Ensuring drivability of planned motions using formal methods

Abstract

Abstract-Motion planning of automated vehicles requires dynamical models to ensure that obtained trajectories are drivable. An often overlooked aspect is that motion planning is usually done using simplified models, which do not always sufficiently conform to the real behavior of vehicles. Thus, collision avoidance and drivability is not necessarily ensured. We address this problem by modeling vehicles as differential inclusions composed of simple dynamics and set-based uncertainty; conformance testing is used to determine the required uncertainty. To quickly provide the set of solutions for these uncertain models, we use precomputed reachable sets (i.e., the union of all possible solutions) for pre-selected motion primitives. The reachable sets of vehicles are obtained through the novel combination of optimization techniques and reachability analysis in the controller synthesis -they enable us to guarantee safety by checking their mutual non-intersection for consecutive time intervals. The benefits of our approach are demonstrated by numerical experiments.

Planning and Decision-Making for Autonomous Vehicles

“…Online verification of general maneuvers would require a probabilistic representation of other traffic participants and scenarios, which is still computationally challenging because of the high complexity. The drivability of planned motions can also be checked for, and guaranteed, via reachability analysis (132). Instead of verifying car controllers online, an alternative is to build a library of local and verified road models, such as intersections and road segments, that are composed together to certify safety over networks (133).…”

Towards conformant models of automated electric vehicles

“…The conformance method is based on [1], where a recorded output trace (of the SUT) is compared with the model for feedforward controller under certain disturbances. If traces errors are into specified bounds the model is trace conformed, but if values are out of bounds the model must be improved due was not able to accomplish the requirements.…”

“…The current work presents an automated vehicle verification approach based on trace conformance and its basis are in the work done by [1]. In this paper, the trace conformance is mainly to verify the abstract vehicle model used to control the system with robustness.…”

A modal interface contract theory for guarded input/output automata with an application in traffic system design

“…We propose an implementation based on computing robust controllers or "primitives" that can restrict the vehicles to a waypoint graph structure even in the presence of stochastic disturbance. In particular, the vehicle dynamics are given bẏ We use a formal, set-based algorithm [13], [14], [15] to obtain controllers that steer cars from one node to another on the waypoint graph with each node being a set of states of the car's dynamics around a nominal state. The reason a set of states is used is because of the disturbance present.…”