On Provably Safe Obstacle Avoidance for Autonomous Robotic Ground Vehicles

Abstract

Abstract-Nowadays, robots interact more frequently with a dynamic environment outside limited manufacturing sites and in close proximity with humans. Thus, safety of motion and obstacle avoidance are vital safety features of such robots. We formally study two safety properties of avoiding both stationary and moving obstacles: (i) passive safety, which ensures that no collisions can happen while the robot moves, and (ii) the stronger passive friendly safety in which the robot further maintains sufficient maneuvering distance for obstacles to avoid collision as well. We use hybrid system models and theorem proving techniques that describe and formally verify the robot's discrete control decisions along with its continuous, physical motion. Moreover, we formally prove that safety can still be guaranteed despite location and actuator uncertainty.

ModelPlex: verified runtime validation of verified cyber-physical system models

“…In dL , we can, for example, use nondeterministic assignment from an interval to model sensor uncertainty and piece-wise constant actuator disturbance (e. g., as in [26]), or differential inequalities for actuator disturbance (e. g., as in [38]). Such models include nondeterminism about sensed values in the controller model and often need more complex physics models than differential equations with polynomial solutions.…”

“…The axiomatic-style prototype synthesizes correct-by-construction monitors and produces a proof of correctness during the synthesis without the need to recheck. To evaluate our method, we synthesize monitors for prior case studies of nondeterministic hybrid models of autonomous cars, train control systems, and robots (adaptive cruise control [20], intelligent speed adaptation [25], the European train control system [38], and ground robot collision avoidance [26]), see Table 2. For the model, we list the dimension in terms of the number of function symbols and state variables, as well as the size of the safety proof for proving (2), i. e., number of proof steps and the number of proof branches.…”

Hybrid Theorem Proving of Aerospace Systems: Applications and Challenges

“…KeYmaera has been used successfully for verifying properties of systems involving cars, trains, aircraft, and robots: local lane controllers for highway car traffic [14], left-turn assist controllers for cars at intersections [15], intelligent speed adaptation for variable speed limit control and incident management by traffic centers on highways [16], cooperation protocols of the European Train Control System [17], airplane collision avoidance [18,19], obstacle avoidance for ground robots [20], and force feedback to the surgeon from a surgical robot [21].…”

“…For example, we currently bound the beliefs of the entities in our verification of a robot collision avoidance problem [20] by some static confidence region centered at the true location of robot; the width of this region is based on sensor quality. The robot's estimate of its position corresponds to the immediate sensor information.…”

“…Therefore either we need to recommend that planes use inefficient policies that, like in [20], do not filter, or further restrict the sequences that a proof's adversary can employ. We want to restrict the adversary to sequences that never have subsequences that are too unlikely, for example asserting that all measurement subsequences of length k have some minimum probability.…”