Quadratic approximation based heuristic for optimization-based coordination of automated vehicles in confined areas

We investigate the problem of coordinating multiple automated vehicles (AVs) in confined areas. This problem can be formulated as an optimal control problem (OCP) where the motion of the AVs is optimized such that collisions are avoided in cross-intersections, merge crossings, and narrow roads. The problem is combinatorial and solving it to optimality is prohibitively difficult for all but trivial instances. For this reason, we propose a heuristic method to obtain approximate solutions. The heuristic comprises two stages: In the first stage, a Mixed Integer Quadratic Program (MIQP), similar in construction to the Quadratic Programming (QP) sub-problems in Sequential Quadratic Programming (SQP), is solved for the combinatorial part of the solution. In the second stage, the combinatorial part of the solution is held fixed, and the optimal state and control trajectories for the vehicles are obtained by solving a Nonlinear Program (NLP). The performance of the algorithm is demonstrated by a simulation of a non-trivial problem instance.Comment: To be published in the 61st IEEE Conference on Decision and Control (CDC 2022). arXiv admin note: substantial text overlap with arXiv:2210.1473

A Stochastic Model Predictive Control Approach for Driver-Aided Intersection Crossing With Uncertain Driver Time Delay

We investigate the problem of coordinating human-driven vehicles in road intersections without any traffic lights or signs by issuing speed advices. The vehicles in the intersection are assumed to move along an a priori known path and to be connected via vehicle-to-vehicle communication. The challenge arises with the uncertain driver reaction to a speed advice, especially in terms of the driver reaction time delay, as it might lead to unstable system dynamics. For this control problem, a distributed stochastic model predictive control concept is designed which accounts for driver uncertainties. By optimizing over scenarios, which are sequences of independent and identically distributed samples of the uncertainty over the prediction horizon, we can give probabilistic guarantees on constraint satisfaction. Simulation results demonstrate that the scenario-based approach is able to avoid collisions in spite of uncertainty while the non-stochastic baseline controller is not.Comment: Submitted to European Control Conference 2019 (ECC19

Quadratic approximation based heuristic for optimization-based coordination of automated vehicles in confined areas

We investigate the problem of coordinating multiple automated vehicles (AVs) in confined areas. This problem can be formulated as an optimal control problem (OCP) where the motion of the AVs is optimized such that collisions are avoided in cross-intersections, merge crossings, and narrow roads. The problem is combinatorial and solving it to optimality is prohibitively difficult for all but trivial instances. For this reason, we propose a heuristic method to obtain approximate solutions. The heuristic comprises two stages: In the first stage, a Mixed Integer Quadratic Program (MIQP), similar in construction to the Quadratic Programming (QP) sub-problems in Sequential Quadratic Programming (SQP), is solved for the combinatorial part of the solution. In the second stage, the combinatorial part of the solution is held fixed, and the optimal state and control trajectories for the vehicles are obtained by solving a Nonlinear Program (NLP). The performance of the algorithm is demonstrated by a simulation of a non-trivial problem instance

Optimization based coordination of autonomous vehicles in confined areas

Confined areas present an opportunity for early deployment of autonomous vehicles (AV) due to the absence of non-controlled traffic participants. In this paper, we present an approach for coordination of multiple AVs in confined sites. The method computes speed-profiles for the AVs such that collisions are avoided in cross-intersection and merge crossings. Specifically, this is done through the solution of an optimal control problem where the motion of all vehicles is optimized jointly. The order in which the vehicles pass the crossings is determined through the solution of a Mixed Integer Quadratic Program (MIQP). Through simulation results, we demonstrate the capability of the algorithm in terms of performance and satisfaction of collision avoidance constraints

A Safety Monitoring Concept for Fully Automated Driving

Safe motion planning for automated vehicles requires that a collision-free trajectory can be guaranteed. For that purpose, we propose a monitoring concept that would ensure safe vehicle states. Determining these safe states, however, is usually a computationally demanding task. To alleviate the computational demand, we investigate the possibility to compute the safe sets offline. To achieve this, we leverage backward reachability theory and compute the N-step robust backward reachable set offline. Based on the current disturbances, we demonstrate the possibility to adapt this set online. The safety guarantees are then provided by computing the robust one-step forward prediction of the state vector and checking if these states are members of the adapted safe set. The numerical example demonstrates that the approach is capable of avoiding hazardous vehicle states under an unsafe motion planning algorithm

An iterative algorithm for volume maximization of N-step backward reachable sets for constrained linear time-varying systems

In this paper, we consider the computation of robust N-step backward reachable sets for state-and input con-strained linear time-varying systems with additive uncertainty. We propose a method to compute a linear, time-varying control law that maximizes the volume of the robust N-step reachable set for the closed-loop system. The proposed method is an extension of recent developments and involves the recursive solution of N semi-definite programs (SDP). We demonstrate the performance of the proposed method on the lateral control problem for emergency maneuvers of autonomous vehicles and compare it to results obtained when backward reachability is applied to the same system and a naively designed controller

A stochastic model predictive control approach for driver-aided intersection crossing with uncertain driver time delay

We investigate the problem of coordinating human-driven vehicles in road intersections without any traffic lights or signs by issuing speed advices. The vehicles in the intersection are assumed to move along an a priori known path and to be connected via vehicle-to-vehicle communication. The challenge arises with the uncertain driver reaction to a speed advice, especially in terms of the driver reaction time delay, as it might lead to unstable system dynamics. For this control problem, a distributed stochastic model predictive control concept is designed which accounts for driver uncertainties. By optimizing over scenarios, which are sequences of independent and identically distributed samples of the uncertainty over the prediction horizon, we can give probabilistic guarantees on constraint satisfaction. Simulation results demonstrate that the scenario-based approach is able to avoid collisions in spite of uncertainty while the non-stochastic baseline controller is not

Distributed scenario model predictive control for driver aided intersection crossing

The automation of road intersections has significant potential to improve traffic throughput and efficiency. While the related control problem is usually addressed assuming fully automated vehicles, we focus on the problem of issuing appropriate speed advices to the driver in order to optimize traffic flow in intersections without any traffic lights or signs. Therefore, a distributed scenario-based model predictive control regime is proposed which accounts for uncertainties in the driver reaction to speed advices issued by the control system. In the scenario approach, we draw independently and identically distributed samples from a bounded uncertainty set and optimize over scenarios which reflect a potential driver reaction. Based on the number of samples, we can give guarantees on avoiding collisions under acting uncertainties. Simulation results demonstrate that the scenario approach is capable of avoiding collisions when the driver reacts uncertain while the nominal approach is not

A stochastic model predictive control approach for driver-aided intersection crossing with uncertain driver time delay

\u3cp\u3eWe investigate the problem of coordinating human-driven vehicles in road intersections without any traffic lights or signs by issuing speed advices. The vehicles in the intersection are assumed to move along an a priori known path and to be connected via vehicle-to-vehicle communication. The challenge arises with the uncertain driver reaction to a speed advice, especially in terms of the driver reaction time delay, as it might lead to unstable system dynamics. For this control problem, a distributed stochastic model predictive control concept is designed which accounts for driver uncertainties. By optimizing over scenarios, which are sequences of independent and identically distributed samples of the uncertainty over the prediction horizon, we can give probabilistic guarantees on constraint satisfaction. Simulation results demonstrate that the scenario-based approach is able to avoid collisions in spite of uncertainty while the non-stochastic baseline controller is not.\u3c/p\u3