Grace X. Gao

Long Kiu Chung, Adam Dai, Derek Knowles et al.

Neural networks have recently become popular for a wide variety of uses, but have seen limited application in safety-critical domains such as robotics near and around humans. This is because it remains an open challenge to train a neural network to obey safety constraints. Most existing safety-related methods only seek to verify that already-trained networks obey constraints, requiring alternating training and verification. Instead, this work proposes a constrained method to simultaneously train and verify a feedforward neural network with rectified linear unit (ReLU) nonlinearities. Constraints are enforced by computing the network's output-space reachable set and ensuring that it does not intersect with unsafe sets; training is achieved by formulating a novel collision-check loss function between the reachable set and unsafe portions of the output space. The reachable and unsafe sets are represented by constrained zonotopes, a convex polytope representation that enables differentiable collision checking. The proposed method is demonstrated successfully on a network with one nonlinearity layer and approximately 50 parameters.

Shubh Gupta, Grace X. Gao

For reliable operation on urban roads, navigation using the Global Navigation Satellite System (GNSS) requires both accurately estimating the positioning detail from GNSS pseudorange measurements and determining when the estimated position is safe to use, or available. However, multiple GNSS measurements in urban environments contain biases, or faults, due to signal reflection and blockage from nearby buildings which are difficult to mitigate for estimating the position and availability. This paper proposes a novel particle filter-based framework that employs a Gaussian Mixture Model (GMM) likelihood of GNSS measurements to robustly estimate the position of a navigating vehicle under multiple measurement faults. Using the probability distribution tracked by the filter and the designed GMM likelihood, we measure the accuracy and the risk associated with localization and determine the availability of the navigation system at each time instant. Through experiments conducted on challenging simulated and real urban driving scenarios, we show that our method achieves small horizontal positioning errors compared to existing filter-based state estimation techniques when multiple GNSS measurements contain faults. Furthermore, we verify using several simulations that our method determines system availability with smaller probability of false alarms and integrity risk than the existing particle filter-based integrity monitoring approach.

Shubh Gupta, Grace X. Gao

Reliably assessing the error in an estimated vehicle position is integral for ensuring the vehicle's safety in urban environments. Many existing approaches use GNSS measurements to characterize protection levels (PLs) as probabilistic upper bounds on the position error. However, GNSS signals might be reflected or blocked in urban environments, and thus additional sensor modalities need to be considered to determine PLs. In this paper, we propose a novel approach for computing PLs by matching camera image measurements to a LiDAR-based 3D map of the environment. We specify a Gaussian mixture model probability distribution of position error using deep neural network-based data-driven models and statistical outlier weighting techniques. From the probability distribution, we compute the PLs by evaluating the position error bound using numerical line-search methods. Through experimental validation with real-world data, we demonstrate that the PLs computed from our method are reliable bounds on the position error in urban environments.