# Linear Differential Games for Cooperative Behavior Planning of Autonomous Vehicles Using Mixed-Integer Programming

arXiv: https://arxiv.org/abs/2109.15122 · HTML: https://mlsanity.com/paper/2109.15122/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Cooperative and V2X driving, one of 9 directions in End-to-end autonomous driving.
- Builds on 5 of its 16 references that are in the map.
- First posted on arXiv 30 Sep 2021.

## Placed in

- End-to-end autonomous driving / [Cooperative and V2X driving](https://mlsanity.com/driving/cooperative-and-v2x-driving/)

## Builds on (most cited first, 5 of 5)

- [Stochastic Dynamic Games in Belief Space](https://mlsanity.com/paper/1909.06963/) (2019)
- [A Non-Cooperative Game Approach to Autonomous Racing](https://mlsanity.com/paper/1712.03913/) (2017)
- [Warm Start of Mixed-Integer Programs for Model Predictive Control of Hybrid Systems](https://mlsanity.com/paper/1910.08251/) (2019)
- [Bridging the Gap between Open Source Software and Vehicle Hardware for Autonomous Driving](https://mlsanity.com/paper/1905.02980/) (2019)
- [Optimal Behavior Planning for Autonomous Driving: A Generic Mixed-Integer Formulation](https://mlsanity.com/paper/2003.13312/) (2020)

## Built on by (most cited first, 1 of 1)

- [Autonomous Vehicles on the Edge: A Survey on Autonomous Vehicle Racing](https://mlsanity.com/paper/2202.07008/) (2022)

## Abstract (arXiv)

Cooperatively planning for multiple agents has been proposed as a promising method for strategic and motion planning for automated vehicles. By taking into account the intent of every agent, the ego agent can incorporate future interactions with human-driven vehicles into its planning. The problem is often formulated as a multi-agent game and solved using iterative algorithms operating on a discretized action or state space. Even if converging to a Nash equilibrium, the result will often be only sub-optimal. In this paper, we define a linear differential game for a set of interacting agents and solve it to optimality using mixed-integer programming. A disjunctive formulation of the orientation allows us to formulate linear constraints to prevent agent-to-agent collision while preserving the non-holonomic motion properties of the vehicle model. Soft constraints account for prediction errors. We then define a joint cost function, where a cooperation factor can adapt between altruistic, cooperative, and egoistic behavior. We study the influence of the cooperation factor to solve scenarios, where interaction between the agents is necessary to solve them successfully. The approach is then evaluated in a racing scenario, where we show the applicability of the formulation in a closed-loop receding horizon replanning fashion. By accounting for inaccuracies in the cooperative assumption and the actual behavior, we can indeed successfully plan an optimal control strategy interacting closely with other agents.