This paper describes the comprehensive safety framework that underpinned the development, release process, and regulatory approval of BMW's first SAE Level 3 Automated Driving System. The framework combines established qualitative and quantitative methods from the fields of Systems Engineering, Engineering Risk Analysis, Bayesian Data Analysis, Design of Experiments, and Statistical Learning in a novel manner. The approach systematically minimizes the risks associated with hardware and software faults, performance limitations, and insufficient specifications to an acceptable level that achieves a Positive Risk Balance. At the core of the framework is the systematic identification and quantification of uncertainties associated with hazard scenarios and the redundantly designed system based on designed experiments, field data, and expert knowledge. The residual risk of the system is then estimated through Stochastic Simulation and evaluated by Sensitivity Analysis. By integrating these advanced analytical techniques into the V-Model, the framework fulfills, unifies, and complements existing automotive safety standards. It therefore provides a comprehensive, rigorous, and transparent safety assurance process for the development and deployment of Automated Driving Systems.

Automated vehicles require carefully designed cost functions, which are challenging to specify due to the complexity of the behavior they need to cover. Inverse reinforcement learning is a principled methodology for deriving cost functions, but it requires high-quality expert demonstrations, which are expensive to obtain. Recently, scenario-based testing has emerged as a promising approach for validation of driving behavior. In this paper, we introduce a novel methodology that circumvents the need for costly expert driving demonstrations by harnessing scenario-based testing. Our Test-Driven Inverse Reinforcement Learning approach leverages Bayesian inference, utilizing the outcomes of scenario tests as observations to infer cost functions. We rigorously evaluate our method on simulated and real-world scenarios and demonstrate its ability to learn cost functions that successfully pass the respective scenario tests. We also show that the learned cost function generalizes well by also passing scenario tests from an unseen validation set and illustrate that few scenario tests are sufficient to learn meaningful cost functions. This innovative framework not only streamlines the cost function specification process but also offers a cost-effective and practical solution for advancing automated driving systems.

Model predictive control (MPC) is a powerful, optimization-based approach for controlling dynamical systems. However, the computational complexity of online optimization can be problematic on embedded devices. Especially, when we need to guarantee fixed control frequencies. Thus, previous work proposed to reduce the computational burden using imitation learning (IL) approximating the MPC policy by a neural network. In this work, we instead learn the whole planned trajectory of the MPC. We introduce a combination of a novel neural network architecture PlanNetX and a simple loss function based on the state trajectory that leverages the parameterized optimal control structure of the MPC. We validate our approach in the context of autonomous driving by learning a longitudinal planner and benchmarking it extensively in the CommonRoad simulator using synthetic scenarios and scenarios derived from real data. Our experimental results show that we can learn the open-loop MPC trajectory with high accuracy while improving the closed-loop performance of the learned control policy over other baselines like behavior cloning.

Achieving feasible, smooth and efficient trajectories for autonomous vehicles which appropriately take into account the long-term future while planning, has been a long-standing challenge. Several approaches have been considered, roughly falling under two categories: rule-based and learning-based approaches. The rule-based approaches, while guaranteeing safety and feasibility, fall short when it comes to long-term planning and generalization. The learning-based approaches are able to account for long-term planning and generalization to unseen situations, but may fail to achieve smoothness, safety and the feasibility which rule-based approaches ensure. Hence, combining the two approaches is an evident step towards yielding the best compromise out of both. We propose a Reinforcement Learning-based approach, which learns target trajectory parameters for fully autonomous driving on highways. The trained agent outputs continuous trajectory parameters based on which a feasible polynomial-based trajectory is generated and executed. We compare the performance of our agent against four other highway driving agents. The experiments are conducted in the Sumo simulator, taking into consideration various realistic, dynamically changing highway scenarios, including surrounding vehicles with different driver behaviors. We demonstrate that our offline trained agent, with randomly collected data, learns to drive smoothly, achieving velocities as close as possible to the desired velocity, while outperforming the other agents.

Open challenges for deep reinforcement learning systems are their adaptivity to changing environments and their efficiency w.r.t. computational resources and data. In the application of learning lane-change behavior for autonomous driving, the number of required transitions imposes a bottleneck, since test drivers cannot perform an arbitrary amount of lane changes in the real world. In the off-policy setting, additional information on solving the task can be gained by observing actions from others. While in the classical RL setup this knowledge remains unused, we use other drivers as surrogates to learn the agent's value function more efficiently. We propose Surrogate Q-learning that deals with the aforementioned problems and reduces the required driving time drastically. We further propose an efficient implementation based on a permutation equivariant deep neural network architecture of the Q-function to estimate action-values for a variable number of vehicles in sensor range. We evaluate our method in the open traffic simulator SUMO and learn well performing driving policies on the real highD dataset.

