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

arXiv: https://arxiv.org/abs/2607.10975 · HTML: https://mlsanity.com/paper/2607.10975/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Reinforcement learning for driving, one of 9 directions in End-to-end autonomous driving.
- Builds on 21 of its 37 references that are in the map.
- First posted on arXiv 13 Jul 2026.

## Placed in

- End-to-end autonomous driving / [Reinforcement learning for driving](https://mlsanity.com/driving/reinforcement-learning-for-driving/)

## Builds on (most cited first, 21 of 21)

- [Large Scale Interactive Motion Forecasting for Autonomous Driving : The Waymo Open Motion Dataset](https://mlsanity.com/paper/2104.10133/) (2021)
- [NuPlan: A closed-loop ML-based planning benchmark for autonomous vehicles](https://mlsanity.com/paper/2106.11810/) (2021)
- [Control Barrier Functions: Theory and Applications](https://mlsanity.com/paper/1903.11199/) (2019)
- [Causal Confusion in Imitation Learning](https://mlsanity.com/paper/1905.11979/) (2019)
- [Control Barrier Function Based Quadratic Programs for Safety Critical Systems](https://mlsanity.com/paper/1609.06408/) (2016)
- [Parting with Misconceptions about Learning-based Vehicle Motion Planning](https://mlsanity.com/paper/2306.07962/) (2023)
- [Waymax: An Accelerated, Data-Driven Simulator for Large-Scale Autonomous Driving Research](https://mlsanity.com/paper/2310.08710/) (2023)
- [Categorizing Variants of Goodhart's Law](https://mlsanity.com/paper/1803.04585/) (2018)
- [On a Formal Model of Safe and Scalable Self-driving Cars](https://mlsanity.com/paper/1708.06374/) (2017)
- [Liability, Ethics, and Culture-Aware Behavior Specification using Rulebooks](https://mlsanity.com/paper/1902.09355/) (2019)
- [Bridging the Imitation Gap by Adaptive Insubordination](https://mlsanity.com/paper/2007.12173/) (2020)
- [Rethinking Imitation-based Planner for Autonomous Driving](https://mlsanity.com/paper/2309.10443/) (2023)
- [Rule-based Optimal Control for Autonomous Driving](https://mlsanity.com/paper/2101.05709/) (2021)
- [CLOVER: Closed-Loop Value Estimation and Ranking for End-to-End Autonomous Driving Planning](https://mlsanity.com/paper/2605.15120/) (2026)
- [Safety of the Intended Driving Behavior Using Rulebooks](https://mlsanity.com/paper/2105.04472/) (2021)
- [When Planners Meet Reality: How Learned, Reactive Traffic Agents Shift nuPlan Benchmarks](https://mlsanity.com/paper/2510.14677/) (2025)
- [Responsibility-Sensitive Safety: an Introduction with an Eye to Logical Foundations and Formalization](https://mlsanity.com/paper/2206.03418/) (2022)
- [nuPlan-R: A Closed-Loop Planning Benchmark for Autonomous Driving via Reactive Multi-Agent Simulation](https://mlsanity.com/paper/2511.10403/) (2025)
- [Real-time MPC with Control Barrier Functions for Autonomous Driving using Safety Enhanced Collocation](https://mlsanity.com/paper/2401.06648/) (2024)
- [IGDrivSim: A Benchmark for the Imitation Gap in Autonomous Driving](https://mlsanity.com/paper/2411.04653/) (2024)
- [Traffic-Rule-Compliant Trajectory Repair via Satisfiability Modulo Theories and Reachability Analysis](https://mlsanity.com/paper/2412.15837/) (2024)

## Abstract (arXiv)

Autonomous-vehicle motion planners must resolve conflicts among safety, regulation, comfort, and efficiency in real time while exposing those decisions for audit. We present W-SQP, a weighted tiered-slack nonlinear model predictive controller (NMPC) that compiles nine driving-rule families into a four-tier shared-slack nonlinear program solved online with CasADi and IPOPT; the name denotes the weighted quadratic slack penalty, not a sequential-quadratic-programming solver. Strongly separated tier penalties bias residual violations toward lower-priority rules while leaving actuation bounds hard. The controller replans from its executed state at 10,Hz and records per-rule residuals on every cycle. A 90,ms solver-time limit returns an anytime iterate that is projected through the vehicle dynamics before execution; median and maximum observed wall-clock solve times were 28 and 104,ms. We evaluate W-SQP in closed loop on 150 Waymo Open Motion Dataset scenarios in Waymax against reactive and proposal-and-select baselines, and introduce a log-independent protocol that separates safety and regulatory compliance from resemblance to the recorded human trajectory. Under this protocol, W-SQP shows no systematic group-level deficit relative to expert replay on the log-independent safety and regulatory rules, with several localized regressions in the hardest, highest-divergence scenarios. The results characterize W-SQP as an auditable, priority-biased, anytime-capable NMPC prototype rather than a hard-real-time or formally safe controller.