A Multi-Step Approach to Accelerate the Computation of Reachable Sets for Road Vehicles

Abstract

We propose an approach for the fast computation of reachable sets of road vehicles while considering dynamic obstacles. The obtained reachable sets contain all possible behaviors of vehicles and can be used for motion planning, verification, and criticality assessment. The proposed approach precomputes computationally expensive parts of the reachability analysis. Further, we partition the reachable set into cells and construct a directed graph storing which cells are reachable from which cells at preceding time steps. Using this approach, considering obstacles reduces to deleting nodes from the directed graph. Although this simple idea ensures an efficient computation, the discretization can introduce considerable over-approximations. Thus, the main novelty of this paper is to reduce the over-approximations by intersecting reachable sets propagated from multiple points in time. We demonstrate our approach on a large range of scenarios for automated vehicles showing a faster computation time compared to previous approaches while providing the same level of accuracy.

Computing Specification-Compliant Reachable Sets for Motion Planning of Automated Vehicles

“…We refer to [1, Appendix B] for a detailed explanation of the computation complexity of propagation and creation of base sets. The method for accelerating the reachable set computation in [22] did not consider dynamic velocity and acceleration constraints; how this method can be coupled with our reachability analysis should be investigated in the future.…”

TraModeAVTest: Modeling Scenario and Violation Testing for Autonomous Driving Systems Based on Traffic Regulations

“…For example, Tuncali et al [39] transformed the problem of finding fault-inducing scenarios into a function minimization problem, where a robustness function is defined in a given virtual environment to minimize the input parameters that can minimize the robustness function and find the initial settings for the specified scenarios. Furthermore, search-based methods generate test cases guided by the results of simulation experiments, and have been widely applied as an important approach to model-driven scenario generation [40][41][42][43]. Scenario generation based on search techniques involves modeling the spatial behavior of AVs, parameterizing scenario parameters within the spatial scope, and generating specific scenarios using a parameter value search [44].…”

CommonRoad-Reach: A Toolbox for Reachability Analysis of Automated Vehicles

“…• CppReachableSet interacts with ReachableSet (C++), which is a C++ implementation of the polytopic set propagation method. • PyGraphReachableSetOffline precomputes reachability graphs for the graph-based reachability analysis according to [3].…”

“…2) Graph-based propagation method: The second provided method is the graph-based propagation method presented in [3]. In contrast to the polytopic propagation, the reachable sets are derived by traversing a precomputed reachability graph G R and removing edges that collide with the forbidden states.…”

“…This study presents a toolbox for computing the reachable sets of AVs for motion planning applications. The toolbox integrates two methods presented in our previous works: polytopic set propagation [2] and graph-based propagation [3].…”