In autonomous driving applications, reinforcement learning agents often have to perform complex behavior, which can translate into optimizing multiple objectives while following certain rules. Encoding traffic rules and desires such as safety and comfort via classical methods based on reward shaping (i.e. a weighted combination of different objectives in the reward signal) or Lagrangian methods (including auxiliary losses in the optimization) can be very hard and cumbersome. In this work, we propose to instead shape the action-space at the maximization step of Q-learning. We further introduce a formulation for fixed-horizon estimation of auxiliary costs under the current target-policy based on truncated value- functions to encode the desire of comfortable driving ensuring interpretable behavior. We compare our algorithm to reward shaping and Lagrangian methods in the application of high- level decision making in autonomous driving, considering rules for safety, keeping right and comfort. We train and evaluate our agent in the open-source simulator SUMO on a variety of scenarios with different driver types and traffic situations. Additionally, we apply our method on the real HighD data set, showing the real-world applicability and simplicity of Q- learning with Action-space Shaping.

Planning for robotic systems is frequently formulated as an optimization problem. Instead of manually tweaking the parameters of the cost function, they can be learned from human demonstrations by Inverse Reinforcement Learning (IRL). Common IRL approaches employ a maximum entropy trajectory distribution that can be learned with soft reinforcement learning, where the reward maximization is regularized with an entropy objective. The consideration of safety constraints is of paramount importance for human-robot collaboration. For this reason, our work addresses maximum entropy IRL in constrained environments. Our contribution to this research area is threefold: (1) We propose Constrained Soft Reinforcement Learning (CSRL), an extension of soft reinforcement learning to Constrained Markov Decision Processes (CMDPs). (2) We transfer maximum entropy IRL to CMDPs based on CSRL. (3) We show that using importance sampling in maximum entropy IRL in constrained environments introduces a bias and fails to achieve feature matching. In our evaluation we consider the tactical lane change decision of an autonomous vehicle in a highway scenario modeled in the SUMO traffic simulation.

Well-established optimization-based methods can guarantee an optimal trajectory for a short optimization horizon, typically no longer than a few seconds. As a result, choosing the optimal trajectory for this short horizon may still result in a sub-optimal long-term solution. At the same time, the resulting short-term trajectories allow for effective, comfortable and provable safe maneuvers in a dynamic traffic environment. In this work, we address the question of how to ensure an optimal long-term driving strategy, while keeping the benefits of classical trajectory planning. We introduce a Reinforcement Learning based approach that coupled with a trajectory planner, learns an optimal long-term decision-making strategy for driving on highways. By online generating locally optimal maneuvers as actions, we balance between the infinite low-level continuous action space, and the limited flexibility of a fixed number of predefined standard lane-change actions. We evaluated our method on realistic scenarios in the open-source traffic simulator SUMO and were able to achieve better performance than the 4 benchmark approaches we compared against, including a random action selecting agent, greedy agent, high-level, discrete actions agent and an IDM-based SUMO-controlled agent.

The common pipeline in autonomous driving systems is highly modular and includes a perception component which extracts lists of surrounding objects and passes these lists to a high-level decision component. In this case, leveraging the benefits of deep reinforcement learning for high-level decision making requires special architectures to deal with multiple variable-length sequences of different object types, such as vehicles, lanes or traffic signs. At the same time, the architecture has to be able to cover interactions between traffic participants in order to find the optimal action to be taken. In this work, we propose the novel Deep Scenes architecture, that can learn complex interaction-aware scene representations based on extensions of either 1) Deep Sets or 2) Graph Convolutional Networks. We present the Graph-Q and DeepScene-Q off-policy reinforcement learning algorithms, both outperforming state-of-the-art methods in evaluations with the publicly available traffic simulator SUMO.

Popular Maximum Entropy Inverse Reinforcement Learning approaches require the computation of expected state visitation frequencies for the optimal policy under an estimate of the reward function. This usually requires intermediate value estimation in the inner loop of the algorithm, slowing down convergence considerably. In this work, we introduce a novel class of algorithms that only needs to solve the MDP underlying the demonstrated behavior once to recover the expert policy. This is possible through a formulation that exploits a probabilistic behavior assumption for the demonstrations within the structure of Q-learning. We propose Inverse Action-value Iteration which is able to fully recover an underlying reward of an external agent in closed-form analytically. We further provide an accompanying class of sampling-based variants which do not depend on a model of the environment. We show how to extend this class of algorithms to continuous state-spaces via function approximation and how to estimate a corresponding action-value function, leading to a policy as close as possible to the policy of the external agent, while optionally satisfying a list of predefined hard constraints. We evaluate the resulting algorithms called Inverse Action-value Iteration, Inverse Q-learning and Deep Inverse Q-learning on the Objectworld benchmark, showing a speedup of up to several orders of magnitude compared to (Deep) Max-Entropy algorithms. We further apply Deep Constrained Inverse Q-learning on the task of learning autonomous lane-changes in the open-source simulator SUMO achieving competent driving after training on data corresponding to 30 minutes of demonstrations.

