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

Abstract

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.

arXiv comment11 pages, 14 figures

References in corpus (3)

• Hierarchical Reinforcement Learning for Self-Driving Decision-Making without Reliance on Labeled Driving Data
• An Empirical Study of ADMM for Nonconvex Problems
• Safe Planning for Self-Driving Via Adaptive Constrained ILQR

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• Sequential Convex Programming for Collaboration of Connected and Automated Vehicles
• Neural-iLQR: A Learning-Aided Shooting Method for Trajectory Optimization