# Spatial Envelope MPC: High Performance Driving without a Reference

arXiv: https://arxiv.org/abs/2509.18506 · HTML: https://mlsanity.com/paper/2509.18506/

## 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 10 of its 68 references that are in the map.
- First posted on arXiv 23 Sep 2025.

## Placed in

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

## Builds on (most cited first, 10 of 10)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Explaining How a Deep Neural Network Trained with End-to-End Learning Steers a Car](https://mlsanity.com/paper/1704.07911/) (2017)
- [Autonomous Vehicles on the Edge: A Survey on Autonomous Vehicle Racing](https://mlsanity.com/paper/2202.07008/) (2022)
- [Autonomous Overtaking in Gran Turismo Sport Using Curriculum Reinforcement Learning](https://mlsanity.com/paper/2103.14666/) (2021)
- [Optimization-Based Collision Avoidance](https://mlsanity.com/paper/1711.03449/) (2017)
- [Guaranteed bounds on the Kullback-Leibler divergence of univariate mixtures using piecewise log-sum-exp inequalities](https://mlsanity.com/paper/1606.05850/) (2016)
- [Indy Autonomous Challenge -- Autonomous Race Cars at the Handling Limits](https://mlsanity.com/paper/2202.03807/) (2022)
- [Formula RL: Deep Reinforcement Learning for Autonomous Racing using Telemetry Data](https://mlsanity.com/paper/2104.11106/) (2021)
- [Composing Control Barrier Functions for Complex Safety Specifications](https://mlsanity.com/paper/2309.06647/) (2023)
- [Risk-Based Safety Envelopes for Autonomous Vehicles Under Perception Uncertainty](https://mlsanity.com/paper/2107.09918/) (2021)

## Abstract (arXiv)

This paper presents a novel envelope based model predictive control (MPC) framework designed to enable autonomous vehicles to handle high performance driving across a wide range of scenarios without a predefined reference. In high performance autonomous driving, safe operation at the vehicle's dynamic limits requires a real time planning and control framework capable of accounting for key vehicle dynamics and environmental constraints when following a predefined reference trajectory is suboptimal or even infeasible. State of the art planning and control frameworks, however, are predominantly reference based, which limits their performance in such situations. To address this gap, this work first introduces a computationally efficient vehicle dynamics model tailored for optimization based control and a continuously differentiable mathematical formulation that accurately captures the entire drivable envelope. This novel model and formulation allow for the direct integration of dynamic feasibility and safety constraints into a unified planning and control framework, thereby removing the necessity for predefined references. The challenge of envelope planning, which refers to maximally approximating the safe drivable area, is tackled by combining reinforcement learning with optimization techniques. The framework is validated through both simulations and real world experiments, demonstrating its high performance across a variety of tasks, including racing, emergency collision avoidance and off road navigation. These results highlight the framework's scalability and broad applicability across a diverse set of scenarios.