This paper presents a novel reinforcement learning (RL) framework to design cascade feedback control policies for 3D bipedal locomotion. Existing RL algorithms are often trained in an end-to-end manner or rely on prior knowledge of some reference joint or task space trajectories. Unlike these studies, we propose a policy structure that decouples the bipedal locomotion problem into two modules that incorporate the physical insights from the nature of the walking dynamics and the well-established Hybrid Zero Dynamics approach for 3D bipedal walking. As a result, the overall RL framework has several key advantages, including lightweight network structure, sample efficiency, and less dependence on prior knowledge. The proposed solution learns stable and robust walking gaits from scratch and allows the controller to realize omnidirectional walking with accurate tracking of the desired velocity and heading angle. The learned policies also perform robustly against various adversarial forces applied to the torso and walking blindly on a series of challenging and unstructured terrains. These results demonstrate that the proposed cascade feedback control policy is suitable for navigation of 3D bipedal robots in indoor and outdoor environments.

How many scenarios are sufficient to validate the safe Operational Design Domain (ODD) of an Automated Driving System (ADS) equipped vehicle Is a more significant number of sampled scenarios guaranteeing a more accurate safety assessment of the ADS Despite the various empirical success of ADS safety evaluation with scenario sampling in practice, some of the fundamental properties are largely unknown. This paper seeks to remedy this gap by formulating and tackling the scenario sampling safety assurance problem from a set invariance perspective. First, a novel conceptual equivalence is drawn between the scenario sampling safety assurance problem and the data-driven robustly controlled forward invariant set validation and quantification problem. This paper then provides a series of complete solutions with finite-sampling analyses for the safety validation problem that authenticates a given ODD. On the other hand, the quantification problem escalates the validation challenge and starts looking for a safe sub-domain of a particular property. This inspires various algorithms that are provably probabilistic incomplete, probabilistic complete but sub-optimal, and asymptotically optimal. Finally, the proposed asymptotically optimal scenario sampling safety quantification algorithm is also empirically demonstrated through simulation experiments.

Vehicle performance metrics analyze data sets consisting of subject vehicle’s interactions with other road users in a nominal driving environment and provide certain performance measures as outputs. To the best of the authors’ knowledge, the vehicle safety performance metrics research dates back to at least 1967. To date, there still does not exist a community-wide accepted metric or a set of metrics for vehicle safety performance assessment and justification. This issue gets further amplified with the evolving interest in Advanced Driver Assistance Systems and Automated Driving Systems. In this paper, the authors seek to perform a unified study that facilitates an improved community-wide understanding of vehicle performance metrics using the lead-vehicle interaction operational design domain as a common means of performance comparison. In particular, the authors study the diversity (including constructive formulation discrepancies and empirical performance differences) among 33 base metrics with up to 51 metric variants (with different choices of hyper-parameters) in the existing literature, published between 1967 and 2022. Two data sets are adopted for the empirical performance diversity analysis, including vehicle trajectories from normal highway driving environment and relatively high-risk incidents with collisions and near-miss cases. The analysis further implies that (i) the conceptual acceptance of a safety metric proposal can be problematic if the assumptions, conditions, and types of outcome assurance are not justified properly, and (ii) the empirical performance justification of an acceptable metric can also be problematic as a dominant consensus is not observed among metrics empirically.

This article studies the class of scenario-based safety testing algorithms in the black-box safety testing configuration. For algorithms sharing the same state–action set coverage with different sampling distributions, it is commonly believed that prioritizing the exploration of high-risk states and actions leads to a better sampling efficiency. Our proposal disputes the above intuition by introducing an impossibility theorem that provably shows that all the safety testing algorithms of the aforementioned difference perform equally well with the same expected sampling efficiency. Moreover, for testing algorithms covering different sets of states and actions, the sampling efficiency criterion is no longer applicable as different algorithms do not necessarily converge to the same termination condition. We then propose a testing aggressiveness definition based on the almost safe set concept along with an unbiased and efficient algorithm that compares the aggressiveness between testing algorithms. Empirical observations from the safety testing of bipedal locomotion controllers and vehicle decision-making modules are also presented to support the proposed theoretical implications and methodologies.

A typical scenario-based evaluation framework seeks to characterize a black-box system's safety performance (e.g., failure rate) through repeatedly sampling initialization configurations (scenario sampling) and executing a certain test policy for scenario propagation (scenario testing) with the black-box system involved as the test subject. In this letter, we first present a novel safety evaluation criterion that seeks to characterize the actual operational domain within which the test subject would remain safe indefinitely with high probability. By formulating the black-box testing scenario as a dynamic system, we show that the presented problem is equivalent to finding a certain almost robustly forward invariant set for the given system. Second, for an arbitrary scenario testing strategy, we propose a scenario sampling algorithm that is provably asymptotically optimal in obtaining the safe invariant set with arbitrarily high accuracy. Moreover, as one considers different testing strategies (e.g., biased sampling of safety-critical cases), we show that the proposed algorithm still converges to the unbiased approximation of the safety characterization outcome if the scenario testing satisfies a certain condition. Finally, the effectiveness of the presented scenario sampling algorithms and various theoretical properties are demonstrated in a case study of the safety evaluation of a control barrier function-based mobile robot collision avoidance system.

A connected and automated vehicle safety metric determines the performance of a subject vehicle (SV) by analyzing the data involving the interactions among the SV and other dynamic road users and environmental features. When the data set contains only a finite set of samples collected from the naturalistic mixed multi-modal traffic driving environment, a metric is expected to generalize the safety assessment outcome from the observed finite samples to the unobserved cases by specifying in what domain the SV is expected to be safe and how safe the SV is, statistically, in that domain. However, to the best of our knowledge, none of the existing safety metrics is able to justify the above properties with an operational domain specific, guaranteed complete, and provably unbiased safety evaluation outcome. In this paper, we propose a novel safety metric that involves the α-shape and the ε-almost robustly forward invariant set to characterize the SV's almost safe operable domain and the probability for the SV to remain inside the safe domain indefinitely, respectively. The empirical performance of the proposed method is demonstrated in several different operational design domains through a series of cases covering a variety of fidelity levels (real-world and simulators), driving environments (highway, urban, and intersections), road users (car, truck, and pedestrian), and SV driving behaviors (human driver and self driving algorithms).