Abstract
According to a recent survey by the National Highway Traffic Safety Administration, human errors cause 90% of automobile accidents. Autonomous vehicles that use computer-based control systems have high potential to prevent such human errors and delayed reactions. However, the reference paths and trajectories computed by such systems, which are safe by design, are not followed exactly by the vehicle due to various uncertainties in vehicle’s dynamics and environment (uncertain model parameters, tire slip, measurement noises, etc.). These deviations of the real trajectory from the desired trajectory due to uncertainties can violate lane boundaries and lead to collisions. Therefore, assessing the safety of the vehicle’s real trajectory is essential for passenger safety. The most common approach to solving this safety verification problems is to simulate a large number of trajectories using samples of each uncertain parameter and initial condition and then check that all of these trajectories are safe. However, the computational cost of this approach increases exponentially with the dimensions of the uncertainties. A promising alternative is to compute a rigorous enclosure of the set of the vehicle trajectories consistent with the uncertainties and the system model using reachability analysis. The vehicle’s safety can be then verified with certainty by comparing the reachable set with obstacles. However, practical vehicle models are usually highly nonlinear and have large uncertainties. For such models, existing reachability methods are either too computationally demanding for online safety verification or produce bounds that are too conservative for effective safety checking.
In this talk, we will present a new method based on differential inequalities (DI) for rigorously bounding the reachable sets of nonlinear and uncertain vehicle models with sufficient speed and accuracy to be used for online safety verification. Advanced DI methods based on the use of redundant model equations (e.g., invariants) have recently been shown to produce very accurate enclosures efficiently for many examples in the chemical engineering domain (e.g., reactors and separation systems). Unfortunately, this approach depends on the special structure of reaction and separation models, which often enables highly nonlinear and uncertain terms to be cancelled by considering appropriate linear combinations of the states. In order to apply this approach to closed-loop vehicle dynamics, two key challenges must be addressed. First, the governing ordinary differential equation (ODE) for each state typically consists of just a single nonlinear term, and the same term is not repeated in the ODEs for multiple states. Thus, the term-cancellation strategy is almost entirely ineffective. Furthermore, the models in this domain are closed-loop models and the presence of a feedback law causes a significant interval dependency problem, leading to very conservative bounds. In this presentation, we discuss some preliminary new strategies for overcoming both of these challenges. We find that the choice of coordinate system for the closed-loop model is critical for obtaining sharp bounds. Moreover, we find that adding redundant model equations in the form of Lyapunov-like functions for the closed-loop systems is highly effective at reducing the conservatism of the reachable set enclosures computed by DI. These strategies will be demonstrated for several test cases in path and trajectory tracking.
Biography Xuejiao Yang is a Ph.D. student in the Department of Chemical and Biomolecular Engineering at Georgia Tech University. She received her B.S. degree in Chemical Engineering in 2015 from Dalian University of Technology, Dalian, China. Her research interests include reachability analysis, fault detection and diagnosis, and safety verification.