# Alternating Direction Method of Multipliers for Constrained Iterative LQR in Autonomous Driving

arXiv: https://arxiv.org/abs/2011.00462 · HTML: https://mlsanity.com/paper/2011.00462/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Nov 2020.

## Built on by (most cited first, 11 of 11)

- [Towards Socially Responsive Autonomous Vehicles: A Reinforcement Learning Framework with Driving Priors and Coordination Awareness](https://mlsanity.com/paper/2309.09726/) (2023)
- [CoDriveVLM: VLM-Enhanced Urban Cooperative Dispatching and Motion Planning for Future Autonomous Mobility on Demand Systems](https://mlsanity.com/paper/2501.06132/) (2025)
- [IR-STP: Enhancing Autonomous Driving with Interaction Reasoning in Spatio-Temporal Planning](https://mlsanity.com/paper/2311.02850/) (2023)
- [Fast and Modular Autonomy Software for Autonomous Racing Vehicles](https://mlsanity.com/paper/2408.15425/) (2024)
- [Integrated Decision Making and Trajectory Planning for Autonomous Driving Under Multimodal Uncertainties: A Bayesian Game Approach](https://mlsanity.com/paper/2409.13993/) (2024)
- [Integrated Intention Prediction and Decision-Making with Spectrum Attention Net and Proximal Policy Optimization](https://mlsanity.com/paper/2408.03191/) (2024)
- [Synergizing Decision Making and Trajectory Planning Using Two-Stage Optimization for Autonomous Vehicles](https://mlsanity.com/paper/2411.18974/) (2024)
- [Integrating Higher-Order Dynamics and Roadway-Compliance into Constrained ILQR-based Trajectory Planning for Autonomous Vehicles](https://mlsanity.com/paper/2309.14566/) (2023)
- [Deterministic Policy Gradient Primal-Dual Methods for Continuous-Space Constrained MDPs](https://mlsanity.com/paper/2408.10015/) (2024)
- [Reachable Sets-based Trajectory Planning Combining Reinforcement Learning and iLQR](https://mlsanity.com/paper/2503.17398/) (2025)
- [Safe and Nonconservative Contingency Planning for Autonomous Vehicles via Online Learning-Based Reachable Set Barriers](https://mlsanity.com/paper/2509.07464/) (2025)

## Abstract (arXiv)

In the context of autonomous driving, the iterative linear quadratic regulator (iLQR) is known to be an efficient approach to deal with the nonlinear vehicle model in motion planning problems. Particularly, the constrained iLQR algorithm has shown noteworthy advantageous outcomes of computation efficiency in achieving motion planning tasks under general constraints of different types. However, the constrained iLQR methodology requires a feasible trajectory at the first iteration as a prerequisite when the logarithmic barrier function is used. Also, the methodology leaves open the possibility for incorporation of fast, efficient, and effective optimization methods to further speed up the optimization process such that the requirements of real-time implementation can be successfully fulfilled. In this paper, a well-defined motion planning problem is formulated under nonlinear vehicle dynamics and various constraints, and an alternating direction method of multipliers (ADMM) is utilized to determine the optimal control actions leveraging the iLQR. The approach is able to circumvent the feasibility requirement of the trajectory at the first iteration. An illustrative example of motion planning for autonomous vehicles is then investigated. A noteworthy achievement of high computation efficiency is attained with the proposed development; comparing with the constrained iLQR algorithm based on the logarithmic barrier function, our proposed method reduces the average computation time by 31.93%, 38.52%, and 44.57% in the three driving scenarios; compared with the optimization solver IPOPT, our proposed method reduces the average computation time by 46.02%, 53.26%, and 88.43% in the three driving scenarios. As a result, real-time computation and implementation can be realized through our proposed framework, and thus it provides additional safety to the on-road driving tasks.