# Multi-Profile Quadratic Programming (MPQP) for Optimal Gap Selection and Speed Planning of Autonomous Driving

arXiv: https://arxiv.org/abs/2401.06305 · HTML: https://mlsanity.com/paper/2401.06305/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Jan 2024.

## Built on by (most cited first, 3 of 3)

- [Predictive Planner for Autonomous Driving with Consistency Models](https://mlsanity.com/paper/2502.08033/) (2025)
- [Importance Sampling-Guided Meta-Training for Intelligent Agents in Highly Interactive Environments](https://mlsanity.com/paper/2407.15839/) (2024)
- [Frenet Corridor Planner: An Optimal Local Path Planning Framework for Autonomous Driving](https://mlsanity.com/paper/2505.03695/) (2025)

## Abstract (arXiv)

Smooth and safe speed planning is imperative for the successful deployment of autonomous vehicles. This paper presents a mathematical formulation for the optimal speed planning of autonomous driving, which has been validated in high-fidelity simulations and real-road demonstrations with practical constraints. The algorithm explores the inter-traffic gaps in the time and space domain using a breadth-first search. For each gap, quadratic programming finds an optimal speed profile, synchronizing the time and space pair along with dynamic obstacles. Qualitative and quantitative analysis in Carla is reported to discuss the smoothness and robustness of the proposed algorithm. Finally, we present a road demonstration result for urban city driving.