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.

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).

The purpose of this work is to combine the concepts of sliding mode control and internal model control to design a Dynamical Sliding Mode Control (DMSC). The Internal Model Control (IMC) structure is used to obtain a simple and easy way to design the controller. This new approach eliminates the major sliding mode control problem: chattering. The process is reduced to a first-order-plus-deadtime (FOPDT) model, and it is divided in two components an invertible one and other non-invertible. A lead term is added to the invertible term and a lead-lag model is obtained and used to get the desired controller. The approach is tested in a high order system with elevated deadtime. The performance of the controller is tested under tracking and regulation conditions: change in the set point, persistent disturbance applied at a determined time, and addition of noise. Finally, a robustness test is conducted to prove how well the controller works when the plant ages. In every of these cases, the performance of the controller is satisfactory, also neither chattering nor instabilities are presented.

A standardized robot-testing algorithm should satisfy accuracy, efficiency, and very importantly, repeatability-consistently yielding similar outcomes across multiple executions by different stakeholders. Achieving repeatability grows challenging with increasing complexity, intelligence, diversity, and inherent stochasticity in testing methods, robotic platforms, and environments. While existing efforts address repeatability through ethical, hardware, or procedural means, this study specifically targets algorithm-level repeatability, focusing on statistical query (SQ) algorithms commonly used in standardized evaluations. We propose a lightweight, adaptive modification for any SQ-based routine, including Monte Carlo, importance sampling, and adaptive sampling, guaranteeing provable repeatability with bounded accuracy and efficiency. Effectiveness is demonstrated across three cases: standardized manipulator testing, intelligent risk assessment for automated vehicles, and performance evaluation of humanoid robot locomotion.