Nonlinear Model Predictive Control for Distributed Motion Planning in Road Intersections Using PANOC

Abstract

The coordination of highly automated vehicles (or agents) in road intersections is an inherently nonconvex and challenging problem. In this paper, we propose a distributed motion planning scheme under reasonable vehicleto-vehicle communication requirements. Each agent solves a nonlinear model predictive control problem in real time and transmits its planned trajectory to other agents, which may have conflicting objectives. The problem formulation is augmented with conditional constraints that enable the agents to decide whether to wait at a stopping line, if safe crossing is not possible. The involved nonconvex problems are solved very efficiently using the proximal averaged Newton method for optimal control (PANOC). We demonstrate the efficiency of the proposed approach in a realistic intersection crossing scenario. A. Katriniok is with Ford Research

A Comprehensive Survey on Cooperative Intersection Management for Heterogeneous Connected Vehicles

“…In [244], the authors studied a V2V TP based regime where each vehicle solved a non-linear MPC using the proximal averaged Newton method for optimal control (PANOC) and sent its planned path to other vehicles. Feng et al [245] employed a joint optimal control on both signal and trajectory using dynamic programming and control theory respectively with a goal to optimize fuel and travel time.…”

Control-sharing Control Barrier Functions for Intersection Automation under Input Constraints

“…1, it suffices to utilize linear affine mapping functions, that is, X i (s i ) := p x,i,0 + p x,i,1 s i , Y i (s i ) := p y,i,0 + p y,i,1 s i . with constants p x,i,0 , p x,i,1 , p y,i,0 , p y,i,1 ∈ R. Depending on the use case, these mapping functions can of course be more complex, e.g., by applying B-Spline functions to represent the paths of turning agents [3]. Likewise, every agent's yaw angle can be described as a function ψ i (s i ) of its path coordinate s i .…”

“…There is a rich body of literature on methods that have been applied to tackle the control problem at hand [1]. Optimization-based methods like model predictive control are an appealing choice for such kind of motion planning problems to explicitly accommodate constraints or exploit anticipated trajectories of conflicting agents [2], [3]. However, it is oftentimes challenging to solve the underlying optimization problems in real-time, especially when they are nonconvex.…”

“…While our previous research work has primarily built upon model predictive control (MPC) [3], [6], this contribution aims to evaluate the potential of utilizing CBFs for intersection automation. Given that CBFs have also their limitations and drawbacks [5], [7], our overall motivation (which goes far beyond the scope of this paper) is to investigate the pros and cons of both concepts on the example of intersection automation and to potentially come up with a suitable combination of the two.…”

Proximal Gradient Algorithms under Local Lipschitz Gradient Continuity: A Convergence and Robustness Analysis of PANOC

“…Because of these favorable properties, PANOC was originally meant as a nonlinear MPC solver particularly suited for embedded applications subject to limited hardware capabilities, such as land and aerial vehicles [22,24,13] and robotics [2,23,3]; see also [17,11] for extensive surveys and comparisons with other popular methods. Its success in the field led to a reconsideration of the spectrum of problems that the solver could be applied to.…”