonomous driving planning?

W-SQP addresses motion planning that must resolve conflicts across a priority-ordered rulebook at control rate while staying auditable, so engineers can identify which rule was relaxed and by how much.

How does W-SQP represent and handle priorities among driving rules?

W-SQP builds a weighted soft-constrained quadratic-penalty NMPC that compiles nine rule families into a four-tier shared-slack nonlinear program, using penalty design to provide a priority bias rather than strict lexicographic preservation.

What does the evaluation show about safety and regulatory performance?

On 150 WOMD scenarios, W-SQP shows no systematic group-level deficit for sixteen log-independent safety and regulatory rules, with an aggregate mean difference relative to expert replay reported for safety/regulatory groups and larger differences attributed to two log-coupled rules.

Jul 16, 2026

Upload by Skyler