In many real world applications, reinforcement learning agents have to optimize multiple objectives while following certain rules or satisfying a list of constraints. Classical methods based on reward shaping, i.e. a weighted combination of different objectives in the reward signal, or Lagrangian methods, including constraints in the loss function, have no guarantees that the agent satisfies the constraints at all points in time and can lead to undesired behavior. When a discrete policy is extracted from an action-value function, safe actions can be ensured by restricting the action space at maximization, but can lead to sub-optimal solutions among feasible alternatives. In this work, we propose Constrained Q-learning, a novel off-policy reinforcement learning framework restricting the action space directly in the Q-update to learn the optimal Q-function for the induced constrained MDP and the corresponding safe policy. In addition to single-step constraints referring only to the next action, we introduce a formulation for approximate multi-step constraints under the current target policy based on truncated value-functions. We analyze the advantages of Constrained Q-learning in the tabular case and compare Constrained DQN to reward shaping and Lagrangian methods in the application of high-level decision making in autonomous driving, considering constraints for safety, keeping right and comfort. We train our agent in the open-source simulator SUMO and on the real HighD data set.

In many real-world decision making problems, reaching an optimal decision requires taking into account a variable number of objects around the agent. Autonomous driving is a domain in which this is especially relevant, since the number of cars surrounding the agent varies considerably over time and affects the optimal action to be taken. Classical methods that process object lists can deal with this requirement. However, to take advantage of recent high-performing methods based on deep reinforcement learning in modular pipelines, special architectures are necessary. For these, a number of options exist, but a thorough comparison of the different possibilities is missing. In this paper, we elaborate limitations of fully-connected neural networks and other established approaches like convolutional and recurrent neural networks in the context of reinforcement learning problems that have to deal with variable sized inputs. We employ the structure of Deep Sets in off-policy reinforcement learning for high-level decision making, highlight their capabilities to alleviate these limitations, and show that Deep Sets not only yield the best overall performance but also offer better generalization to unseen situations than the other approaches.

Machine learning techniques have been shown to outperform many rule-based systems for the decision-making of autonomous vehicles. However, applying machine learning is challenging due to the possibility of executing unsafe actions and slow learning rates. We address these issues by presenting a reinforcement learning-based approach, which is combined with formal safety verification to ensure that only safe actions are chosen at any time. We let a deep reinforcement learning (RL) agent learn to drive as close as possible to a desired velocity by executing reasonable lane changes on simulated highways with an arbitrary number of lanes. By making use of a minimal state representation, consisting of only 13 continuous features, and a Deep Q-Network (DQN), we are able to achieve fast learning rates. Our RL agent is able to learn the desired task without causing collisions and outperforms a complex, rule-based agent that we use for benchmarking.

In order to determine a cooperative driving strategy, it is beneficial for an autonomous vehicle to incorporate the intended motion of surrounding vehicles within its own motion planning. However, as intentions cannot be measured directly and the motion of multiple vehicles often are highly interdependent, this incorporation has proven challenging. In this paper, the problem of maneuver estimation is addressed, focusing on situations with close interaction between traffic participants. Therefore, we define collective maneuvers based on trajectory homotopy, describing the relative motion of multiple vehicles in a scene. Representing maneuvers by sample trajectories, maneuver-dependent prediction models of the vehicle states can be defined. This allows for a Bayesian estimation of maneuver probabilities given observations of the real motion. The approach is evaluated by simulation in overtaking scenarios with oncoming traffic and merging scenarios at an intersection.

In this work, we present a Reinforcement Learning (RL) based approach for autonomous driving in highway scenarios, including interaction with other vehicles. The method used is Fitted Q-iteration [1] with Extremely Randomized Trees [2] as a function approximator.We demonstrate that Reinforcement Learning based concepts can be successfully applied and can be used to teach a RL agent to drive autonomously in an intelligent way, by following traffic rules and ensuring safety. By combining RL with the already established control concepts, we managed to build an agent that achieved promising results in the realistic simulated environment.

Safety is the most important aspect of systems which have to perform collision-free motions in dynamic environments. Formal verification methods, such as reachability analysis, are capable of guaranteeing safety for a given model and given assumptions (e. g. bounded velocity and acceleration). However, certain assumptions can be violated by dynamic obstacles during the execution of the verified motion plan, exposing the system to potential collisions. To compensate for the invalidated verification, this paper introduces the Point of No Return (PNR) and the Point of Guaranteed Arrival (PGA) by incorporating invariably safe sets. These concepts allow one to divide the planned trajectory into safe sections and safety-critical passageways. For the former, we are able to provide safety guarantees for an infinite time horizon. For the latter, we present a method to minimize such safety-critical passageways prior to execution and thus reduce the risk of potential collisions if assumptions are violated during execution. The safety benefits are highlighted by a numerical example of overtaking maneuvers of self-driving vehicles.